U.S. patent number 5,353,790 [Application Number 07/822,461] was granted by the patent office on 1994-10-11 for method and apparatus for optical measurement of bilirubin in tissue.
This patent grant is currently assigned to Board of Regents, The University of Texas System. Invention is credited to Steven L. Jacques, David G. Oelberg, Iyad Saidi.
United States Patent |
5,353,790 |
Jacques , et al. |
October 11, 1994 |
**Please see images for:
( Certificate of Correction ) ** |
Method and apparatus for optical measurement of bilirubin in
tissue
Abstract
A method and apparatus for the determination of bilirubin
concentration in tissue such as skin, particularly neonatal skin.
Light reflected from the skin under test is analyzed to determine
bilirubin concentration in the skin, corrected for
maturity-dependent optical properties of the skin, the amount of
melanin in the skin and the amount of blood in the skin. Reflected
red to infrared light is used to determine maturity-dependent
optical properties, reflected red light is used to determine
melanin content, and reflected yellow-orange light is used to
determine the amount of blood in the skin. Then, these quantities
are used, in combination with reflected blue light, to calculate
cutaneous bilirubin concentration.
Inventors: |
Jacques; Steven L. (Houston,
TX), Oelberg; David G. (Houston, TX), Saidi; Iyad
(Houston, TX) |
Assignee: |
Board of Regents, The University of
Texas System (Austin, TX)
|
Family
ID: |
25236107 |
Appl.
No.: |
07/822,461 |
Filed: |
January 17, 1992 |
Current U.S.
Class: |
600/315; 250/574;
356/317; 356/39; 356/51; 600/473; 600/476; 606/3 |
Current CPC
Class: |
G01N
21/4738 (20130101); A61B 5/0075 (20130101); A61B
5/14546 (20130101); A61N 5/0621 (20130101); G01N
2201/065 (20130101) |
Current International
Class: |
G01N
21/47 (20060101); A61B 006/00 () |
Field of
Search: |
;128/633,664,665,653.1
;606/3 ;356/39-41 ;250/574,226,228 |
References Cited
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|
Primary Examiner: Pfaffle; K. M.
Attorney, Agent or Firm: Arnold, White & Durkee
Claims
What is claimed is:
1. A method for the transcutaneous determination of bilirubin
concentration in tissue, comprising:
illuminating said tissue with light;
detecting a frequency spectrum of light reflected from said
tissue;
calculating, from a first portion of said spectrum, a first
parameter indicative of a maturity of said tissue;
calculating, from a second portion of said spectrum, a second
parameter indicative of an amount of melanin in said tissue;
calculating, form a third portion of said spectrum, a third
parameter indicative of a blood content of said tissue;
calculating, from a fourth portion of said spectrum, a fourth
parameter indicative of an uncorrected bilirubin concentration in
said tissue; and
calculating a connected bilirubin concentration in said tissue as a
function of said first, second, third and fourth parameters.
2. The method of claim 1, wherein said first portion of said
spectrum is red to infrared light.
3. The method of claim 2, said red to infrared light having
wavelengths in the range of 650 nm to 800 nm.
4. The method of claim 1, wherein said second portion of said
spectrum is red light.
5. The method of claim 4, said red light having a wavelength of
approximately 650 nm.
6. The method of claim 1, wherein said third portion of said
spectrum is yellow-orange light.
7. The method of claim of 6, said yellow-orange light having a
wavelength of approximately 585 nm.
8. The method of claim 1, wherein said fourth portion of said
spectrum is blue light.
9. The method of claim 8, wherein said blue light has a wavelength
of approximately 460 nm.
10. The method of claim 1, further comprising:
calculating, from a fifth portion of said spectrum, a fifth
parameter indicative of a depth of blood within said tissue;
and
calculating a concentration of bilirubin in said tissue as a
function of said first, second, third, fourth and fifth
parameters.
11. The method of claim 10, wherein said fifth portion of said
spectrum is purple-blue light.
12. The method of claim 11, wherein said purple-blue light has a
wavelength of approximately 420 nm.
13. An apparatus for detecting a concentration of bilirubin in
tissue, comprising:
a light source adapted to direct light onto tissue under test;
a light detector, adapted to detect a spectrum of light reflected
form said tissue; and
a computer means, connected to said light source and light
detector, for calculating a first parameter indicative of a
maturity of said tissue form a magnitude of a first portion of said
spectrum, for calculating a second parameter indicative of an
amount of melanin in said tissue from a second portion of said
spectrum, for calculating a third parameter indicative of a blood
content of said tissue from a third portion of said spectrum, for
calculating a fourth parameter indicative of a raw bilirubin
concentration form a fourth portion of said spectrum, and for
calculating bilirubin concentration in said tissue as a function of
said first, second, third and fourth parameters.
Description
BACKGROUND AND SUMMARY OF THE INVENTION
1.1 Background
The invention relates to transcutaneous optical measurement of
blood components and contaminants, particularly, transcutaneous
measurement of hyperbilirubinemia in neonates.
1.1.1 Reflectance Spectroscopy
Throughout this disclosure, material appearing in brackets refers
to the references listed in Appendix D.
There has been an increasing interest in the use of low level light
as a diagnostic tool in medicine [Andreozi 1987, Kato 1985, Kopola
1990, Pettit 1990, Richards-Kortum 1990, Wukitsch 1988, Yamanuchi
1980]. This concept has become more appealing with the simultaneous
development of appropriate and inexpensive light sources, detection
devices, and optical fibers that allow for minimal invasiveness.
Such application of light depends on the measurement of reflection
or fluorescence and aims to qualitatively or quantitatively assess
the presence of a substance in the tissue, or determine the
pathological state of the tissue. Optical transducers of
non-optical properties, such as pressure or pH, can be designed
when the optical fibers ends are combined with flexible membranes
or chemicals [Katzir 1988].
Light diffusely reflected from a tissue has traveled within the
tissue, and non-invasively provides rapid quantitative measurements
of pigments within the tissue. The reflection of light from a
tissue is dependent on the ratio of the scattering coefficient to
the absorption coefficient within the tissue. Therefore, the
absorbance within a tissue can be delineated from a single
reflection measurement if the scattering properties of the tissue
are known. Empirically developed algorithms for the interpretation
of reflected spectra are suitable when the concentration of only
one pigment concentration is varied, and the scattering properties
of the tissue are fixed. These algorithms are vulnerable to errors
as the scattering coefficient, or the absorption coefficient of
other pigments in the tissue vary between tissue samples.
1.1.2 Hyperbilirubinemia
Bilirubin is produced from the breakdown of hemoglobin in red blood
cells. Under normal conditions the bilirubin is conjugated by
glucoronyl transferase, an enzyme present in the liver, and then
excreted through the biliary system. Hyperbilirubinemia describes
the state where there is excessive bilirubin in the body.
Newborn infants, and particularly premature ones, are susceptible
to hyperbilirubinemia. Often this is due to the lack of functioning
glucoronyl transferase enzyme in their liver, or excessive red
blood cell breakdown associated with erythroblastosis fetalis
[Maisels 1988]. Extreme hyperbilirubinemia places neonates at risk
of kernicterus, the leakage of bilirubin into the basal ganglia in
the brain, and potentially causes neuronal retardation. For this
reason, it is desirable to regularly monitor the bilirubin
concentrations in the body.
Bilirubin from the blood stains the skin (cutaneous bilirubin) in
addition to other tissues of the body. Jaundice refers to the
condition when the bilirubin is visible in the skin and sclera. The
kinetics of transfer of bilirubin from the blood to the skin are
not well understood, but appear to be dependent on various
physiological factors in addition to serum bilirubin
concentration.
1.1.3 Transcutaneous Bilirubinometry
Non-invasive measurements of the bilirubin concentration in the
skin may eliminate the need to draw blood (serum) samples from
neonares for bilirubin analysis. Numerous attempts have been made
to measure cutaneous bilirubin non-invasively. These attempts
include the development of visual reference standards, and more
recently transcutaneous reflectance spectroscopy [Hannemann 1978,
Hannemann 1982, Hegyi 1986, Kenny 1984, Schumacher 1990, Yamanuchi
1980]. FIG. 1 shows the absorption spectra of bilirubin, oxidized
blood, and melanin, the dominant absorbers in the skin. The
concentration of these pigments in the skin are highly variable.
Since these three pigments have very distinct absorption spectra,
the absorption due to cutaneous bilirubin should be determinable by
correct analysis of the reflectance spectra.
Reflectance bilirubinometers have obtained reasonable correlations
between bilirubin levels determined transcutaneously and serum
bilirubin concentrations in homogeneous patient populations, but
have failed to give satisfactory correlations when used over a
heterogeneous population [Hannemann 1982]. Since patient
populations are rarely homogeneous, transcutaneous bilirubinometers
have not been widely accepted clinically [Schumacher 1990].
The key to correct interpretation of cutaneous reflectance spectra,
is to understand how the measured reflectance is affected by: (i)
pigments in different locations of the skin, (ii) in skin with
different scattering properties, and (iii) with different
combinations of other absorbers, such as blood and melanin.
1.2 Summary Of Invention
The present invention largely avoids the above-noted discrepancies
of prior art reflectance bilirubinometers by providing for the
correction of errors in the reflectance measurement of bilirubin
due to, for example, gestational maturity, melanin content and
blood content of the tissue such as skin of an individual being
tested.
More specifically, the present invention contemplates illuminating
the skin surface or other tissue of an individual under test, and
detecting a spectrum of reflected light. Various portions of the
spectrum are analyzed to determine gestational maturity of the
tissue, as well as melanin and blood content of the tissue, in
addition to an uncorrected measurement of bilirubin content. Then,
calculations are performed using these four quantities to provide a
corrected concentration of bilirubin.
As a by-product of the present invention, measurement of
gestational maturity of the skin of neonates is provided.
More specifically, reflected blue light is used to determine
uncorrected absorption due to bilirubin. Then, reflected red to
infrared light is used to determine absorption due to
maturity-dependent optical properties of the skin, reflected red
light is used to determine the amount of absorption due to melanin
in the skin, and reflected yellow-orange light is used to measure
absorption due to blood in the skin. Once the optical absorption
due to blood melanin and maturity-dependent optical properties of
the skin are measured, the contribution of these factors to the
absorption of blue light can be calculated and subtracted from the
uncorrected absorption of blue light to yield absorption due to
bilirubin alone. Once this is known, the concentration of bilirubin
in the skin can be calculated.
The location and quantity of pigments, and the scattering
properties of the skin, are important considerations for correct
reflectance analysis. Therefore, the architecture and optical
properties of neonatal skin have to be determined, and a model
developed. The physical bases and mathematical descriptions of
optical properties are explained in Appendix A. FIG. 2 shows a
histological cross section of a neonatal skin sample. The cross
section reveals skin surface 101, epidermis 102, dermis 103 and
hypodermis 104. In accordance with the present invention a skin
model is developed. Epidermis 102 contains all the melanin, and is
modelled as an absorbing layer. Dermis 103 includes collagen fiber
bundles 106. Interspersed with collagen fiber bundles 106 are
fibroblasts that maintain bundles 106. Blood is present in plexi
that branch into a capillary network and feed the dermis. Dermis
103 is modelled as predominantly a scattering medium with some
absorption. The blood and billirubin are modelled as being
diffusely present throughout dermis 103. Hypodermis 104 is composed
primarily of collagen matrix mixed with fat cells. Hypodermis 104
shares its blood supply with dermis 103, and is modelled as an
extension of dermis 103. This model has been developed based on
histological evidence, and its suitability verified by optical
property and Monte Carlo data presented in sections 2, 3, and 4.
The model accounts for the melanin in the skin which is located in
the epidermis 102, the topmost layer of the skin, and for the
dermis 103 which is primarily composed of a collagen fiber bundle
matrix and is maintained by interspersed fibroblasts.
This disclosure is separated into sections in order to more clearly
describe the scope of the invention. In addition, several
Appendices are included for completeness.
In section 2, the optical properties of neonatal dermis are
measured in vitro, and the results are reported. A method to
determine the optical properties from reflectance and transmission
measurements performed in an integrating sphere is discussed. The
collagen fiber bundle diameters and concentration are measured in
representative skin samples, and Mie theory of scattering is used
to relate the number of collagen fiber bundles per unit volume and
their size distribution to the dermal scattering.
In section 3, reflectance measurements by distant and surface
detectors are discussed. An experimental method and Monte Carlo
computer simulations to determine the collection efficiency of a
surface optical transducer are presented. The model can be used to
systematically study how variations in the optical properties and
in the geometry of the transducer affect the collection efficiency
of a transducer under design. The effect of epidermal melanin on
the measured reflectance is also analyzed, and a method to use the
measured reflectance to determine the absorption in a tissue of
known scattering coefficient is presented.
In section 4, variations in scattering properties, melanin content,
blood depth, skin thickness, and cutaneous bilirubin in neonatal
skin samples are discussed. The effect of these variations on the
measured reflectance spectra are analyzed. A method to determine
the skin scattering and the melanin content in vivo is
presented.
In section 5, the optical model of skin, and the considerations of
how skin scattering, bilirubin, blood, and melanin affect
reflectance are combined to develop an algorithm to determine
cutaneous bilirubin in accordance with the present invention. Monte
Carlo simulations are used to evaluate the bilirubin algorithm, and
compare it to traditional analysis of measured reflectance without
consideration of radiative transport theory. The algorithm
developed is applied to clinical reflectance measurements obtained
in neonates, and the results presented.
In Appendix A, the coefficients which describe light interaction
with tissue are presented, and light transport in tissue is
discussed. In Appendix B, a convolution procedure to determine the
optical patch collection efficiency from Monte Carlo data is
presented, and this procedure is implemented in a computer program.
In Appendix C, the effect of skin thickness on the measure
reflectance spectra is analyzed. Appendix D lists the references
appearing throughout this patent disclosure, as Appendix E presents
a source code listing of the algorithm of the present
invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a graph of the absorption spectra of bilirubin,
oxygenated hemoglobin and dopa-melanin.
FIG. 2 is a histological section of neo-natal skin.
FIG. 3A and 3B are of an integrating sphere spectrophotometer used
to measure the diffuse reflection and transmission of tissue
samples, in accordance with the present invention.
FIG. 4 is a graph of reduced scattering coefficient as a function
of gestational maturity.
FIG. 5 is a graph of the absorption and scattering coefficients
determined for neonatal skin samples of varying gestational
maturity.
FIG. 6 is a graph of the average absorption coefficient for
neonatal skin as a function of wavelength.
FIGS. 7A, B and C are graphs of the reduced scattering coefficient
as a function of wavelength predicted by Mei theory for various
collagen fiber bundle characteristics.
FIG. 8A is an optical patch, in accordance with the present
invention.
FIG. 8B is a Monte Carlo prediction of the reflectance profile as a
function of radius, for the optical patch of FIG. 8A.
FIG. 9 illustrates the parameters that define the collection of
light from a unit surface area by a distant detector.
FIG. 10 illustrates reflectance measurement where light is
delivered to a medium as a point source.
FIG. 11 is a graph of the reflectance signal as a function of the
distance from the detector to the reflective surface, with light
delivered to the reflective medium as a point source.
FIG. 12 illustrates reflectance measurement where light is
delivered to a reflective medium as a broad-beam source through a
fiber.
FIG. 13 is a graph of the reflective signal as a function of
distance from the detector to the reflective surface with light
delivered to the reflective surface with a broad-beam source.
FIGS. 14A and 14B illustrate measurement of the reflective
characteristics of phantoms.
FIG. 15 is a graph of the predicted and experimental results for
the collection fraction of the optical patch of FIG. 8A.
FIG. 16 is a graph of optical patch collection fraction and true
reflection as a function of epidermal absorption.
FIG. 17 is a graph of collection fraction and true total reflection
as a function of absorption in an infinite medium simulating
dermis.
FIG. 18 is a graph of measured reflection, predicted by Monte Carlo
simulations, as a function of absorption coefficient.
FIG. 19 is a flow chart of the iterative method of the present
invention to use optical patch measurement to determine absorption
coefficient in a tissue of known scattering properties.
FIG. 20 is a graph of measured extrapolated reflection values at
837 nm as a function of gestational age.
FIG. 21 is a graph of the distribution of measured extrapolated
reflection values at 837 nm for neonates and adults.
FIG. 22 is a graph of the defective path length as a function of
effective penetration depth.
FIG. 23 is a graph of the change of optical density due to the
addition of unit absorption, as a function of the absorption and
scattering coefficients in tissue.
FIG. 24 is a graph of the in vivo melanin optical density spectra
measured with the optical patch of FIG. 8A.
FIG. 25 is a graph of the in vivo melanin optical density spectra
measured on neonates with the optical patch of FIG. 8A.
FIG. 26 is a graph of the demographic distribution of melanin
pigmentation, measured as the negative slope of the optical density
spectrum.
FIG. 27 is a graph of the demographic distribution of blood content
in the skin of 47 neonates.
FIG. 28 is a graph of the optical density predicted by Monte Carlo
computer simulations, in accordance with the present invention, is
a function of depth of the blood in the skin.
FIG. 29 is a graph of the ratio of the blood in the skin at two
measuring wavelengths, as a function of the depth of the blood
layer.
FIG. 30 is a graph of the measured distribution of the ratio of the
optical density at 420 nm relative to the optical density at 585
nm.
FIG. 31 is a graph of the distribution of measured skin thickness
as a function of a gestational maturity.
FIG. 32 is a graph of the demographic distribution of cutaneous
bilirubin concentrations measured in the skin of 47 neonates.
FIG. 33 is a graph of the optical density predicted by Monte Carlo
simulations, in accordance with the present invention, as a
function of cutaneous bilirubin concentrations for neonatal skin of
three maturities.
FIG. 34 is a graph of the predicted absorption at 460 nm as a
function of bilirubin concentration for neonatal skin of three
maturities.
FIG. 35 is a flow chart comparing two methods of determining
cutaneous bilirubin concentration.
FIG. 36 is a graph of the optical density spectrum of melanin
subtracted from the measured optical density spectrum.
FIG. 37a is a block diagram of a hardware embodiment of the present
invention.
FIG. 37b is a flow chart of the method of the present invention to
determine cutaneous bilirubin concentrations from measured
reflectance spectra.
FIG. 37c is a more detailed flowchart of the method of the present
invention depicted in FIG. 37b.
FIGS. 38A, 38B and 39 are graphs illustrating the function of the
present invention.
FIG. 40 is a flow chart of a method, in accordance with the present
invention, to refine the method illustrated in FIG. 37 to determine
cutaneous bilirubin concentrations.
FIG. 41A is a two dimensional array showing the variation of total
score as a function of parameters defining the relationship between
reduced scattering coefficient and gestational age.
FIG. 41B is a graph of the scattering coefficient of skin at 460 nm
as a function of gestational maturity.
FIG. 42 illustrates the parameters used to describe the collection
of light by the optical patch of FIG. 8A.
FIGS. 43A, B and C illustrate the three cases of the geometry of
collection of light by optical patch of FIG. 8A.
FIG. 44 illustrates the relative dimensions of the absorptionless
medium modeled by the Monte Carlo simulation of the present
invention.
FIG. 45 is a graph of the measured reflection of skin of finite
thickness as a fraction of the measured reflection of infinitely
thick skin, displayed as a function of skin thickness.
FIG. 46 is a graph of the measured reflection of skin of finite
thickness as a fraction of measured reflection of infinitely thick
skin, displayed as a function of wavelength.
FIG. 47 is a more detailed flow chart of the skin thickness
correction procedure of the method illustrated in the flow chart of
FIG. 37.
DETAILED DESCRIPTION OF THE INVENTION
Section 2
Optical Properties of Neonatal Skin
2.1 Introduction
The optical interaction coefficients, or optical properties, of
tissues describe the behavior of light in tissue. They are the
absorption coefficient, .mu..sub.a, the scattering coefficient,
.mu..sub.s, and the anisotropy, g (See Appendix A). The combination
.mu..sub.s (1-g) is called the reduced scattering coefficient, and
it describes the effective amount of scattering in a tissue.
Knowledge of the optical properties is important for the
development of diagnostic and therapeutic applications of light to
tissue.
For diagnostic applications, knowledge of the optical properties,
and of radiative transport theory, enable the development of
fundamentally correct diagnostic algorithms that can accommodate
the inhomogeneities of tissue samples. The importance of knowing
the optical properties of skin for the development of
transcutaneous reflectance spectroscopy will be discussed further
in sections 3, 4 and 5. Furthermore, the optical properties are
desired for the development of therapeutic applications of light,
since they dictate the dosimetry of light in the tissue.
The optical properties of adult skin have been studied in the past
[Jacques 1987b, Prahl 1989, Anderson 1981, van Gemert 1989,
Marchesini 1989, Jacques 1990], but those of neonatal skin samples
have not been determined. In this chapter the absorption and
scattering properties of neonatal skin are determined, and the
relationship between the scattering coefficients and gestational
maturity of the infant is studied. The micro-structure of the
dermis is studied quantitatively. The measured scattering
coefficients are related to a combination of Mie theory scattering
by the collagen fiber bundles in the dermis, and Rayleigh
scattering by smaller particles.
The measured optical coefficients determined in this section are
utilized in subsequent sections to study how variables in the skin,
such as absorption, maturity, and thickness, influence the measured
reflectance spectra. The optical interaction coefficients of
neonatal skin are an essential component of the method of the
present invention developed to transcutaneously determine the
cutaneous bilirubin concentration.
2.2 Materials And Methods
2.2.1 Tissue Samples
Twenty abdominal skin samples were obtained from pediatric
autopsies. The estimated gestational age of the subjects varied
from 19 weeks to full term (.about.38 weeks gestation), and the age
of the newborn at death varied from zero to 5 months old. The
samples were obtained from a racially heterogeneous population. The
samples were excised during autopsy, and sealed in an air-tight bag
to maintain their moisture content, but without addition of saline
to avoid swelling. The skin was then separated from the
subcutaneous tissue with a scalpel and forceps, and placed between
glass microscope slides of known thickness that were separated by
calibrated spacers of the same thickness as the tissue. This method
enforced a uniform tissue thickness with a well defined
air/glass/tissue interface, and prevented tissue desiccation. The
thickness of the sample, d, was verified by measurements with
digital calipers of the glass and tissue sandwich. The average
thickness of the skin was 888.+-.301 .mu.m (mean.+-.S.D., n=20),
and the average area of the skin sample was approximately 1.5
cm.sup.2. The two surfaces of the skin will be referred to as the
epidermal and the subcutaneous sides. Experiments were conducted
twice, first irradiating the epidermal surface and then irradiating
the subcutaneous surface with light. Melanin is present only on the
epidermal side, so if melanin content is significant, the epidermal
exposure would suffer more than the subcutaneous exposure. The
influence of epidermal melanin pigmentation is assessed by
determining if the optical properties obtained from either exposure
differ markedly. In twelve of the twenty subjects, there was no
significant difference in measurements using epidermal versus
subcutaneous exposure, implying negligible melanin content.
A separate study of the water content of the skin samples indicated
that typical hydration was 65.+-.4% (mean.+-.S.D., n=10), based on
the difference in mass between fresh and oven-dried samples.
2.2.2 Reflectance And Transmission Measurements
The total reflectance, R.sub.t, equals the diffuse reflectance,
R.sub.d, that is backscattered by the tissue plus the specular
reflectance, R.sub.sp, from the front air/glass/tissue interface of
the sample. The total transmission, T.sub.t, equals the diffusely
scattered transmission, T.sub.d, plus the unscattered collimated
transmission, T.sub.c. The optical experiments measured R.sub.d and
T.sub.t using an integrating sphere as shown in FIG. 3A, and
measured R.sub.d using an integrating sphere as shown in FIG.
3B.
The integrating sphere (Labsphere Inc., North Sutton, N.H.) had a
4-inch diameter and an inner wall reflectivity of 98.6% (based on
unpublished experiments). The measurements in laboratory units (mA
of detector diode current) of the diffuse reflectance, M.sub.R, and
total transmission, M.sub.T, of the skin samples were recorded when
the sample was placed at the reflectance and transmission port
respectively. The specular reflectance, R.sub.sp, from the front
air/glass/tissue interface escaped the sphere through the entrance
port and was not measured. A small background signal due to stray
light, M.sub.o, was measured when nothing was placed at either port
and light simply entered the front port and exited at the back
port. A calibration measurement, M.sub.std, of diffuse reflectance
from a standard plate of Spectralon.TM. with a known reflectance of
99.4% (Labsphere Inc., North Sutton, N.H.) was also recorded.
Spectrometric data were obtained using a Xenon tube light source
(Model-77822, Oriel Corp., Stamford, Conn.) and a 5-nm bandwidth
grating monochrometer (Model-77250, Oriel Corp.) that was manually
scanned between 400 and 750 nm in increments of 10 nm.
2.2.3 Data Analysis
The total diffuse reflectance, R.sub.d, of the skin sample, from
both the epidermal and dermal sides, was calculated: ##EQU1##
The total transmission, T.sub.t, of light through the skin, was
calculated: ##EQU2##
Reflectance and transmission defined by Equations 2-1 and 2-2 and
based on measurements performed in an integrating sphere are
slightly lower than true values. First, the sphere throughput
efficiency is less when a lossy sample is at a port than when the
calibrating standard (SPECTRALON.RTM.) is at the port. Secondly,
additional losses occur due to the lateral diffusion of light in
the tissue sample and in the glass slide beyond the edges of the
sphere port. This effect is accentuated when a thicker glass slide
is placed between the tissue sample and the integrating sphere
port.
To correct for these losses, an experiment to determine the
correction factors was performed. Solutions with known optical
properties were prepared from fixed concentrations of intralipid
and trypan blue. The optical properties of the intralipid and
trypan blue were determined by collimated transmission, total
reflectance, and added absorber measurements [Wilson 1986, Cheong
1990]. The true total reflectance and transmittance from a known
thickness of these solutions were calculated using an 8-flux
adding-doubling routine (explained in the next paragraph). Samples
from these solutions were also placed in cuvettes, and their
reflectance and transmittance measured with the integrating sphere
recorded. The correction factors were then derived by relating the
measured reflectance and transmittance values to the true values
predicted by adding-doubling. The expressions for calculating the
true reflectance and transmittance from the measured values
are:
and
where penetration depth, .delta., is defined as: ##EQU3## and where
.mu..sub.a and .mu..sub.s ' were calculated by an iterative 8-flux
inverse adding-doubling calculation of the uncorrected reflectance
and transmittance.
The corrected values of diffuse reflectance, R.sub.d, total
transmission, T.sub.t, for each wavelength, and thickness, d, were
then analyzed using an iterative 8-flux inverse adding-doubling
routine by Scott Prahl, Department of Electrical Engineering,
University of Texas at Austin [Prahl 1989]. The adding-doubling
method was originally developed by van de Hulst to calculate the
reflectance and transmission of a slab of known thickness [van de
Hulst 1980]. The transmission and reflectance from a very thin slab
is calculated by assuming knowledge of a single-scattering event,
and the results are used to predict the behavior of successively
doubled slab thicknesses until the final sample thickness is
reached, yielding the reflectance and transmission of the tissue
sample. The iterative inverse routine (an 8-flux calculation [Prahl
1989]) yielded a unique pair of .mu..sub.a and .mu..sub.s (1-g)
values from a pair of R.sub.d and T.sub.t measurements at each
wavelength for a sample of known thickness. The errors in deduced
optical properties are less than 10% for accurate measurements of
R.sub.d and T.sub.t [Saidi 1990]. Samples were optically too thick
at wavelengths below 450 nm to allow sufficient transmission for
accurate analysis. Therefore, no results are reported at these
shorter wavelengths.
2.2.4 Mistology
Histological samples were obtained from four representative skin
samples, and were stained with H&E and Masson's trichrome
stains. The collagen fiber bundle content of the skin samples was
measured using a videometric image analysis system (VT150, American
Innovision Inc., San Diego, Calif.). With the image analyzer, lines
perpendicular to the epidermal surface were projected on each image
captured for a histological sample. The numbers and diameters of
the collagen fiber bundles were measured along each of these
projections, and a collagen concentration coefficient was
calculated, defined as the number of collagen fiber bundles per mm.
The collagen concentration coefficient was used to calculate the
concentration of collagen fiber bundles for the histological
sample. The mean collagen fiber bundle diameter along each
projection was also measured.
2.3 Results
The results are presented first in terms of the changes in optical
properties at a single wavelength as a function of gestational age.
Secondly, the wavelength dependence of optical properties are
presented for three representative ages. Finally, the
ultrastructural measurements of fiber bundle size and concentration
are presented.
The scattering coefficient at 650 nm increased linearly with age,
as shown in FIG. 4. Age is defined as the estimated gestational
period plus the postnatal period before death. Similar
relationships were observed for the scattering coefficient at other
wavelengths (not shown). Also plotted are the .mu..sub.s (1-g)
values for adult skin based on 3 samples included in this study and
on reported values in the literature (see Section 2.4). The
scattering of neonatal skin at about 60 weeks is comparable to the
scattering of adult skin. There is considerable variation in
.mu..sub.s (1-g) amongst adult skin samples.
The wavelength dependence of the absorption and reduced scattering
coefficients, .mu..sub.a and .mu..sub.s (1-g), for 12 non-pigmented
neonatal skins are plotted in FIG. 5. The optical properties
differed by less than 10% when calculated from measurements which
delivered light to either the epidermal or subcutaneous sides of
the skin. Therefore, the effect of melanin pigmentation was
negligible. The reduced scattering coefficients for three ages, 20,
35, and 50 weeks, were determined by interpolation of the
.mu..sub.s (1-g) data as a function of age (see FIG. 4). In FIG. 4,
results from the present study are shown with open circles, and
results reported in the literature are shown with other symbols.
Scattering is stronger at shorter wavelengths. Scattering increases
with age, apparently as collagen fiber bundles increase in size and
concentration, as discussed below. The mean values of .mu..sub.a
for all subjects versus wavelength are also shown, along with
standard deviations at selected wavelengths. There was no obvious
dependence of .mu..sub.a on age.
A linear fit of the .mu..sub.s (1-g) data as a function of age
(similar to that in FIG. 4) performed at 50-nm wavelength intervals
between 450 and 750 nm yields a y-intercept, y.sub.int (.lambda.),
and a slope, m(.lambda.), for each wavelength. The scattering
coefficient at a specified gestational maturity, and wavelength is
equal to:
where .mu..sub.s (1-g) is expressed in cm.sup.-1, and maturity is
expressed in weeks. The empirical fit of the y-intercept,
Y.sub.int, as a function of wavelength is:
and the fit of the slope, m, is:
where .lambda. is the wavelength expressed in nm.
The absorption coefficient of the skin did not change predictably
with gestational age. A characteristic absorption spectrum for
hemoglobin was observed in the 500-600 nm range for most (7 of 9)
stillbirths, while not observed in the .mu..sub.a spectra of any of
the neonates that died postnatally. A measure of the absorption
coefficient due to hemoglobin was calculated by subtracting the
.mu..sub.a at 650 nm where hemoglobin absorption is very low, from
the .mu..sub.a at 585 nm where there is significant hemoglobin
absorption. This calculated difference, .DELTA..mu..sub.a 585-650,
attributed to hemoglobin was 4.4 (.+-.3.8 SD, n=7) cm.sup.-1 for
stillbirths and 1.6 (.+-.1.4 SD, n=10) cm.sup.-1 for the neonates
that died postnatally. This implies that the stillbirths contained
a higher concentration of blood in their skin than did the liveborn
neonates.
The average absorption coefficient of the skin, shown in FIG. 5
varied significantly in the 400 to 600-nm range due to variation in
bilirubin and blood content in the in vitro skin samples. A fit of
the absorption coefficient measured above 620 nm is:
FIG. 6 shows the approximate relative contributions of skin, blood,
and bilirubin absorption to the total absorption coefficient of
skin. The expression for skin absorption, .mu..sub.a skin as a
function of wavelength, .lambda. (in nm), is:
This expression for .mu..sub.a skin was determined in section 5,
and fits the measured absorption coefficients well at wavelengths
over 620 nm where the absorption due to blood and bilirubin become
negligible. As discussed in section 5.5, this expression for
.mu..sub.a is also consistent with the shorter wavelength spectrum
in vivo.
2.4 Discussion
2.4.1 Optical Properties
In the epidermis, it is the absorption due to melanin which
restricts the penetration of light. In the dermis, however, there
is little absorption, except by bilirubin and hemoglobin, so that
scattering is an important optical parameter that strongly
influences the penetration of light. The scattering coefficients of
the epidermis and dermis are similar, while the absorption
coefficients can differ [van Gemerr 1989]. By selecting
non-pigmented skin samples, in which calculated optical properties
were the same (<10% difference) regardless of whether the
radiation was delivered to either the epidermal or subcutaneous
sides, the essential optical properties of the skin were determined
with minimal effect of melanin. The optical absorption spectrum of
0-melanin is known [Kollias 1985, Jacques 1991], and so melanin
pigmentation can be quantitatively added to any computational
models used to predict the penetration of light in variably
pigmented infants.
Adult .mu..sub.s (1-g) data cited in the literature are included in
FIG. 4 (using symbols other than unfilled circles) for comparison
with the neonatal values. There is considerable variation in
reported values for adult skin.
2.4.2 Hemoglobin Absorption
The vascular development of the skin is defined during the first
trimester of gestation [Johnson 1989]. Therefore, all skin samples
in our study were expected to have well established vascular
supplies, and this was confirmed by microscopic analysis of the
histological sections. There was an increase in absorption due to
hemoglobin in the skin of stillborns relative to the skin of
neonares that expired postnatally.
Fetuses that expire are suspended in amniotic fluid until they are
delivered. Blood continues to perfuse the tissues, and intrauterine
cutaneous autolysis begins soon after expiration. This can lead to
extravasation of the red blood cells, and hemolysis of these cells
can lead to generalized dissemination of the hemoglobin in the
skin. Infants that die postnatally, however, are usually laid in a
supine position which causes pooling of the blood in the back. The
abdominal skin samples obtained did not contain significant
quantities of hemoglobin that had perfused the skin.
2.4.3 Scattering vs. Gestational Maturity
The most notable optical property that changed with gestational
maturity is the reduced scattering coefficient, .mu..sub.s (1-g).
This parameter is sensitive to changes in the skin structural
composition that accompany gestational maturation. Collagen fiber
bundles are the most important scattering elements in the dermis
(as discussed in the next section), and the increase in scattering
with gestational age may be explained by the accompanying increase
in the size and concentration of the collagen fiber bundles.
Studies with scanning electron microscopy and immunogold labeling
have revealed that there is an increase in the ratio of type I to
type III collagen with gestational age [Smith 1982, Smith 1987,
Burgeson 1987]. As gestation progresses, there is an increase in
the concentration of collagen fibers, more collagen fibers are
associated in fiber bundles, and these bundles have thicker
diameters [Smith 1982, Smith 1987, Burgeson 1987]. Quantitative
video image analysis of the histological samples confirmed that
both the number of the collagen fiber bundles, and the size of
these fibers increase with gestational age.
2.4.4 Mie And Rayleigh Light Scattering In Dermis
A description of dermal scattering based on classical theory light
scattering by cylinders and small particles is presented. Such a
description bridges between the macroscopic scattering observed
clinically and measured experimentally, and the theory of light
scattering by ideal structures similar to the ultrastructural
components of dermis.
We consider both Mie scattering by structures similar in size to
the wavelength of light (i.e., collagen fibrils and bundles) and
non-Mie scattering by structures that are small in comparison to
the wavelength of light. Mie scattering is treated by the Mie
theory for scattering by cylinders [Bohren 1983], and has an
anisotropic scattering profile (g>0). Non-Mie scattering is
treated as Rayleigh scattering which has a .lambda..sup.-4
wavelength dependence and on the average has an isotropic
scattering profile (g=0).
The dermis is primarily composed of collagen fiber bundles.
Although oriented in a variable manner in the dermis, the collagen
fiber bundles are nevertheless dominated by a general orientation
parallel to the skin surface [Montagna 1974, Smith 1986]. Mie
theory can model these bundles as infinitely long cylinders and
predict the scattering from each fiber [Bohren 1983]. The theory
predicts the scattering coefficient, .mu..sub.s, and the angular
dependence of scattering, p(.theta.). The anisotropy, g, was
calculated based on p(.theta.) (see Equation A-7 in Appendix A).
The scattering in a medium with suspended particles is determined
by the size of the particles, their concentration in the medium,
and the index of refraction mismatch between the medium and the
particles. The effect of these three parameters on the scattering
magnitude and wavelength dependence is illustrated in FIGS. 7a, 7b
and 7c. In each sub-figure the reduced scattering, .mu..sub.s
(1-g), is predicted by Mie theory for collagen fiber bundles
oriented parallel to the skin surface, at a concentration of
2.5.times.10.sup.6 per cm.sup.3 where each fiber bundle has a
diameter of 2.75 .mu.m and an assumed index of refraction of 1.390.
The index of refraction of the medium surrounding the fiber bundles
is assumed to be a lower value, 1.346. These choices of the
refractive indices are explained in the next paragraph.
The index of refraction of the scattering particles and of the
surrounding medium affect the scattering magnitude and wavelength
dependence. Both the ratio of the index of refraction of a particle
relative to that of the surrounding medium, and the absolute values
of the indices of refraction are important determinants of the
scattering cross section of the particle. Assignments of 1.390 and
1.346 for the indices of refraction of the particles and of the
surrounding media respectively will let the reduced scattering
profile predicted by Mie theory in the above model match the
wavelength dependence of 35-week gestational maturity skin. Other
indices-of-refraction pairs may also be chosen to match the 35-week
gestational maturity scattering profile. Indices of refraction of
1.390 and 1.346 are believed to be realistic for hydroxylated
collagen and for extracellular fluid respectively.
The values of fiber bundle size, concentration, and indices of
refraction assumed in FIGS. 7A, 7B and 7C successfully model the
average magnitude and wavelength dependence of scattering in the
dermis of a fetus at about 35 weeks gestational age (see FIG. 5).
In FIGS. 7A, B, and C, the concentration, diameter, and index of
refraction, respectively, of the fiber bundles are varied above and
below the average values. The scattering increases as these three
parameters increase.
In the dermis, in addition to the fiber bundles that have 1-10
.mu.m diameters, there are collagen fibrils approximately 100 nm in
diameter that do not associate into bundles, and a variety of
smaller particles and structures. These scattering elements are
much smaller than visible wavelengths of light, and therefore
contribute to Rayleigh scattering of light that we have modelled as
isotropic scattering.
2.5 Conclusions
The optical properties of neonatal skin were determined in the
visible region from 450-750 nm. The reduced scattering coefficient,
.mu..sub.s (1-g), increases directly with gestational maturity of
the infant, while the absorption coefficient is independent of
gestational maturity. Generalized empirical equations were obtained
that can be applied to obtain the scattering coefficient spectra
for skin of any specified maturity, and dermal absorption spectra
for skin at all maturities.
Mie theory can be used to quantitatively explain the scattering
properties of the collagen fiber bundles within the dermis. The
collagen fiber bundles are the predominant scattering elements in
the skin, and the amount of scattering is strongly dependent on the
concentration, size, and index of refraction of these bundles. The
increase in the reduced scattering coefficient with gestational
maturity is quantitatively accounted for by the accompanying
increase in both concentration and size of the collagen fibers.
Section 3
Reflectance Measurements With An Optical Patch
3.1 Introduction
Transcutaneous reflectance spectroscopy involves the measurement of
light diffusely reflected from the skin. This light has travelled
within the skin, and has had an opportunity to sample the absorbers
inside the skin. Since light reflected from a tissue is diffuse,
the total true reflection can be measured with a distant detector,
or an integrating sphere, where all the reflected light is observed
equally. The total reflectance of a tissue is dependent on the
ratio of its reduced scattering to absorption coefficient, and so
evaluation of the quantity of absorbers within a tissue can be
inferred from the total reflection only with knowledge of the
scattering properties of the tissue. If not all the reflected light
is collected during a reflectance measurement, then the reflected
spectra can be interpreted if the collection characteristics of the
measurement device is known.
For clinical measurements, the devices used should be small,
durable, and easy to use. With these considerations in mind, an
optical patch 107, illustrated in FIG. 8A, has been designed for
transcutaneous reflectance measurements in accordance with the
present invention. The patch 107 includes a bundle 108 of mixed
light delivery and collection fibers 109 and 111, and is placed
flush with the skin surface. FIG. 8B shows the radial reflectance
profile from typical neonatal skin, predicted by a Monte Carlo
computer simulation of light delivered through the optical patch
107. FIG. 8B illustrates that light delivered through the patch
spreads beyond the boundaries of the optical patch, and only a
fraction of the reflected light is collected. The collection
efficiency depends on the light collection and delivery geometry
and on the optical properties of the tissue. Hence, the geometry of
the optical transducer, such as an optical patch or a catheter, and
the optical properties of the tissue being measured affect correct
interpretation of measurements.
The reflected light measured with an optical patch is usually
calibrated relative to a standard reference, such as teflon. The
reflectance, M, measured with the optical patch can be expressed
as: ##EQU4## where S is the total light source efficiency, D is the
total detector efficiency, and f is the collection efficiency of
the optical patch for the material measured. The term f physically
specifies the fraction of the total reflected light that reaches
the collection fibers of the optical patch. The term R.sub.tissue,
or simply R, denotes the true total reflectance of the material
measured (tissue or standard). Note that S. and D cancel in
Equation 3-1, yielding a measurement that is independent of the
light source and detector characteristics.
Equation 3-1 can be written as: ##EQU5##
The combination f.sub.standard R.sub.standard is a constant for a
given standard at any particular wavelength. Calculations of
f.sub.tissue, or simply f, can be converted to f* by division by
the appropriate constant (f.sub.standard R.sub.standard) for the
reference standard at the wavelength of interest.
The fraction, f, of light collected by the optical patch is
dependent on both the absorption, .mu..sub.a, and reduced
scattering, .mu..sub.s ', coefficients of the measured tissue.
Since both R and f are functions of both optical coefficients,
either .mu..sub.a and .mu..sub.s ' can be determined if the other
is known and the reflectance is measured. In our case the
absorption coefficient is desired while the scattering coefficient
of the tissue is known. When measurements are performed relative to
a reflectance standard reference, consideration of the collection
efficiency, f.sub.standard, of the optical patch for the standard
reference used is as important as the reflectivity of the standard,
R.sub.standard.
The reflectance of a tissue is dependent on the quantity of
absorbers within the tissue, and also on the location of the
absorbers. Melanin in the skin, which differentiates skin color
between people, is present only in the epidermis. The epidermis is
the topmost layer of the skin, and is approximately 50 .mu.m thick.
Because of its localization in the epidermis, melanin is expected
to affect the reflectance of the skin, and the collection
efficiency of the optical patch differently than do diffuse
absorbers in the skin.
In Subsection 3.2, the measurement of the true reflectance of a
material is discussed. In Subsection 3.3, physical measurements on
phantoms are preformed to determine the collection efficiency of
the optical patch 107 as a function of the optical properties of
the tissue. In Subsection 3.4, Monte Carlo computer simulations are
used to predict the collection efficiency of optical patch 107. In
Subsection 3.5, the effect of a thin superficial layer, simulating
epidermis, on reflectance and on the optical patch collection
efficiency is predicted by Monte Carlo computer simulations.
Finally, in Subsection 3.6, an iterative method to determine
.mu..sub.a from the measurement, M, is presented. This method
requires knowledge of the scattering properties of the tissue, and
the equations relating .mu..sub.a and .mu..sub.s ' to R and f*.
3.2 Measurement Of Diffuse Reflectance
To measure the true reflectance of a material, the detector has to
be placed relatively far away from the material. A fraction of the
light remitted from the surface reaches the distant detector. The
fraction of the reflected light that reaches the detector can be
calculated when performing absolute measurements. When measurements
are calibrated relative to a standard of known reflection, the
collection fraction remains constant when the reflectance of the
sample and of the standard are measured. The light reaching a
distant detector depends on several factors, namely the geometry of
the light collection arrangement and the profile of the remitted
diffuse light. FIG. 9 illustrates the collection fraction for a
distant detector 112, and defines the angles and distances which
describe the collection geometry of a distant detector.
The reflection signal, C(r,.theta.,d.omega.), recorded by a distant
detector 112 in FIG. 9 is expressed as:
where G(r,.theta.,d.omega.) is a geometrical factor which accounts
for the fraction of reflected light reaching the detector, S is the
light from the source, D is the detector 112 response, and R is the
true reflectance of the material. As shown in FIG. 9, G, and
consequently C, are dependent on the distance, r, of the detector
112 from the material, the angle, .theta., of the detector from the
normal, and the solid angle of collection, d.omega..
The angular distribution of the reflected light is dependent on the
reflective material and the angel of incidence of the light
introduced to the material. In an ideally diffusing material, or
Lambertian reflector, the reflected light is isotropic and the
angular distribution of the reflected irradiance is independent of
the angel of incidence. For a Lambertian surface, the light
collected by the detector and G(d,.theta.) are dependent on
cos(.theta.), as indicated in FIG. 9. All matte surfaces can be
considered Lambertian when the angles of incidence and detection
are small. The Lambertian approximation is invalid only at extreme
angles [Kortum 1969].
The term G(d,.theta.) should not be confused with the term f
introduced in Subsection 3.1. Both terms refer to collection
fractions, but G(d,.theta.) refers only to the fraction of
reflected light from a unit surface area, dA, and is dependent only
on the location of detector 112 relative to dA. G(d,.theta.) is
applicable when the light detector is far from the reflective unit
surface, dA. In this situation, despite any spatial distribution of
reflectance profile, R(.rho.), gives the amount of light remitted
from the surface as a function of the radial distance, .rho., from
the center of the reflective source to the point of remittance. The
term f, however, referred to the collection fraction for
measurements at the tissue surface, and so this collection fraction
depended on the diffuse reflection profile, R(.rho.), and therefore
was also dependent on the optical properties of the tissue.
The diffuse reflectance was measured as a function of distance
between the detector and the reflective surface. The effect on the
measured signal of varying the reflected light profile was
determined, and is described in Subsections 3.2.1 and 3.2.2.
3.2.1 Point Source Delivery
If the dimensions of the surface area from which the light is
remitted from a medium is small relative to d, then the reflected
light is distributed in a hemisphere 113 centered at the reflective
source 114. This geometry is illustrated in FIG. 10. The distance,
d, of the detector 116 from the surface is equivalent to the radius
of the hemisphere 113 over which the light is distributed. The
surface area of such a hemisphere 113 is 2.pi.d.sup.2. The detector
collects the light in a constant area, A, of this hemisphere, and
so the light detected, G(d,.theta.) is equal to: ##EQU6##
The angle of collection, .theta., remained constant at 0.degree.,
and therefore G(d,.theta.) is a function only of 1/d.sup.2.
The logarithm of the above equation gives:
Therefore, the plot of detected light, log[C(d,.theta.0], and
distance, log[d], should have a slope of -2.
FIG. 10 illustrates the experimental arrangement used to verify the
behavior of reflected signal as a function of distance when the
light is delivered to the reflective material as a point source.
The reflective material used was an optically thick block of teflon
(dimensions 20 cm.times.20 cm.times.5 cm). The argon laser beam 117
(488 nm), delivered normally to the block of teflon 118, spread
from the point of delivery before remission.
The measured reflected signal plotted versus distance of the
detector is shown in FIG. 11. It can be seen from this figure, the
predicted relationship in Equation 3-6 holds as the height, d,
becomes large relative to the diameter of the collection fiber and
the diffuse remittance area. At distances close to the reflective
surface, this relationship does not hold as the remittance source
is not small relative to the radius of the imaginary
hemisphere.
3.2.2 Broad-Beam Source Delivery
If light is delivered to the reflective surface as a broad beam,
the area of light delivery is not always small relative to the
distance of the collection fiber. FIG. 12 shows the experimental
arrangement used to study the reflected signal when the light is
not delivered to the reflecting material at a single point, but
rather as a broad beam. The experiment was performed with teflon as
the reflective material 119 (see previous section for
description).
The results are shown with logarithmic scales in FIG. 13. The
hemispheric approximation is seen to hold only when the distance,
d, is large relative to the diameter of the area of light delivery.
Comparing the results in FIG. 13 with those in FIG. 11, it can be
seen that broadening of the light source delivery area results in
an increase in the distance, d, required before the hemispherical
approximation holds. When d is small (<8 cm), the reflectance
signal does not decrease as rapidly with increasing d as predicted
by the hemispherical approximation. The reason being that decreases
in the signal (as1/d.sup.2) from each point on the surface is
compensated by an increase, with d, in the area of the reflectance
source viewed by the fiber.
3.2.3 Conclusions
Based on the definitions of diffuse reflectance and on the above
observations, the following considerations should be heeded in
order to appropriately measure true reflectance from a surface. The
source delivering light to the reflective surface needs to be small
relative to the dimensions of the reflective medium, such that all
the light is either absorbed in the medium or remitted from the
surface. The distance of the detector form the reflective surface
should be large relative to the dimensions of the remittance area.
This will assure that changes in the amount of light seen by the
detector, due to variations in the remitted profiles, are small.
Finally, when measurements are performed relative to a standard of
known reflectance, the delivery and collection geometry should be
kept constant for both measurements. These guidelines will be
considered when the true reflectance of phantoms and tissues are
measured.
3.3 Physical Measurements Of Collection Efficiency
True reflectance, R, is related to measured reflectance, M, using
an optical patch by a factor f*, as discussed in Equation 3-2. In
order to relate optical patch measurements to true reflectance
measurements, the collection efficiency of the optical patch, f*,
has to be known. In a series of phantoms in which the optical
coefficients were known, f*, was determined by measuring the true
reflectance, R, and the optical patch measurement, M: ##EQU7##
The relationships between the optical interaction coefficients of
the medium, .mu..sub.a and .mu..sub.s ', and f* were determined for
these phantoms. Later, in Section 3.4, Monte Carlo simulations are
used to predict f* as a function of the tissue optical interaction
coefficients.
3.3.1 Phantom Preparation
Liquid phantoms in which the optical properties are known precisely
were prepared. The scattering elements in the phantoms were 579-nm
polystyrene microspheres for which the scattering coefficient,
.mu..sub.a, and the anisotropy, g, of the microspheres are
calculated by Mie theory, and verified by collimated transmission
measurements. Trypan blue, for which the absorption coefficient was
carefully measured, was used as an absorption medium in the
phantoms. A series of phantoms were made in which the reduced
scattering coefficient, .mu..sub.a (1-g), ta 630 nm was set at 6
cm.sup.-1, 24 cm.sup.-1, 42 cm.sup.-1, and 60 cm.sup.-1. The
absorption coefficient of the phantom at 630 nm was varied between
0 cm.sup.-1 and 20 cm.sup.-1 by the addition of trypan blue to the
phantom.
3.3.2 Measurement Technique
The optical patch measurement of each phantom, SDf.sub.phantom
R.sub.phantom, normalized by optical patch measurement of teflon,
SDf.sub.teflon R.sub.teflon, to yield M of each phantom 121 as
made, as illustrated in FIG. 14A. The measurement of the phantom,
GSDR.sub.phantom, normalized by measurement of a standard,
GSDR.sub.standard, was then obtained by means of a distant
detector, as illustrated in FIG. 14B, to determine the true
R.sub.phantom. The calibration method relative to reflection
standards is described mathematically in Subsection 3.3.2a and
3.3.2b. In both situations depicted in FIGS. 14a and b, the light
from the collection optical fiber was spectrally separated by a
diffraction grating, and measured with a CCD camera (Photometrics
Series 200). The true reflectance for each of the phantoms was
measured relative to the reflectance of a standard of known
reflectance (spectralon.TM., Labsphere Inc., North Sutton, N.H.;
R.sub.standard =0.994). The measurements of the phantoms with the
optical patch were calibrated relative to measurements on teflon,
SDf.sub.teflon R.sub.teflon, as is done with clinical
transcutaneous measurements, to yield:
a) Measured Reflectance with the optical patch
When the light reflected from the phantom is measured with the
optical patch, as shown in FIG. 14A, light remitted from the
phantom 121 and reaching the patch 107, can be represented as:
where S and D again represent the source and detector terms,
f.sub.phantom is the fraction of reflected light that actually
reaches the detector, and R.sub.phantom is the true reflectance of
the phantom.
Since the readings measured on the phantom need to be standardized,
a standard is also measured. Again, the light reaching the detector
can be represented as:
where f.sub.standard and R.sub.standard are analogous to
f.sub.phantom and R.sub.phantom defined above. The measurement of
the phantom, M.sub.phantom, relative to that of the standard can
then be reduced to: ##EQU8##
The collection efficiency f* at any wavelength of interest is
therefore equal to: ##EQU9##
Recalling Equation 3-2, the reflectance measured with the optical
patch, M, can be described as the product of f* and the true
reflection, R, of the material.
b) True Reflectance of the Phantoms
The light collected with a distant detector, C.sub.phantom, from
reflection of the phantom is expressed as:
where S represents the light delivered by the source, D represents
the detector efficiency, and G represents the amount of light
reaching the detector due to the geometry of collection, and
R.sub.phantom represents the reflection of the phantom. Since the
source and detector are both not at extreme angles relative to the
normal of the phantom surface, the reflected light can be assumed
to be remitted as a true Lambertian, and differences between the
angular profiles of the reflected light from the different
materials are not significant [Kortum 1969]. The properties of a
Lambertian reflector are described in Subsection 3.2.
Similarly, the light collected, C.sub.standard, from reflection
measurements with a distant detector for the standard is:
where R.sub.standard is the reflection of the standard used. Since
the terms in common in Equations 3-15 and 3-14 can be factored out,
the true reflection of the phantom, R.sub.phantom, can be
calculated as: ##EQU10##
Also, measurements of teflon were made to specify R.sub.teflon, so
that later calculation of fR.sub.teflon was possible.
3.3.3 Results
The collection efficiency of the optical patch 107 was found to
increase with both the absorption and scattering coefficients of
the measured material (See FIG. 15).
After further analysis of the f* measurements at 630 nm in phantoms
of known optical properties, the collection efficiency, f*, was
found to be inversely dependent on .delta./.mu..sub.t 'd.sup.2,
where .delta. is the penetration depth of the light in the tissue
and is equal to: ##EQU11## and .mu..sub.t ' is the reduced
attenuation coefficient, and is equal to:
and d is the diameter of the optical patch. The term
.delta./.mu..sub.t '.sup.2 is dimensionless. At any fixed
wavelength, e.g. 630 nm, the product f.sub.standard R.sub.standard
is constant, and so f of the material is equal to the determined f*
divided by f.sub.standard R.sub.standard for the wavelength
studied. The relationship between the collection efficiency of the
optical patch, f, and .delta./.mu..sub.t 'd.sup.2 determined by the
measurements on phantoms is illustrated in FIG. 15. Also shown in
FIG. 15 are the results of f predicted by Monte Carlo as described
in the next section. From this relationship, the collection
efficiency of the optical patch can be determined for any specified
optical properties in the tissue. The effective collection
efficiency, f*, is sensitive to the reflectance, r.sub.standard,
and the collection efficiency, f.sub.standard, of the material used
as a reference.
3.4 Monte Carlo Determinations Of Collection Efficiency
The Monte Carlo computer model is a stochastic model of the
transport of photons in a medium in which there are defined rules
of interactions of the photons with the medium. The Monte Carlo
computer model provides a useful tool for studying the light
transport in tissue [Keijzer 1989, Prahl 1989a]. A model tissue or
phantom can be homogeneous, or contain i layers with distinct
optical properties (.mu..sub.a, .mu..sub.s, g). The Monte Carlo
computer program simulates the launching of photons of unit weight,
W=1, into a tissue. The weight, W.sub.j,n, is related to the amount
of light energy associated with the n.sup.th photon at its j.sup.th
step within the tissue. Each photon on the average interacts with
the tissue after a mean free path of 1/.mu..sub.t, where .mu..sub.t
=.mu..sub.a +.mu..sub.s. The computer generates each incremental
step, dl.sub.j, by using a random number (RND) generator: dl.sub.j
=-1n(RND)/.mu..sub.t. At each interaction, a fraction .mu..sub.a
/.mu..sub.t of the current photon weight, or a weight W.sub.j,n
.mu..sub.a /.mu..sub.t, is deposited as absorbed energy, and a
fraction .mu..sub.s /.mu..sub.t, or a weight W.sub.j,n .mu..sub.s
/.mu..sub.t, is scattered into a new angle.
The angle at which the photon scatters is determined by the
Henyey-Greenstein function [Henyey 1941]. The Henyey-Greenstein
function describes the angular profile of light scattering for a
given anisotropy, g. The computer can keep track of the step length
dl.sub.j,k,n of the j.sup.th step of the n.sup.th photon i the
i.sup.th layer of tissue, and calculate the cumulative pathlength,
L.sub.i,n, of each photon in each layer: ##EQU12## where J is the
total number of steps that have been taken.
If a photon, n, of weight W.sub.n,j traveling in a medium reaches
the upper surface of the medium at step j, a fraction of this
photon may escape as reflected light. The fraction, u, that escapes
is determined by Fresnel's laws, and is dependent on the angel of
incidence of the photon, and the index of refraction of the medium
[Prahl 1989a]. The remaining weight of the photon, (1-u)W.sub.n,j,
is internally rejected and continues its propagation in the medium.
The fraction that was internally reflected may be absorbed bin the
medium, or may be partially remitted at a later time. For each
n.sup.th photon, there are J.sub.n occurrences of photon weight
escape. When the photon weight, W.sub.n, drops below a threshold
level equal to 1/N, then photon migration is terminated according
to a survival roulette algorithm described by Prahl et al. [Prahl
1989a].
Monte Carlo simulations provide statistical determinations of the
distribution of light within a medium, and the amount of light
emitted at each position from the light input location. The
accuracy of the results increase with the number of photons
simulate, N, and the error in the results are proportional to
1/.sqroot.N. Monte Carlo simulations are time inefficient, and to
repeat simulations for each specified set of optical properties is
unnecessarily repetitious. It is desirable to use redundant
information from Monte Carlo simulations to enable repeated
calculations of the reflection from media with variable optical
properties.
To enable the repeated calculations, Monte Carlo simulations are
used to generate, for each photon launched, the distance of
emission from its point of delivery into the medium, r.sub.-- em,
and the its pathlength of travel in an absorptionless medium,
L.sub.i, for each layer i in the medium. Many photons are
simulated, and these distances are recorded, for each photon, in
dimensionless units. This procedure is explained in Subsection
3.4.1. The L and r.sub.-- em distributions can then be used to
predict the remission profile for a medium with any desired
absorption and scattering coefficients, as explained in Subsection
3.4.2. The remission profile is then used to calculate the
collection efficiency of the optical patch in a medium, and this is
explained in Subsection 3.4.3.
3.4.1 Photon Histories In An Absorptionless Medium
When the Monte Carlo simulation is conducted with zero absorption
specified, then photons are terminated when they are emitted from
the medium, and there is never any absorption. Whenever a fraction
of photon n is emitted at the J.sub.th step of its propagation, the
pathlength in each layer i, L.sub.i,n, is calculated by Equation
3-19, and the distance from the input position in which the photon
was emitted, r.sub.-- emn.sub., j, are noted in dimensionless units
of effective scattering lengths. The Monte Carlo program keeps
track of L.sub.i,n, and r.sub.-- em.sub.n,j in units of distance
(cm), and they are converted to dimensionless units of effective
scattering lengths by the following equations:
where .mu..sub.s '0 is the scattering coefficient of the
absorptionless medium simulated by the Monte Carlo program during
generation of L.sub.i,n and r.sub.-- em.sub.n,J for each photon
emission event.
For each photon simulated, there may be more than one emission
event from the medium. Each time an emission event takes place, the
photon fraction emitted, the pathlength of travel in each layer,
L.sub.i,n, and the point of emission, r.sub.-- em.sub.n,j, are
recorded in a single file. We refer to this file as the "photon
histories file". Table 3.1 shows an excerpt from a sample photon
histories file for a two layer model. As can be seen in this table,
for each photon, there usually are several emission events, each
time a fraction of the photon weight is emitted.
TABLE 3.1 ______________________________________ V VI I IV
pathlength pathlength emis- II III emitted in layer 1, in layer
sion photon r.sub.-- em weight, L.sub.1 2, L.sub.2 event number
(D.U.) W.sub.0 (D.U.) (D.U.) ______________________________________
1 1 11.466 0.9469 1.159 216.42 2 1 11.56 0.0273 1.2319 220.1 3 1
9.436 0.0014 1.4701 469.34 4 2 19.858 0.9514 0.99636 388.72 5 2
19.131 0.0219 1.6258 388.72 6 2 18.732 0.0016 2.1436 388.72 7 2
18.871 0.0007 2.9374 393.24 8 2 19.717 0.0002 4.1846 393.24 9 3
7.4592 0.9432 0.19463 200.12 10 3 6,495 0.0315 0.69934 209.54 11 4
0.77266 0.9463 0.41998 16.279 12 4 3.9246 0.0286 1.0853 26.33 13 4
10.543 0.0007 1.7824 441.32 14 5 1.114 0.9136 0.23726 2.1554 15 5
1.7175 0.0597 0.55202 3.4894 16 5 7.1016 0.0023 0.74358 68.178 17 5
6.8808 0.0006 2.8618 153.69 . . . . . . . . . . . . . . . . . .
______________________________________
3.4.2 Calculation Of Reflectance Profile
The photo pathlengths, L.sub.i,n, and the radii of emission,
r.sub.-- em.sub.n,J, stored in the photon histories file are
subsequently used to predict the profile of reflectance for a
medium with any specified optical coefficients, .mu..sub.a and
.mu..sub.s '. In this new medium, for each emission event, the
photon weight emitted, W, is calculated as from the recorded
pathlength and absorptionless emission weight, W.sub.o, as:
##EQU13## where N.sub.i is the number of layers in the Monte Carlo
model, and .mu..sub.a is the specified absorption coefficient in
the medium. Since L.sub.i is specified in dimensionless units of
effective scattering lengths (see Equation 3-20), then .mu..sub.a
also is expressed in dimensionless units. The absorption
coefficient, .mu..sub.a, in dimensionless units is related to the
dimensional form (cm.sup.-1) as: ##EQU14## where .mu..sub.a ' is
the scattering coefficient in the medium. When a uniform medium is
simulated, (i.e. where the absorption of all layers is equal), then
the same .mu..sub.a value is specified for all the layers.
The radial profile of remission (in discrete form) can be
calculated from the photon remission data. We define radial
remission profile, R(k) as the amount of light (in watts or
photons) emitted from the surface annulus with inner radius equal
to the product of k and .DELTA.r.sub.-- em, and with annular
thickness .DELTA.r.sub.-- em.
For a given radius of remission, r.sub.-- em, the value of the
discrete radius, k, is chosen according to the following
condition:
where k=0,1,2, . . . K.sub.max. The maximum discrete radius
considered is K.sub.max. Photon weights found to be emitted at
radii, r.sub.-- em, larger than .DELTA.r.sub.-- em K.sub.max are
added to the remission profile element R(K.sub.max). The
programming statements used to determine k are included in Appendix
B. The radial remission profile, R(k) can then be calculated by
adding all photons, n, which are remitted at the discrete radius,
k, i.e. which satisfy the condition in (3-upper): ##EQU15##
The remission profiles, R(k), are calculated for media with
different specified optical properties. For given optical
properties, .mu..sub.s ', the absorption coefficient is calculated
in dimensionless units (Equation 3-23). The radial remission
profile, R(k) is then calculated by Equation 3-24, and 3-25. The
Li,n, and r.sub.-- em data for substitution i equations 3-16 and
3-17 are obtained by reading successive lines in the photon
histories file (see Table 3.1). The remission profile, R(k) is then
used directly in the convolution procedure to find the collection
efficiency of the optical patch (see Section 3.4.3, and Appendix
B).
In conclusion, this procedure is used to calculate the radial
remission profiles for media with different optical properties. For
each set of optical properties the photon histories file is used
and there is no need to run a new Monte Carlo simulation.
3.4.3 Convolution Of Remission Profiles
If the radial dependence of reflection, R(.rho.), from a point
source, as described above, is known, the radial dependence for a
beam of finite parameters can be calculated by convolution of the
radial profile with the input beam profile. Furthermore, the amount
of light escaping from a defined area can be calculated if the
input and output areas are specified. In this section the
convolution of the remission profile predicted by Monte Carlo is
described for the case where the input and output areas are two
concentric circles. This method is then used to calculate the
collection efficiency of the optical patch.
If the light is delivered as a uniform circle with radius
R.sub.patch, then the fraction of reflected light that is remitted
and collected within a concentric collection circle of radius
R.sub.patch is: ##EQU16##
The total collected light, and total lost light described above are
summed individually as the input is convolved across R.sub.patch.
The geometry description and equations used to calculate the
collection efficiency from reflection radial profiles are developed
in Appendix B. The equations presented in Appendix B can be applied
for other devices with similar delivery and collection
geometries.
3.4.5 Results
The collection efficiency, f, for an optical patch measurement from
a uniform medium is predicted by Monte Carlo as described above, is
also plotted in FIG. 15. The simulations coincide with the
measurements in phantoms, which predict a unique relationship
between f and .delta./.mu.t'd.sup.2. Monte Carlo calculations of f
were performed for a variety of optical patch diameters (d=2.1 mm,
4.2 mm, and 6.3 mm) and the non-dimensional relationship presented
above was verified.
The relationship was fit by a third order polynomial, so that it
may be utilized later to predict f if the optical properties are
known. The polynomial fit was: ##EQU17## The correlation
coefficient, r, for this polynomial fit is 0.996.
The Monte Carlo method described here can be used to determine the
collection efficiency of an optical collection device with equal
delivery and collection areas, such as another transcutaneous
reflectance measurement device, or a catheter used for in vivo
fluorescence detection. In addition to information on the absolute
collection efficiency of an optical device, this method can be used
to derive information on the spectral distortion introduced by the
optical device due to different collection efficiencies at
different wavelengths. With modifications, the Monte Carlo model
can be used to determine the collection characteristics of devices
with more complex delivery and collection geometries.
3.5 Collection Efficiency With A Thin Superficial Absorbing Layer:
The Pigmented Epidermis Problem
The Monte Carlo method described above could simulate a multi-layer
tissue, as already explained. We wanted to use this feature to
study the effect a thin absorbing layer has on the optical patch
collection efficiency. This would simulate the epidermis in skin,
which has scattering properties similar to the underlying dermis,
but higher absorbing properties because of melanin. The thickness
of the epidermis is very small compared to the dermis (.apprxeq.50
.mu.m for the epidermis compared to .apprxeq.900 .mu.m for the
dermis). A two-layer Monte Carlo simulation in which the
superficial layer was very thin compared to the infinitely thick
underlying layer was used to simulate this.
3.5.1 Monte Carlo Thin Layer Simulation
A two layer Monte Carlo simulation was run in which the superficial
layer (layer 1) had a thickness of 0.1 effective scattering lengths
(See equation 3-20) and the underlying layer (layer 2) had a
thickness of 60 effective scattering lengths. Layers 1 and 2
simulate the epidermis, and in infinite dermis respectively. An
example of the output photon histories file for this model was
shown in Table; 3.1, and as it can be seen the pathlength traveled
by each photon in each layer, 1, and 2, was recorded independently
as L.sub.1 and L.sub.2. Using this model we are able to vary the
absorption coefficient in the epidermis and dermis independently by
assigning separate absorption coefficients, .mu..sub.a1 and
.mu..sub.a2, for layers 1 and 2. When the remission profile from
the two-layer model is calculated, Equation 3-25 is written as:
##EQU18## to accommodate the two absorption coefficients,
.mu..sub.a1 and .mu..sub.a2, the remission profiles are convolved
to find the collection efficiency, as described in subsection
3.4.5.
3.5.2 Results
The introduction of an absorbing layer has only a minimal effect of
the collection efficiency of the optical patch, and the collection
efficiency is still primarily determined by the optical properties
in the bulk tissue. This effect is illustrated in FIG. 16 which
shows the results of the Monte Carlo simulation in which absorption
in the epidermis can result in significant decreases in the total
reflection of the tissue, yet will only marginally increase the
collection efficiency of the optical patch. For comparison, FIG. 17
shows the effect absorber in the bulk tissue has on both the
reflection and the collection efficiency of the optical patch.
Therefore, one can conclude that the absorbance from the epidermis
has to be considered separately than diffuse absorbance present in
the rest of the tissue. The optical density of the epidermal
absorption can be subtracted linearly from the total optical
density of the skin, since the effect on R is linear.
Light is attenuated as it passes through the epidermis. The
reflectance from the skin can be expressed as the product of two
components, namely the reflectance of the dermis, R.sub.dermis, and
a term specifying the attenuation of light by the epidermis:
where the term exp(-.mu..sub.a.epidermis <L>.sub.epidermis),
describes the attenuation of light in the epidermis, and where
<L>.sub.epidermis is the average pathlength of photons in the
epidermis before remission. Therefore, the effect of absorption in
the epidermis on the reflection from the skin is much simpler to
describe mathematically than that of absorption in the dermis.
Equation 3-30 can be rewritten as:
FIG. 16 shows the relationship between the log of reflectance from
the skin and the epidermal absorption, as predicted by Monte Carlo
computer simulations. A similar relationship (not shown) exists
between the log of the reflectance measured with the optical patch,
f*M, and the epidermal absorption, since f does not vary
significantly with epidermal absorption. Since the relationship
between 1n(R) and .mu..sub.a epidermis is linear, Equations 3-30
and 3-31 appear to be good approximations of the relationships
between measured reflectance from the skin and the epidermal
absorption. The slope of the plot of 1n(R.sub.skin) vs .mu..sub.a
epidermis, shown in FIG. 16, is equal to <L>.sub.epidermis.
The average pathlength, <L>.sub.epidermis in the Monte Carlo
model shown in FIG. 16 is equal to 186.3 .mu.m, or about 3.72 time
the thickness of the epidermis.
3.6 Determining Absorbance From Measured Reflection
The collection efficiency, F*, of an optical patch with a fixed
geometry, has been shown in subsection 3.4 to be dependent in a
predictable manner on .mu..sub.a and .mu..sub.s '. The relationship
between f* and .mu..sub.a and .mu..sub.s ' is unique, such that for
any given .mu..sub.a and .mu..sub.s ' only one solution for F*
exists.
A unique relationship also exists between the true reflection, R,
and the ratio of .mu..sub.s ' to .mu..sub.a. The total reflection,
R, from a tissue as predicted by diffusion theory is given by
[Flock 1989]: ##EQU19## where a' is the reduced albedo
[a'=.mu..sub.s '/(.mu..sub.a +.mu..sub.s ')], and where ##EQU20##
where r.sub.int is the total internal reflectance due to the index
of refraction mismatch (air/skin) at the surface, and is
empirically related to the tissue refractive index, n:
Alternately, the total reflection from a tissue is predicted by
Monte Carlo computer simulations, and is equal to [Jacques 1989a]:
##EQU21## for a tissue refractive index of 1.37. In both equations,
t here is an assumption of a smooth air/tissue interface. The role
of skin surface roughness on r.sub.int is not yet investigated.
Diffusion theory and Monte Carlo calculations of total reflection
R, shown above in Equations 3-32, and 3-35, agree well for a wide
range of optical properties. The Monte Carlo equations are selected
for calculations since they are more accurate when the optical
properties have a low albedo and reflectance is less than 0.40.
Since, recalling Equation 3-12, ##EQU22## and both f and R are
predictable functions of .mu..sub.a and .mu..sub.s ', then M can
always be predicted from .mu..sub.a and .mu..sub.s ' for a given
standard. FIG. 18 illustrates this and shows the effect .mu..sub.a
has on the measured reflection M at 630 nm for three different
scattering coefficients.
The absorption coefficient, .mu..sub.a, can not be solved uniquely
by reduction of the above equations. However, if one knows M,
.mu..sub.s ', and the f.sub.standard R.sub.standard at which the
measurement was made, the absorption coefficient can be obtained by
implementation of an iterative procedure. This iterative procedure
is illustrated in FIG. 19, and is described below.
Referring to FIG. 19, the optical patch measurement, M, and the
reduced scattering coefficient, .mu..sub.s ', are known for the
tissue being measured. An initial starting value for .mu..sub.a is
guessed in block 126, and the value of f and R are calculated by
means of Equations 3-27 and 3-28, and Equations 3-32 and 3-33
respectively in block 127. The value of f* is determined by
dividing f by the value of f.sub.standard R.sub.standard at the
particular wavelength used. The negative log of the product f*R,
-log(f*R), is the predicted optical density and is compared to the
measured optical density, -log(M) in block 129. If -log(f*R) is
less than -log(M) as determined by block 131, then the value of
.mu..sub.a is increased slightly, an if -long(f*R) is greater than
-log(M), then .mu..sub.a is decreased, and the calculation of f*
and R are repeated. This procedure is repeated until the value of
-log(f*R) is equal to the measured, -log(M), within an assigned
tolerance, .epsilon.. This iterative procedure is implemented in
Section 5 to find the diffuse absorbance within a tissue from the
measured reflectance.
3.7 Conclusions
Total reflection can be measured by either collecting all the
reflected light, or collecting a constant fraction of the reflected
light by means of a distant detector. Practical biomedical devices
for measuring reflectance, such as the optical patch introduced in
chapter 1, collect only a fraction of the reflected light. This
collected fraction, f, is dependent on the optical properties of
the tissue, and therefore is also wavelength dependent. Correct
interpretation of measured reflectance spectra, M(.lambda.),
requires knowledge of f(.lambda.) to yield true reflectance spectra
R(.lambda.).
The efficiency of the optical patch was determined physically by
determining the true reflectance, R, and measured reflectance, M,
for a series of phantoms of known optical coefficients. The
collection efficiency of the optical patch was found to be
dependent on .delta./.mu..sub.t 'd.sup.2, where .delta. is the
penetration depth in the measured medium (Equation 3-17),
.mu..sub.t ' is the total attenuation coefficient (equation 3-18),
and d is the diameter of the optical patch.
Knowledge of the collection characteristics of the optical patch,
and the dependence of reflectance on the optical coefficients, can
be combined to determine the absorption coefficient within a tissue
of known scattering coefficients from reflectance measurements with
the optical patch.
Section 4
Considerations Of Skin Variation
4.1 Introduction
In Section 3 the importance of optical properties and of
measurement device geometry for the interpretation of reflectance
signals were discussed. If the optical properties of a tissue, the
measurement device geometry, the architecture of structures within
the skin, and the relative amounts of different absorbers were
fixed, then reflectance spectroscopy algorithms could theoretically
be developed empirically without attention to the light transport
in tissue. Such analysis has been applied to determine the
bilirubin concentration in neonares, and has performed well when
measurements were conducted on specific very homogeneous
populations but perform poorly with heterogeneous populations
[Yamanuchi 1980, Hegyi 1981, Hannemann 1982, Kenny 1984]. The
potential success of such techniques are limited due to the
variation in skin optical properties and possibly due to variation
in the location of different absorbers in the skin. For example,
the melanin content, the depth of the blood plexus beneath the
surface, and the scattering properties of the skin may vary between
subjects. The predominant absorbers in the skin are present in
different layers. The melanin is present in the epidermis, the
topmost layer of the skin. The blood is predominantly present in
the dermal blood plexi. The bilirubin originates in the blood
plexus, but seeps into the dermis, and is also taken up by the
epidermis [Kapoor 1973]. The absorbers in the different layers,
namely diffuse absorbers in the dermis, blood in the blood plexi,
and melanin in the epidermis, may have to be considered separately
since their effect on the measured reflectance will vary with their
depth in the skin.
Consideration of the skin architecture, the possible variations in
optical properties between individuals, and the effect these
variations will have on the reflectance measurements, will enable
development of algorithms that fundamentally are designed to
determine the absorption of bilirubin in heterogeneous populations.
Blood depth, skin thickness, epidermal absorption, and skin
maturity can vary between subjects. To determine the importance of
these potential sources of variation on the measured reflectance,
they are considered individually in this section.
4.2 Variation In Maturity
In section 3, a significant linear relationship between scattering
properties of the skin and gestational maturity was reported at all
visible wavelengths. This relationship implies that the measured
reflectance will increase with maturity, given that absorption does
not vary significantly. The reflection of blue, green, and red
light from neonatal skin has been reported to increase with the
gestational age of the neonate [Krauss 1976, Ballowitz 1970]. This
relationship was reported to hold for neonares of both races up to
32 weeks gestation, and continued to hold within each racial group
(black/white) thereafter until term. Changes in reflectance after
birth were not studied. Colored filters were used to select the
light color. Melanin absorbs light throughout the visible spectrum,
and so the observed differences in reflectance between racial
groups is due to the melanin. The increase in reflectance with
gestational age within each racial group, presumably is due to the
increase in scattering properties with gestational maturity (see
Section 2.3, 2.3). For the purpose of analysis of the reflected
spectra, where one needs to know the scattering properties of the
measured skin, it is imperative that variations in the scattering
properties of a neonate's skin can be determined regardless of the
amount of melanin pigmentation.
The measured optical density of the skin, OD, between 650 and 750
nm can be extrapolated to 837 nm, OD.sub.837. OD is defined as:
The extrapolated dermal reflection at 837 nm, R.sub.837, can be
calculated from OD.sub.837 as:
This extrapolated value, f*R.sub.837, is invariant with the melanin
pigmentation in human skin. Therefore, R.sub.837 is dependent only
on the scattering properties of the skin, and the relative maturity
of the skin can be determined from the optical density spectra of
variably pigmented subjects. The scattering at any wavelength of
interest can then be estimated since the scattering spectrum of
neonatal skin is known for varying gestational maturities (see
Section 2). The changes in scattering coefficient versus wavelength
for neonates of different gestational maturities due to changes in
the sizes of collagen fiber bundles are accounted for by use of the
empirical equations of .mu..sub.s '(.lambda.) as a function of
maturity (eqs. 2-5, 2-6, and 2-7).
4.2.1 Observed Variability In Maturity
FIG. 20 shows f*R.sub.837 measured on the abdomen of 48 newborn
infants versus their gestational age. The gestational age was
determined conventionally by dates, or by the modified Dubowitz
criteria when maternal dates were unreliable [Kirkpatrick 1983]. As
discussed in section 3, the reflectance of tissue is dependent on
the ratio of .mu..sub.s ' to .mu..sub.a [Wilson 1990]. In the
operative range between 20% and 70% reflectance, the following
linear relationship can be used to approximate reflectance from a
material with optical coefficients .mu..sub.a and .mu..sub.s '. In
Equations 4-2 through 4-4 C.sub.0, C.sub.1, C.sub.2, and C.sub.3
stand for constants. ##EQU23## where C.sub.O =-0.5, and C.sub.1
=0.375 (based on approximations of Equations 3.32 and 3.35).
The scattering coefficient of neonatal skin at all wavelengths
increases linearly with gestational age, (see FIG. 4), and can be
expressed as:
where C.sub.2 .apprxeq.0.47 cm.sup.-1 /week of gestational age.
Therefore the extrapolated measurement, f*R.sub.837, can be
expected to increase with the logarithm of gestational age:
where C.sub.3 =C.sub.1 log C.sub.2 -C.sub.1 log .mu..sub.a
+C.sub.O. The collection efficiency of the optical patch of skin
relative to teflon, f*, at 837 nm is about 5.7 (measured on human
skin in a method similar to that explained in Subsection 3.3), and
.mu..sub.a at 837 nm is believed to be in the range of 0.25
cm.sup.-1, based on extrapolation of FIG. 5. Placing the
approximate values in all the constants above, C0, C1, C2, and f*,
the extrapolated reflection at 837 nm can be approximated as:
This relationship is also shown in FIG. 20. From the above
calculations, we find that it is reasonable to expect a logarithmic
relationship between maturity and f*R837. Therefore, we chose to
fit the available data with a logarithmic fit (r=0.79, p<0.001),
also shown in FIG. 20:
The above relationship may be used to supplement existing tests to
determine the gestational age, or level of maturity, of newborn
infants. FIG. 20 also shows the typical error in the reflectance
measurement, and the uncertainty with which the gestational age of
the infant is known before comparison with reflectance
measurements. This shows that the error in the measurement is small
relative to the gestational age uncertainty evaluated by
conventional means. The error in clinical assessment could possibly
account for the dispersion of data in FIG. 20. The actual variation
in f*R versus age is not yet known, since clinical age assessment
is only an estimate. The reflectance measurements can provide a
subjective evaluation of gestational maturity that is not
vulnerable to objective evaluation by the user. FIG. 21 shows the
distribution of extrapolated f-R.sub.837 values measured on a group
of neonates in the intensive care unit (gestational age range:
24-42 weeks), and also measured on a group of adults. As seen in
the figure, the adult population appear to have higher extrapolated
f*R.sub.837 values than does the neonatal population.
4.2.2 Changes In Reflectance With Added Absorber
Changes in the maturity of the skin being measured will have an
effect on the interpretation of the reflected spectra when
attempting to analyze the absorption within the skin. Differences
in the scattering of the skin will result in a change in the
underlying dermal reflectance as explained above, but more
importantly, will alter the change in reflection, .DELTA.R, due to
the addition of absorber, .DELTA..mu..sub.a, within the skin [Saidi
1990]. Scattering affects the pathlength of photons in skin, which
in turn affect the relationship between .DELTA..mu..sub.a and
.DELTA.R. Therefore knowledge of skin optics is important in order
to interpret the observed changes in reflectance in terms of
.DELTA..mu..sub.a due to bilirubin or blood. We can determine how
the optical density changes, .DELTA.O.D., due to changes in
.DELTA..mu..sub.a, and how this relationship is dependent on the
background optical properties. Consequently, we determine the
uncertainty with which we interpret changes in O.D. due to
uncertainty in our knowledge of background .mu..sub.a and
.mu..sub.s '.
The reflection measured at the skin surface can be expressed
as:
where .mu..sub.a is the absorption coefficient within the tissue,
and L.sub.eff is defined as the effective pathlength of the
reflected photons [Saidi 1990, Jacques 1989]. Optical density,
(O.D.=-log.sub.10 [R]), is therefore: ##EQU24##
It is important to note that L.sub.eff is not equal to <L>,
the arithmetic mean of the pathlengths of emitted photons in the
tissue. Changes in the optical density, .DELTA.O.D., seen with
changes in absorption, .DELTA..mu..sub.a, are: ##EQU25##
Therefore the changes seen in skin optical density due to the
addition of bilirubin has to be interpreted in the context of the
L.sub.eff operative in the tissue measured. The effective
pathlength, as shown in FIG. 22, was found to be directly dependent
on the penetration depth of light in the tissue, and so is
dependent on both .mu..sub.a and .mu..sub.s '. The penetration
depth, .delta., of light in tissue was defined in Equation 2-4.
FIG. 22 was generated by diffusion theory calculations of R,
(Equation 3-32), for various .mu..sub.a and .mu..sub.s ', and by
calculation of L.sub.eff (by Equations 4-5, and 2-4). The linear
fit of the data shown in FIG. 22 relating L.sub.eff to .delta.
is:
The coefficient of regression, R, is 0.996, and both L.sub.eff, and
.delta. refer to distances, and are expressed here in units of
centimeters. The relationship discovered above can be approximated
as:
and based on these observations, one can approximate the
reflectance, R, to be dependent on the .mu..sub.a and .delta.
as:
Substitution of Equations 2-4 and 4-9 into Equation 4-7 and
differentiating to the limit as .DELTA..mu..sub.a approaches zero,
and then as .DELTA..mu..sub.s ' approaches zero, one obtains:
##EQU26##
These expressions indicate the sensitivity of O.D. due to
uncertainty in .mu..sub.a and .mu..sub.s '. From Equation 4-11, one
learns that the change in optical density due to addition of
absorber into a medium is dependent on both the .mu..sub.a and
.mu..sub.s ' in the tissue. Therefore, the addition of absorber
into a tissue with one set of optical properties will not yield the
same optical density change as the addition of absorber into
another tissue with different absorption or scattering
coefficients. FIG. 23 shows the change in optical density due to
the addition of unit absorption, as a function of the absorption
and scattering coefficients in the tissue. In the normal range of
optical properties in tissues, the change in optical density of a
tissue due to the addition of absorption will decrease as the
absorption and scattering coefficients of the tissue increase.
Therefore, for example, a skin sample highly perfused with blood
will show a smaller change in optical density due to the addition
of bilirubin, than will a skin sample with little blood, and the
baseline skin optical properties are very important for analyzing
observed optical density changes. This phenomena is illustrated
further in section 5.
Equations 4-11, and 4-12, are also useful for appreciating some of
the uncertainty with which the optical density is predicted due to
uncertainty in the absorption or scattering coefficients in the
tissue. For example typical optical properties in the skin of a
jaundiced neonate at 460 nm are 3 cm.sup.-1 and 40 cm.sup.-1 for
.mu..sub.a and .mu..sub.s ' respectively, and the uncertainty in
these two values are 0.3 cm.sup.-1 and 6 cm.sup.-1. The resulting
uncertainties in the optical density due the uncertainties in
absorption and scattering coefficients are (calculated by Equations
4-11, and 4-12): ##EQU27##
Therefore, uncertainty in both absorption and scattering are
important in leading to uncertainty in predicting the background
optical density of the skin. Interpretation of O.D. Spectra in
terms of bilirubin or blood content are equally affected by
uncertainty in the background skin optical properties of .mu..sub.a
and .mu..sub.s '.
4.3 Variation In Melanin
Melanin pigmentation of the skin is what differentiates skin color
between individuals. The melanin absorption spectra extends
throughout the visible region, and the profile exhibits decreasing
absorption from the blue to the red wavelengths [Jacques 1991,
Kollias 1987, Blois 1966]. The melanin is usually present only in
the epidermis, (see Section 1), and has to be considered separately
from other absorbers that are located in the blood layer or the
dermis. Melanin is an important absorber to be considered in
transcutaneous bilirubinometry since melanin in the epidermis can
lower the measured reflectance significantly.
The reflectance of skin has been found to differ markedly between
neonates of different races after 32 weeks of gestational age
[Krauss 1976]. This difference is due to differences in their
melanin pigmentation. In 48 neonates that we have measured in which
the gestational age varied from 24 to 42 weeks, the reflectance in
the red (650 nm) was found to vary significantly between infants of
different ages after about 33 weeks gestational age.
4.3.1 The Absorption Spectrum Of Melanin
There are some differences in the reported absorption spectra of
melanin [Jacques 1991, Rosen 1990, Kollias 1985, Blois 1966]. Some
of the differences in the reported spectra have been attributed to
different molecular forms of melanin. As discussed in section 3,
melanin pigmentation essentially does not affect the collection
efficiency of the optical patch, f*, since the melanin is usually
present only in the epidermis. Therefore the collection efficiency
of the optical patch can be factored out when attempting to
characterize the melanin absorption spectra by reflectance
spectroscopy of pigmented versus unpigmented sites. The following
equations illustrate how the collection efficiency factor, f*, can
be factored out when measuring the change in optical density due to
melanin, .DELTA.OD.sub.melanin, when comparing the reflection of a
pigmented skin site, R.sub.pig., to that of a non-pigmented skin
site (e.g. vitiligo), R.sub.vit. as seen in the following
equations. ##EQU28##
With the spectrophotometer and optical patch, the optical density
spectra of the dorsal and ventral aspect of the forearm of 17
adults were measured. The dorsal and ventral aspects are
differentially pigmented, and differences in the spectra are
attributed to differences in melanin pigmentation. Five of the 17
spectra were discarded because of visible influence of blood on the
reflectance spectra. This can occur where there is a higher blood
concentration in one aspect of the forearm than the other. The
.DELTA.OD.sub.melanin was calculated using Equation 4-14c.
The average of the melanin absorption spectra measured is shown in
FIG. 24. This spectra correlates well to other measurements of the
melanin spectra reported in the literature [Kolias 1985, Blois
1966]. The melanin absorption spectra was found to essentially
decrease linearly with wavelength in the visible region. Since the
melanin absorption shown varies across the visible spectra in order
of magnitudes, variation in the pigmentation will cause large
absolute changes in the absorption at shorter wavelengths, but the
same magnitude changes will cause relatively minuscule absolute
changes in the very long wavelengths (>800). The melanin
pigmentation measured in the far red wavelength range (650-750 nm)
appears to have a pivot point at around 837 nm. This is in
agreement with observations on melanin pigmentation reported in the
literature [Kolias 1985] from the absorption spectrum of various
concentrations of Dopa-Melanin. Kolias went on to show that the
melanin absorption spectra between 620 and 720 nm, measured in vivo
as discussed, can be expressed as: ##EQU29## where c is a scalar
that is related to the concentration of melanin in the skin and
.lambda. is the wavelength in nm. From the above equation it is
determined that extrapolation of the in vivo melanin absorption
spectra will appear as zero absorption at around 840 nm.
The melanin spectrum in neonates was also measured. The measured
optical density spectra from seventeen neonates were subtracted
from the spectra measured on neonates with higher melanin
pigmentation. The difference between these spectra is due to
melanin. The difference in maturity in the neonate pairs was
removed by subtraction of the extrapolated optical density at 837
nm, OD.sub.837, from the entire melanin spectrum. The extrapolated
value at 837 nm for each of the melanin spectra measured was
therefore equal to zero. The melanin optical density spectra were
then all normalized to unity at 650 nm, and averaged. FIG. 25 shows
the neonates' melanin optical density spectra measured in this way,
and the average of these spectra. It can be seen that below about
600 nm, there is a wide variability in the measured melanin optical
density, due to variations in the blood content in the skin of the
neonate pairs measured. These variations are expected to average to
zero, and the average melanin spectrum, shown in bold, is a good
representation of the optical density difference due to
melanin.
The melanin spectrum measured on neonates, shown in FIG. 25,
increases more gradually at lower wavelengths than the melanin
spectrum measured on adults, shown in FIG. 25. The reason for this
difference in the absorbance spectra is not clear, but may be due
to the fact that neonates have not been subjected to actinic damage
to the skin that occurs with age.
4.3.2 Measurement Of The Melanin Content In Skin
Based on the above observations, the melanin pigmentation has been
reported to be determined by the slope of the optical density
spectra between 650 and 750 nm [Kolias 1985, Rosen 1990]. FIG. 26
shows the melanin content of 47 neonates and 19 adults measured in
this manner. There does not appear to be a significant variation in
the melanin pigmentation between neonates and adults.
The slope of the optical density spectra is expected to vary with
the nature of the scattering coefficient of a tissue to wavelength
(see Section 3). When the collagen fiber bundles in the dermis are
smaller on average (such as in a less mature infant), the
scattering coefficient is expected to fall off more rapidly with
increasing wavelength compared to an older neonate with larger
collagen fibers. This more rapid decrease in scattering will cause
the reflectance spectrum to also fall more rapidly, and so lower
the magnitude of the slope of the optical density spectrum
regardless of the pigmentation. This will alter the pigmentation
determinations that are performed by measuring the slope only.
An alternate method to determine the melanin concentration in skin
that is not sensitive to the maturity of the skin is to determine
the difference between the expected reflectance and the true
reflectance at 650 nm. The expected reflectance, R.sub.expected, of
the dermis at 650 nm can be calculated since the value of the
650-nm absorption coefficient of skin has been measured, and the
650-nm scattering coefficient of skin is known for any given
maturity. The maturity is determined by extrapolation to 837 nm as
explained in Subsection 4.2. The blood and bilirubin are not
significant absorbers at 650 nm, and so they are not expected to
significantly influence the reflectance of the skin at that
wavelength. The collection efficiency of the optical patch can also
be calculated at 650 nm, since both the absorption and the
scattering coefficients are known. The difference between expected
optical density, (-log(f* R.sub.expected)), and the measured
optical density (-log(M)), is due only to the melanin absorption at
650 nm. This method of measuring the melanin content is employed in
the algorithm to determine the cutaneous bilirubin content
developed in section 5.
The expected reflection at 650 nm, R.sub.expected (650), can be
calculated by Equation 3-35 where the absorption coefficient at 650
nm is equal to 0.55 (from FIG. 5 and Equation 2-9). From equations
2-5 through 2-7, the expression for the scattering coefficient at
650 nm can be expressed as:
where the maturity is specified in weeks, and Yint and m are
specified by Equations 2-6 and 2-7.
The difference between the measured optical density, -log(M), and
the calculated optical density, -log(f*R.sub.expected) , is
therefore equal to the melanin optical density, OD.sub.melanin
:
4.4 Variation In Blood Content And Depth
4.4.1 Blood Supply Of The Skin
The dermis is nutritionally supplied by an irregular network of
blood vessels. The blood vessels in the skin are usually in great
excess relative to the requirements of the tissue they serve,
partially because of the cutaneous vessels' function as thermal
regulators. Irregularity is the rule for these blood vessels in the
skin, yet they tend to be distributed in both superficial and deep
plexi. These two plexi have been shown to be interconnected, and
are both part of the total cutaneous network that also supplies the
hypodermis, the fatty collagenous layer below the dermis [Montagna
1974, Winkelmann 1961]. Other smaller plexi between the superficial
and deep plexi, including the second and third venous plexi, ensure
that the blood has continuous distribution throughout the skin
[Lewis 1927].
4.4.2 Variation In Blood Content
The amount of blood present in the skin can vary between infants,
site of measurement, and current physiological state of the infant.
To determine how variation in blood content affects the reflectance
from the skin, the blood in the skin was modeled to be present only
in the papillary dermis as a plexus. The depth of the papillary
plexus was varied in the model between 50 and 500 .mu.m, and the
blood content in the papillary plexus was varied between 5% and 15%
of the plexus volume. Monte Carlo simulations (See Section 3 for
introduction) were used to study the reflectance measured at the
skin surface due to the variation in the blood content and depth in
30-week mature skin (see Subsection 4.2). Three wavelengths
(420,460 and 585 nm) were modeled.
The quantity of blood was found to increase the optical density
measured at the skin surface at all three wavelengths. At 585 nm,
blood is the only significant variable absorber in the dermis, and
so the relationship between 585-nm optical density and blood
quantity can be used to determine the blood content of the skin.
FIG. 27 shows the cutaneous blood concentration measured on 47
neonates in the intensive care unit. The method by which the
cutaneous blood concentration is determined from the measured
reflectance is explained in Section 5.
4.4.3 Variation In Effective Depth Of The Blood
The blood in the skin is not truly localized in a 50-.mu.m
papillary plexus, however there may be variations in the average
depth of the blood beneath the surface. A Monte Carlo model was
used to study if any variations in the blood depth, within an
expected range, will influence the optical measurements performed
at the skin surface. Because shorter wavelengths have shallower
penetration depth than longer wavelength, the optical density
observed with blue light will vary more strongly with changes in
the depth of the blood layer than will the optical density observed
with red light. The effect of depth on the observed optical density
diminishes with longer wavelengths as the penetration depth
increases.
To determine the importance of the depth of the blood below the
skin surface, the blood in the skin was modeled, and the resulting
reflection calculated by Monte Carlo computer simulations, as
explained in section 4.4.2.
FIG. 28 shows the predicted optical density, defined as -log.sub.10
(R), at 420, 460 and 585 nm versus the depth of the papillary
plexus beneath the skin surface. The results shown are for 5% blood
content by volume in the papillary dermis. As can be seen from this
figure, the depth of the blood appears to have an important effect
on the observed optical density of 420-nm light, however, the depth
of the blood does not appear to have a strong effect on the optical
density observed at either 460 or 585 nm. This implies that there
will not be significant variation in the optical density at 460 or
585 nm due to variation in the blood depth. The details of vascular
structure are not expected to affect deduction of blood volume from
the optical density spectra. FIG. 29 shows the ratio of optical
density at 420 relative to that at 585 nm, as a function of
papillary plexus depth. The ratio is obtained by dividing the
optical density predicted by Monte Carlo for 420-nm light, by the
optical density predicted for 585-nm light.
FIG. 30 shows the distribution of the ratio of optical density at
420 nm relative to that at 585 nm, measured on 47 neonates. As can
be inferred from FIG. 28, a typical ratio of 1.2 between OD420 and
OD585 corresponds to an average blood depth of 250 .mu.m beneath
the surface of the skin.
4.4.4 Conclusions
Based on these observation, one can conclude that the optical
densities of the skin at 460 and 585 nm are proportional to blood
content and insensitive to its location in the skin. This fact
makes analysis of reflectance spectra easier since the blood
content can be calculated at 585 nm irrespective of papillary plexi
location, and the total bilirubin content in the skin can be
determined from the measured reflectance despite any spatial
variation that may exist in its distribution within the skin.
4.5 Variation In Skin Thickness
The thickness of adult skin is reported in the literature to vary
according to subject and site, with the mean values reported
between 0.9 and 1.3 nun [Alexander, 1979]. The twenty neonatal post
mortem skin samples obtained for in vitro optical property
measurements had a mean thickness of 888 .mu.m, and a standard
deviation of 301 .mu.m (Section 2). The thickness of these skin
samples was found to have only a weak correlation with gestational
age of the neonate, as seen in FIG. 31. This relationship is:
where maturity is expressed in weeks.
The layer below the dermis is called the hypodermis, and is
composed primarily of collagen fibers and fat cells [Millington
1983]. It is a deep extension of the dermis, and collagen fibers
connect the two layers. The hypodermis also contains special nerve
endings that service the skin, and a sub-dermal plexus of blood
vessels.
Variability in the thickness of the skin can lead to variation in
the reflectance spectra measured at the skin surface. This problem
is of concern primarily at longer wavelengths and for less mature
neonates, where the optical depth of the skin is small. The effect
of skin thickness on the reflected light measured with the optical
patch is analyzed in Appendix C.
The thickness of the skin is found in Appendix C to present a
potential source of error in the reflectance spectra measurements
at the skin surface. Variation in the skin thickness may alter the
reflectance measurements in the 650-750 nm range by about 3%, which
in turn will affect the interpretation of the skin maturity.
Variation in the skin thickness will play a smaller role in
readings in the 400-600 nm range where blood and bilirubin absorb.
The existence of a hypodermis consisting of collagen fibers and fat
beneath the dermis, and measurement of the reflectance with an
optical patch rather than measurement of total reflectance, will
both decrease the effect skin thickness has on the measured
reflectance. Light that has penetrated deeply into the skin has a
higher probability of being diffusely reflected outside the optical
patch collection area than shallow penetrating light. Measurement
of the reflectance with smaller diameter optical patches restricts
the depth sensitivity of the probe and will reduce the error
introduced because of skin sample thickness.
4.6 Variation In Cutaneous Bilirubin
Bilirubin "staining" of skin is the foremost sign of jaundice.
Elevated levels of bilirubin in the serum are translated into
extravascular cutaneous deposition of the bilirubin pigment in the
dermis and epidermis [Turkel 1990, Kapoor 1973]. The relationship
between vascular and cutaneous bilirubin, and the kinetics of
transfer between the two compartments are not well understood. The
ratio of serum bilirubin and cutaneous bilirubin appears to be
affected by a multitude of factors including exchange transfusion,
phototherapy, measurement site, diet, serum albumin concentration,
pH, and gestational and chronological age [Rubaltelli 1971, Hegyi
1986, Hegyi 1983, Schumacher 1990, Engel 1982, Knudsen 1989]. The
equilibrium between serum and cutaneous bilirubin values is
perturbed when there are rapid changes in the bilirubin
concentration in either the skin, such as during phototherapy, or
in the serum, such as after exchange transfusion. As a result of
these factors that disrupt the equilibrium between serum and
cutaneous bilirubin and the variables that affect the kinetics of
transfer of bilirubin into the skin, one expects the correlation
between cutaneous and serum bilirubin readings to be less than
perfect. Serum bilirubin, however, is currently accepted clinically
as the standard method used to quantify the level of jaundice.
FIG. 32 shows a sample distribution of the bilirubin concentration
in the skin of 47 neonates measured in the neonatal intensive care
unit. Some of these neonates were jaundiced. The method employed to
determine the cutaneous bilirubin concentration is explained in
Section 5.
4.7 Conclusions
The increase in scattering properties of neonatal skin with
gestational maturity causes a decrease in the optical density at
837 nm, extrapolated from the measured optical density between 650
and 750 nm. This relationship is used to predict the maturity of in
vivo skin samples. Variation in both the absorption and scattering
coefficient in the dermis will change the sensitivity of optical
density, dOD/d.mu..sub.a, observed due to the addition of absorber,
.DELTA..mu..sub.a, for example bilirubin or blood. This means that
observed changes in the optical density can not be translated to
changes in the bilirubin or blood content in the skin without
analysis of the operative optical properties in the tissue.
The melanin spectra has been measured in vivo, by determining the
.DELTA.O.D for dorsal versus ventral forearm, and by measuring the
.DELTA.OD between variable pigmented neonates. The amount of
melanin in the epidermis can be determined at 650 nm, where there
is negligible absorption due to blood or bilirubin.
Blood is seen histologically to be present in the dermis in a
collection of plexi that are interconnected. Monte Carlo
simulations of light reflection from neonatal skin reveal that the
depth of the blood beneath the surface does not affect the
reflectance of 460-nm or 585-nm light. The reflection of 420-nm
light, however, significantly increases with increasing depth of
the blood vessels beneath the surface. Therefore, based on
histological evidence and the Monte Carlo results, the blood and
bilirubin can be modelled to be diffusely distributed throughout
the dermis.
Monte Carlo simulations indicate that a decrease in the thickness
of the skin lowers the measured reflectance spectrum. The effect
that the skin thickness has on the measured reflectance is
diminished by the fact that the hypodermis, the layer underlying
the dermis, is composed primarily of collagen and fat cells and is
expected to have a high reflectance value. Furthermore, light that
has penetrated deeply into the skin has a higher probability of
being diffusely reflected outside the optical patch collection area
than shallow penetrating light. However, variation in skin
thickness can still be a source of error in determinations of the
skin maturity from the reflectance spectra. Appendix C treats this
problem, and estimates the error.
Bilirubin in the blood stains the epidermis, and there is expected
to be an equilibrium between serum concentrations and cutaneous
bilirubin concentrations. The correlation between serum and
cutaneous bilirubin is expected to be less than perfect and the
equilibrium is affected by several factors, such as blood pH,
albumin concentration, and phototherapy status of the neonate. The
cutaneous bilirubin is considered to be diffuse throughout the
dermis in the model of jaundiced neonatal skin.
Section 5
Determining Cutaneous Billrubin From Reflectance Measurements
5.1 Introduction
As discussed in Section 4, serum bilirubin levels are not expected
to correlate perfectly with cutaneous bilirubin concentrations. The
relationship between the two is influenced by blood pH, albumin
concentration, phototherapy status, and other physiological
parameters. Nevertheless, this invention measures cutaneous
bilirubin in a manner that is independent of skin optics. To
correctly determine the cutaneous bilirubin concentration, one has
to interpret the reflectance with consideration of the variation in
scattering properties of the tissue, and the non-linearity of the
changes in bilirubin with addition of absorption.
In Subsection 5.2, a Monte Carlo model of skin was devised in which
the cutaneous bilirubin concentration was varied in skin of three
different gestational maturities. The reflectance predicted by the
Monte Carlo calculations were analyzed by iterating to find the
absorption coefficient in the skin, as explained in Section 3. This
method of calculating the absorption coefficient which is then
related to the cutaneous bilirubin concentration is compared to the
traditional method in which the optical density is related to the
cutaneous bilirubin concentration.
In Subsection 5.3 the method to determine absorption from a tissue
with known scattering properties, are combined with the model of
skin, and the considerations discussed in Section 4, to develop an
algorithm to determine the cutaneous bilirubin concentration from
optical patch reflectance measurements in accordance with the
present invention. In Subsection 5.4, this algorithm is applied to
measurements performed on neonates, and the algorithm is refined in
Subsection 5.5, based on serum bilirubin values, since that is the
only reference available for the degree of jaundice. In Subsection
5.6, the potential errors in our cutaneous bilirubin determinations
are estimated.
5.2 Monte Carlo Model Of Cutaneous Billrubin
To test the fundamental ability to determine the concentration of
an absorber in skin with different scattering properties, a Monte
Carlo model was used to simulate variably scattering skin with
specified concentrations of uniformly distributed bilirubin in the
dermis. The Monte Carlo model predicts the reflectance from tissues
in which the absorption and scattering coefficients are precisely
known. This model was used to determine whether, and by what kind
of analysis, we can predict the absorption in a tissue with known
scattering properties.
In an in vivo population, a number of variables in the properties
of the skin can vary between patients. For example, blood
concentration, melanin concentration, and the scattering
coefficient in the infant's skin may not be precisely known.
Furthermore the concentration of the cutaneous bilirubin
concentration is not precisely known, since serum concentrations
are measured, and the relationship between serum and cutaneous
concentrations are not fully understood as discussed in Subsection
4.5. With a Monte Carlo model of the skin, however, all the
variables can be controlled while the bilirubin concentration is
varied.
The Monte Carlo model is used to determine if the absorption
coefficient in a tissue can be determined from the reflectance,
once the scattering of the tissue is known. Once verified with the
Monte Carlo model, the algorithms developed based on radiative
transport theory can then be applied to in vivo measurements.
5.2.1 Monte Carlo Simulations
The Monte Carlo model simulated skin in which the scattering
corresponded to 20, 30, and 40 weeks gestational maturity. The
blood was simulated as occupying 5% of a 50-.mu.m thick papillary
plexus layer at 150 .mu.m below the skin surface. This model was
explained in Subsection 4.4. The bilirubin was simulated to be
uniformly distributed throughout the skin. No melanin was included
in the model. The values chosen for the cutaneous bilirubin
concentrations approximate the range of concentrations reached in
skin under normal and jaundiced conditions [Rubaltelli 1971]. The
cutaneous bilirubin concentrations used in the Monte Carlo
simulations, the corresponding absorption values at 460 nm, due to
bilirubin, and the resulting reflectance values predicted by the
Monte Carlo simulations at 460 nm are shown in Table 5.1.
TABLE 5.1 ______________________________________ Skin Maturity
Bilirubin (weeks) Concentration .mu..sub.a at 460 nm 20 30 40
(mg/100 g) (cm.sup.-1) Reflectance
______________________________________ 0 0 0.177 0.182 0.250 1.27
3.25 0.114 0.122 0.168 2.54 6.50 0.076 0.095 0.137 3.81 9.75 0.057
0.081 0.113 5.08 13.0 0.049 0.064 0.095
______________________________________
5.2.2 Analysis By Optical Density Method
The reflectance values predicted by the Monte Carlo simulations
described above emphasize the importance of taking the scattering
of the tissue and radiative transport theory into consideration for
correct analysis of the reflectance spectra. FIG. 33 shows the
optical density at 460 nm as a function of the cutaneous bilirubin
concentration for the three skin maturities tested. The optical
density is equal to -log.sub.10 (R), where R is the reflectance
predicted by the Monte Carlo simulations. The optical densities are
shown to increase with added bilirubin in a nonlinear manner.
Moreover, the relationship between optical density and added
bilirubin varies with the maturity of the skin. (How
(dOD/d.mu..sub.a).DELTA..mu..sub.a bili varies with variable
scattering is discussed in Section 4.2). Simple subtraction of a
baseline optical density measured at another wavelength will not
solve this problem since .DELTA.OD/.DELTA..mu..sub.a is still
variable with maturity. Furthermore, additional absorption due to
another pigment, such as blood, will affect the change in optical
density due to bilirubin absorption.
5.2.3 Analysis By Determining The Tissue Absorption Coefficient
Since direct analysis of the reflectance, or -log(R), can not be
applied to accurately determine the absorption in a tissue,
radiative transport theory can be used as explained in Section 3.
The equations relating absorption within the tissue and scattering
are iterated with the known scattering fixed and the absorption
adjusted until a solution for the measured reflectance is reached.
This method was introduced and explained in Subsection 3.6. FIG. 34
shows the total absorption predicted in this manner at 460 nm for
the Monte Carlo reflectance results as the bilirubin concentration
is varied in the skin. If FIG. 34 is compared to FIG. 33, the
absorption can be seen to be calculated much more reliably if
knowledge of the scattering coefficients of the tissue is utilized,
and the change in optical density with added absorber is not
assumed to be constant.
5.2.4 Conclusions
The Monte Carlo model illustrates what is required to correctly
determine the average bilirubin concentration in the tissue, and
why simpler analysis of the optical density changes in tissue due
to added absorption do not give predictable results. The variation
in such analysis is due to (i) variation in the scattering
properties of the measured tissue, and (ii) variation in
(dOD/d.mu..sub.a).DELTA..mu..sub.a bili when the quantity of other
absorbers (e.g. blood) are variable. Furthermore, the relationship
between changes in optical density, and absorption in the tissue is
not linear. Therefore, linear regression analyses to correlate the
bilirubin concentration in newborn infants to cutaneous optical
density changes will not give good correlations in populations in
which the skin scattering properties, or skin blood concentration
vary.
Finally, transcutaneous reflectance spectra are often measured with
an optical device, such as an optical patch, in which not all the
reflected light is collected [Kopola 1990, Hegyi 1983, Hannemann
1978, Krauss 1976]. The collection efficiency, f*, of the optical
patch is partially dependent on the scattering of the tissue (see
Section 3). Variation in the f* will accentuate the differences in
measured reflectance from skin of different scattering properties.
FIG. 35 summarizes the correct considerations required to determine
the concentration of an absorber in a tissue from measurement of
the reflectance spectra. The fundamental errors in interpretation
of the measured spectra by means of direct analyses of the optical
density measurements are also presented again in this figure.
5.3 Algorithm To Determine The Cutaneous Billrubin
The Monte Carlo model in Subsection 5.2 illustrates the best method
to determine the total absorption coefficient of a tissue from the
reflectance measurements. In Section 3, a method was developed to
determine the absorption coefficient within a tissue of known
scattering properties. In Section 2, the scattering coefficient and
basal absorption coefficient of neonatal skin were determined. In
Section 4, the various sources of variability and their effects on
measured reflectance were discussed individually. These
considerations are combined in this section to derive an algorithm
that can be applied on neonatal skin to determine the cutaneous
bilirubin concentration. This algorithm will be applied on the
neonates measured in vivo, and the results correlated to serum
levels measured.
The basic purpose of the algorithm of the present invention is to
deduce the absorption due to bilirubin from reflected blue light.
However, other tissue components also absorb in the blue light
spectrum, including skin, melanin and blood. According to the
present invention, reflectance at other wavelenghts is used to
specify the maturity-dependent optical properties of skin, the
amount of melanin, and the amount of blood in the skin. Once the
optical absorption of skin, melanin or blood is known at one
wavelength, its contribution to blue light reflectance can be
predicted and subtracted from the total absorption of blue light,
to yield the absorption due to bilirubin alone. From this quantity,
an average concentration of bilirubin in the skin can be
determined.
The wavelengths of reflectance measurements that are specified for
use in this disclosure have been chosen for the reasons articulated
in the following paragraphs. However, it will be understood that in
general the entire reflectance spectrum from 350-800 nm may be used
by the present invention.
To specify the gestational maturity of the skin under test,
reflectance measurements are taken in the red to infrared light
spectrum, for example, in the range of 650-800 nm. These
measurements are then extrapolated to 837 nm to specify the
reflectance at 837 nm, which is related to the gestational maturity
of the neonatal skin. Once the maturity of the skin is established,
the maturity-dependent optical properties are specified (using
equations 2-5 to 2-9). These equations yield the absorption,
.mu..sub.a (.lambda.), and scattering, .mu..sub.s,(.lambda.), as a
function of wavelength, .lambda. for use by the other portions of
the algorithm.
To detect melanin content in the skin, the reflectance, M, of red
light is used, for example, 650 nm. Red light is chosen because the
absorption of blood is substantially negligible. It should be noted
that any wavelength between 600-800 nm could be used to detect
melanin content, but 650 nm provides for a strong absorption by
melanin and avoids strong absorption by blood. The values for
absorption and scattering are then calculated, once again in
accordance with equations 2-5 to 2-9. The predictions of true
reflectance, R650 and the probe collection efficiency, f*650, are
provided by equation 3.3 in section 3.3.3. The product, (f*650)
(R650), or f*R650, yields the expected measurement, M650, in the
absence of the melanin. The optical density due to melanin,
ODmelanin650 can then be specified, and the melanin absorbance in
the yellow-orange spectrum and in the blue range of the spectrum
can be specified. This is then subtracted from optical densities
measured in the blue spectrum and in the yellow-orange spectrum to
yield optical densities essentially independent of melanin, which
allows the remainder of the algorithm to ignore the effects of
melanin and to consider only the effects of skin, blood and
bilirubin.
To specify the blood (hemoglobin) content of the skin, reflectance
in the yellow-orange spectrum is detected, for example, 585 nm.
Bilirubin does not absorb at 585 nm. The choice of 585 nm uses the
isobesic wavelength of hemoglobin absorption, such that the
absorption by blood is the same regardless of the oxygen saturation
of the blood. There are several other isobesic wavelengths for
hemoglobin that could also be used. To convert optical density
detected in the yellow-orange spectrum into an absorption
coefficient, an iterative cycle is used to deduce the absorption in
the yellow-orange region of the spectrum independent of melanin,
and independent of the effects of scattering and probe geometry.
The result is absorption due to skin and blood. The absorption due
to skin, calculated with gestational maturity, is then subtracted
from the total absorption to yield the absorption in the
yellow-orange region of the spectrum which is due to blood alone.
This quantity specifies the amount of blood in the skin.
To determine a raw value for absorption due to bilirubin,
reflectance in the blue light spectrum is detected, for example,
460 nm. The measured reflectance is converted into optical density
in the blue spectrum, which in turn is converted into an absorption
coefficient, using the same iterative procedure as discussed above
with respect to the yellow-orange spectrum. The result is an
absorption coefficient in the blue spectrum due to bilirubin, blood
and skin, independent of bilirubin, and independent of the
scattering and probe geometry. Absorption due to bilirum alone is
then calculated by subtracting absorption due to blood and
absorption due to skin from the total absorption calculated in the
blue spectrum. Once the absorption due to bilirubin is calculated,
the average bilirubin concentration in the skin can be
calculated.
Finally, reflectance measured in the purple-blue spectrum, for
example, 420 nm, is used to detect the depth of blood in order to
calculate a correction factor, .chi., which accounts for spectral
distortion resulting from different penetration depths of the
measuring wavelengths.
5.3.1 Determining The Maturity Of The Infants Skin
The first step in the algorithm is to determine the maturity of the
neonatal skin. The measured optical density between 650 and 800 nm
is extrapolated to 837 nm, as discussed in Subsection 4.2. The
extrapolated reflection at 837 nm, f*R837, was found to be related
to maturity (in weeks) by the following relationship (See FIG.
20):
This relationship was determined by a fit of the f*R.sub.837 values
measured as a function of known gestational maturity. The form of
this relationship was discussed in Subsection 4.2.1 (See Equation
4-3).
5.3.2 Subtraction Of Melanin
As discussed in Section 3 and 4, the melanin is only present in the
epithelium, and so has to be treated separately than absorbers
present diffusely within the skin. As presented in Section 3, the
impact of melanin on the collection efficiency of the optical
patch, f*, can be neglected relative to impact of other absorbers
within the dermis. Therefore, the melanin spectra (shown in FIG.
25) can be subtracted from the measured reflectance spectra,
M(.lambda.), before correction of the spectra for f* is made.
The melanin content of the epidermis is determined at 650 nm, where
the effect of blood and bilirubin on reflectance is relatively
small. At this wavelength, the expected reflectance from the dermis
can be calculated since the scattering and absorption at 650 nm is
known. The optical density at 650 nm due to melanin content is then
calculate as:
where
and where f* and R at 650 are those predicted for the dermis and
are calculated from the optical properties (see Equations 3-27 and
3-35).
The effect of melanin on the optical density spectra at wavelengths
of interest can be calculated by multiplying the OD.sub.melanin
(650) value by a constant. The constant corresponds to the optical
density of melanin at the wavelength of interest relative to that
at 650 nm. Therefore, the component of the measured optical density
at 460 nm due to melanin is:
and that at 585 nm is defined as:
The values of k1 and k2 can be determined from FIG. 25, and are 2.2
and 1.4, respectively.
The measured optical density at 460 nm, OD(460), that has the
effect of melanin removed is therefore:
and that at 585 nm, OD(585), is:
FIG. 36 illustrates how a sample optical density spectra measured
on a neonate is divided into the melanin component, which is
subtracted away, and the remaining measured optical density due to
the skin, blood, and bilirubin.
5.3.3 Determining Absorption Of Blood And Bilirubin
Data presented in Subsection 4.4 showed that the penetration of 460
nm and 585 nm light into neonatal skin was sufficiently deep such
that the reflectance from tissue at those two wavelengths does not
vary significantly with possible variations in the location of the
blood papillary plexus, and bilirubin deposition within the skin.
Therefore, the chromophores at these two wavelengths can be treated
as diffuse absorbers distributed within the tissue.
The optical density after subtraction of the OD.sub.melanin, at any
particular wavelength of interest, is dependent on the scattering
of the tissue, and the absorption due to the tissue, blood, and
bilirubin at that wavelength. The scattering coefficient,
.mu..sub.s ', and the total absorption coefficient, .mu..sub.a,
within the tissue determine the reflectance, R, and the collection
efficiency of the patch, f*. As discussed in Subsection 3.6, the
procedure to find R and f* from the optical coefficients can be
iterated, each time adjusting the absorption coefficient until the
predicted and measured O.D. match. A small reflectance adjustment
factor (which is presented and explained in Appendix C) is
introduced in the iteration procedure to partially correct for skin
thickness error. In this manner, the total absorption coefficient
in the tissue is specified.
The above iterative procedure to determine the absorption
coefficient is implemented at 460 and 585 nm, to obtain .mu..sub.a
460 and .mu..sub.a 585, respectively. At 460 nm, there is
significant absorption from bilirubin blood and skin, while at 585
nm, the absorption due to bilirubin is negligible, and blood and
skin are the only absorbers. As described in Section 2, the
absorption due to skin is known, and is not expected to vary
significantly from person to person, even for neonates of different
gestational ages.
The absorption coefficients that were determined in the skin at 460
and 585 nm attributed to bilirubin and blood, are equivalent to
diffuse absorption and are insensitive to possible variations in
the location of the bilirubin and blood in the skin. This phenomena
was discussed in Subsection 4.4
To calculate the absorption due to blood, the absorption of the
skin is subtracted from the total absorption determined at 585
nm:
The absorption of blood at 460 nm is equal to a fraction of the
absorption at 585 nm, as determined from the blood absorption
spectra. This relationship is expressed as:
where k3 is the factor that relates the absorption coefficient of
blood at 460 nm to the at 585 nm, and is equal to 1.40 [Jacques
1990a, Nahas 1951].
It has been determined that measured optical density decreases as
the depth of blood layer increases, and that the rate at which the
optical density decreases with increasing blood depth varies for
different frequencies. Thus, in equations 5-9, correction factor,
.chi., is used to account for this spectral distortion. The ratio
of the optical density detected at 420 nm, OD420, to the optical
density at 585 nm, OD585, is related to the depth of the blood
layer beneath the skin. In the present application, it has been
determined that .chi. can be set to 1.0.
The bilirubin absorption at 460 nm can then be calculated, by
subtraction of the blood and skin absorption at 460 nm.
The cutaneous bilirubin concentration, [Bilirubin], expressed in
mg/100 g tissue, is related to the bilirubin absorption, .mu..sub.s
bilirubin expressed in cm.sub.-1, by the following expression:
FIG. 37A is a block diagram of a hardware embodiment of the present
invention including optical patch 107 connected to
spectrophotometer 151 and light source 152 through fiber optic
bundle 10B. Spectrophotometer 151 is connected to computer 153,
including display or other output device 154. The structure of
optical patch 107 is discussed above with reference to FIG. 8A.
Spectrophotometer 151 can be, for example, a type 8452A
spectrophotometer available from Hewlett-Packard. Light source 151
can be, for example, a tungsten-halogen lamp that emits a
relatively constant light output for the wavelengths of interest
(300-800 nm). Computer 153 can be, for example, a laptop computer
available from Toshiba, Zenith or Datavue. Computer 153
communicates with spectrophotometer 151 via IEEE-488 bus 156, or
the equivalent.
FIG. 37B, is a block flow chart that summarizes the algorithm of
the present invention that determines the concentration of
cutaneous bilirubin. This algorithm can be applied with a different
optical delivery and collection device, if the relationship between
optical coefficients and f* for optical patch 107 is substituted by
that appropriate for the device used.
Referring to FIG. 37B, in block 141, reflectance from skin under
test is measured at various wavelengths. Control then passes to
block 142 where maturity of the skin is determined. As a
by-product, gestational maturity is determined in block 149.
From block 142, control passes to block 143 where the melanin
content of the skin is determined, and subtracted from the
absorption due to skin calculated in block 142. Control then passes
to iterative loops 144 and 145. In loop 144, the total absorption
coefficient in the blue spectrum is calculated, and in loop 145,
the total absorption coefficient in the yellow-orange spectrum is
calculated. Block 146 calculates the depth of blood in the skin.
Then, the products from blocks 144, 145, and 146 are applied to
block 147 where the absorption due to bilirubin alone is calculated
by substracting the absorption due to blood and skin from the total
absorption of blue light, with blood depth taken into
consideration. Control then passes to block 148 where the cutaneous
bilirubin concentration is calculated.
The flow chart of FIG. 37C presents a more detailed version of the
flow chart of FIG. 37A. The equations used by the algorithm in FIG.
37C are shown in Table 5.2. Appendix E includes a source code
program that embodies the flow chart of FIG. 37C. In practice, a
program written in accordance with a flow chart of FIG. 37C, for
example, like that shown in Appendix E, is loaded into the program
memory of computer 153 in order to operate the hardware shown in
FIG. 37A to perform the transcutaneous bilirubin measurement method
of the present invention.
TABLE 5.2
__________________________________________________________________________
acquire data measure f*R = (=M)at 420,460,585,650-800 nm Sec. 5.3
OD = -log(f*R) Eq. 3-7, 4-1a determine extrapolate OD.sub.650-800
to 847 nm .fwdarw. OD.sub.837 Sec. 4.2 maturity f*R837 = 10
(-M.sub.837) Eq. 4-16 maturity = 10 ((2.72 + f*R.sub.837 /2.43) Eq.
5-1 remove .mu..sub.a 650 = 0.55 .mu..sub.s '650 = -6 +
0.68(maturity) Eq. 2-5, 2-6, 2-7, 2-9 melanin f.sub.650 =
f(.mu..sub.a 650,.mu..sub.s '650) Eq. 3-27 R.sub.650 = f(.mu..sub.a
650,.mu..sub.s '650) Eq. 3-35 f*.sub.650 = (f.sub.650)/0.31 Eq.
3-3, Sec. 3.3.3 predicted.sub.-- M.sub.650 = -log(f*R.sub.650) Eq.
5-3 OD.sub.mel650 = -log(M.sub.650) - (-log(predicted.sub.--
M.sub.650) Eq. 5-2 OD.sub.mel460 = k1 OD.sub.mel650, k1 = 2.2 Eq.
5-4 OD.sub.22mel585 = k2 OD.sub.mel650, k2 = 1.4 Eq. 5-5 OD.sub.460
= -log(M.sub.460) - OD.sub.mel460 Eq. 5-6 OD.sub.585 =
-log(M.sub.585) - OD.sub.mel585 Eq. 5-7 slight adjustment C.sub.460
= 1 -0.26exp(-0.088 maturity) Ex. C-4 factor for C.sub.585 = 1
-0.27exp(-0.057 maturity) Eq. C-5 thickness convert OD .mu..sub.s
'.sub.skin460 = = -15.9 + 1.5 (maturity) Eq. 5-19 to .mu..sub.s
.mu..sub.s '.sub.skin585 = = -12.0 + 1.1 (maturity) Eq. 5-20
initial guess for .mu..sub.a460 and .mu..sub.a585 is 1 cm.sup.-1
Send OD.sub.460 and OD.sub.585 through iterative cycle FIG. 47
yield: .mu..sub.a460, and .mu..sub.a585 linear analysis .mu..sub.a
skin460 = 1.71 (cm.sup.-1), .mu..sub.a skin585 = 0.81 (cm.sup.-1)
Eq. 5-18 of absorption .mu..sub.ablood585 = .mu..sub.a 585 -
.mu..sub.a Eq. 5-8 coefficients .mu..sub.a blood460 = %k3.mu..sub.a
glook585, k3 = 1.40,%.apprxeq.1.0 Eq. 5-9 .mu..sub.a bilirubin =
.mu..sub.a 460 - .mu..sub.a blood460 - .mu..sub.a skin460 Eq. 5-10
[bilirubin].sub.avg in mg/100 g tissue = (.mu..sub.a Eq. 5-11
.sub.bilirubin)(2.56)
__________________________________________________________________________
5.4 Cutaneous Billrubin Prediction In Clinical Measurements
As discussed in Subsection 4.6, the mechanisms of transfer of serum
bilirubin to the skin are not fully understood. Cutaneous
bilirubine concentrations increase with serum concentrations, but
the two concentrations are not perfectly correlated since certain
factors such as acidity, and phototherapy status are known to
disrupt the relationship. The algorithm developed above for the
determination of cutaneous bilirubin concentration is correlated to
serum bilirubin levels here since there is not a better measure of
the cutaneous bilirubin concentrations available.
The algorithm presented in Subsection 5.3 was applied to
transcutaneous reflectance measurements performed with the optical
patch connected to a Hewlett-Packard diode array spectrophotometer
(model 8452-A). Serum bilirubin readings were available for 47 of
the newborn infants measured. The neonates measured varied from 24
to 42 weeks gestational age, and comprised of 18 white, 6 hispanic,
23 black infants. Ten of the neonates measured were undergoing
phototherapy at the time of measurement.
The forehead reflectance measurements were analyzed, since the
forehead of those neonates undergoing phototherapy, was covered
with an eye patch, which avoided photobleaching of the skin site
measured. Also, skin in the cephalic regions of the body is
documented to stain with bilirubin earlier than caudal regions, and
therefore cutaneous levels there are expected to correlate more
closely to serum bilirubin concentrations [Knudsen 1989].
Based on the results of the clinical measurements, some parameters
in the algorithm of FIG. 37B were refined, as discussed in
Subsection 5.5, where the clinical results are presented.
5.5 Algorithm Refinement
To evaluate and refine the algorithm which measures the cutaneous
bilirubin concentration, the following procedure was implemented.
As expressed earlier, there is not a reliable independent measure
of the cutaneous bilirubin concentration. The serum concentrations
are all we have as an indication of the degree of jaundice. For
each neonate measured, we would expect the absorbance of cutaneous
bilirubin, .mu..sub.a bili, predicted by our algorithm to be
proportional to the serum concentration, [Bili]serum, of the
neonate. We chose to refine the algorithm in order to ensure that
the ratio of .mu..sub.a bili to [Bili]serum is independent of the
melanin and blood content of the skin. This assumes that variations
in the rate of transfer of bilirubin from blood to the skin are due
to physiological considerations of the infant, such as blood pH,
and not dependent on the degree of melanin concentration,
Melanin650, and blood content, measured as .mu..sub.a blood (585),
in the skin.
The dependence of .mu..sub.a bili/[Bili].sub.serum on blood and
melanin content was plotted as shown in FIGS. 38A and B. The
.mu..sub.a bili was calculated by the algorithm as presented in
FIG. 37 and Table 5.2. A score was used to evaluate the dependence
of .mu..sub.a bili[Bili].sub.serum on the independent variable,
Melanin650, or .mu..sub.a blood (585). This score is explained in
the next paragraph.
5.5.1 Calculations Of The Score
There is a spread in the values of the fraction, .mu..sub.a
bili/[Bili].sub.serum, and in the value of the independent
variable, Melanin650, or .mu..sub.a blood(585), when they are plot.
Four quadrants, I, II, III, and IV, are assigned on the plot, and
the lines are set according to the median values of .mu..sub.a
bili/[Bili].sub.serum and of the independent variable, as shown in
FIG. 39. The number of points in each quadrant, I, II, III, or IV,
are then assigned as n.sub.1, n.sub.2, n.sub.3 or n.sub.4,
respectively. The score is then calculated as: ##EQU30##
The score for each variable is chosen such that a strong dependence
(with a positive or negative slope) of the fraction, .mu..sub.a
bili/[Bili].sub.serum, on the independent variable will lead to a
score approaching one half, while complete independence of the two
variables will result in a score approaching zero. A score,
Score.sub.blood, was calculated for the dependence of .mu..sub.a
bili[Bili].sub.serum on blood absorption, .mu..sub.a blood (585),
and an independent score, Score.sub.melanin, was calculated for the
dependence of .mu..sub.a bili/[Bili].sub.serum on melanin content,
Melanin650. The total Score is equal to the sum of Score.sub.blood
and Score.sub.melanin, as shown below, and may vary between zero
and one.
5.5.2 Iteration To Optimize Equations Of Optical Coefficients
The algorithm was originally tested with the initial equations used
for the absorption of skin as a function of wavelength (Equation
2-8), and the scattering at 460, 585, and 650 nm as a function of
maturity (from Equation 2-5 through 2-7). These equations are:
______________________________________ .mu..sub.a skin = a exp (-b
.lambda.) = 5 exp(-0.0035 .lambda.) (cm.sup.-1) (5-14) .mu..sub.s
'460 = yint.sub.460 + slope.sub.460 (maturity) (5-15) = -15.7 + 1.6
(maturity) (cm.sup.-1) .mu..sub.s '585 = yint.sub.585 +
slope.sub.585 (maturity) (5-16) = -16.7 + 1.22 (maturity)
(cm.sup.-1) .mu..sub.s '650 = yint.sub.650 + slope.sub.650
(maturity) (5-17) = -15.6 + 1.0 (maturity) (cm.sup.-1)
______________________________________
For each of the neonates measured, the fraction of .mu..sub.a
bili/[Bili].sub.serum, was calculated and used to determine the
total Score for the algorithm. To find the minimum Score, the
parameters in the Equations 5-14 through 5-17 were varied in a
range that resulted in changes in the optical properties of less
than about 15%. Parameters which yielded non-sensible results (for
example .mu..sub.a bilirubin, or .mu..sub.a blood values less than
zero) were disregarded. The procedure followed to adjust these
parameters is illustrated in FIG. 40. After the procedure in FIG.
40 was followed, the new expressions for .mu..sub.a skin(.lambda.),
.mu..sub.s '460(maturity), and .mu..sub.s '650(maturity), were
obtained, and are presented below. These values are included in
Table 5.2 where the final algorithm to deduce the cutaneous
bilirubin concentration is presented.
5.5.3 Results
The fraction .mu..sub.a bili/[Bili].sub.serum is plot as a function
of Melanin650 and .mu..sub.a blood in FIGS. 38a and b,
respectively. The data for these graphs were generated using the
final functions for .mu..sub.a skin, .mu..sub.s '460(maturity),
.mu..sub.s '585(maturity), .mu..sub.s '650(maturity). These
functions are:
______________________________________ .mu..sub.a skin = a exp (-b
.lambda.) = 27 exp(-0.0006 .lambda.) (cm.sup.-1) (5-18) .mu..sub.s
'460 = yint.sub.460 + slope.sub.460 (maturity) (5-19) = -15.9 + 1.5
(maturity) (cm.sup.-1) .mu..sub.s '585 = yint.sub.585 +
slope.sub.585 (maturity) (5-20) = -12.0 + 1.1 (maturity)
(cm.sup.-1) .mu..sub.s '650 = yint.sub.650 + slope.sub.650
(maturity) (5-21) = -6.0 + 0.68 (maturity) (cm.sup.-1)
______________________________________
Equation 5-18 above expresses the absorption due coefficient of
skin as a function of wavelength (.lambda. in nm) in terms of
parameters a and b. The reduced scattering coefficient of skin at
460 and 585, and 650 nm as a function of maturity (in weeks) are
expressed in Equations 5-19 and 5-20, and 5-21 above.
Also shown in FIG. 38a and b are the values of .mu..sub.a
abili/[Bili].sub.serum as a function of Melanin650 and .mu..sub.a
blood calculated using the original expressions for optical
coefficients (Equations 5-14, 5-16 and 5-16 and 5-17). From these
graphs the Score.sub.blood and Score.sub.melanin, and consequently
the total Score was calculated.
FIG. 41a illustrates how the Score varies as the parameters that
define .mu..sub.s '460(maturity) namely, yint.sub.460 and
slope.sub.460, were varied. The FIG. 41b shows how the new estimate
of .mu..sub.s '460 as a function of maturity, shown in Table 5.2,
compares to the original function shown from Equation 5-14. FIG.
41b also shows the in vitro measurements of .mu..sub.s '460 as a
function of maturity. It can be seen that the variation in the
measured .mu..sub.s '460 and the final expression used in the
algorithm is on average less than 10%, which is within the error
with which we can optical properties from in vitro measurements. A
graph showing how the new function for skin absorption as a
function of wavelength compares with data measured in vitro was
shown in FIG. 6. The difference between the final values of optical
properties arrived at here, and the in vitro measurements may be
contributed to due to differences in hydration between in vitro
skin samples and in vitro skin. The difference between the initial
and final values of the scattering coefficient at 585 nm was also
less than 10%.
5.6 Estimate Of Errors
When the cutaneous bilirubin concentration is determined from the
transcutaneous reflectance measurements, there is a degree of
uncertainty in the bilirubin determination because of intersubject
as well as intrasite variations in measurements. Intrasite
variation means the variation in reflectance measurements performed
repeatedly on the same in vitro skin site on a single subject.
Intersubject variations are possible variations in skin properties
between individuals, which will lead to changes in the cutaneous
bilirubin determinations. To estimate the uncertainty with which
the cutaneous bilirubin concentrations are reported, the cutaneous
bilirubin concentrations were determined under a variety of
conditions.
To estimate the uncertainty caused by simple measurement
(intrasite) variation, the algorithm was used to predict the
cutaneous bilirubin concentration for ten measurements performed on
the same patient at the same skin site. All the ten measurements
were performed in a three-minute period. The standard deviation in
the calculated cutaneous bilirubin concentrations, and in the
equivalent serum bilirubin concentrations, are reported in Table
5.3.
TABLE 5.3 ______________________________________ Estimated Standard
Effect on Predicted Effect on Pre- Deviation Cutaneous Bilirubin
dicted Serum (+ S.D.), Absorption Bilirubin (% Coefficient, +
Concentration, + Variance) S.D. S.D.
______________________________________ Measure- +4% .+-.0.188
(cm.sup.-1) .+-.0.69 (mg/dl) ment (f*R) Skin +250 .mu.m .+-.0.095
(cm.sup.-1) .+-.0.35 (mg/dl) Thickness Scattering +15% .+-.0.414
(cm.sup.-1) .+-.1.51 (mg/dl) Coefficient Absorption +15% .+-.0.225
(cm.sup.-1) .+-.0.82 (mg/dl) Coefficient Cumulative .+-.0.516
(cm.sup.-1) .+-.1.88 (mg/dl) Standard Deviation
______________________________________
The main sources of intersubject variations that can lead to errors
in the transcutaneous bilirubin determinations are skin thickness,
and skin optical property estimates, as discussed in Section 4.
Skin thickness is partially corrected for by lowering the estimated
reflectance from skin of given optical properties in the algorithm
iteration procedure, as discussed in Appendix C. Variation in the
skin thickness, however, can still yield intersample variation in
the etimated skin reflectance.
To determine the effect of skin thickness variation on
transcutaneous bilirubin concentrations, the bilirubin algorithm
was run on all the clinical samples with the measured reflectance
adjusted according to the changes expected due to variation in skin
thickness. The skin thickness was simulated to vary by 250 .mu.m,
the standard deviation in the mean skin thickness measured on in
vitro skin samples on viable neonates (>24 weeks gestation). The
resulting variation in the cutaneous and serum bilirubin estimates
is reported in Table 5.3.
To determine the effect of skin optical properties on the
transcutaneous bilirubin concentrations, the bilirubin algorithm
was run on the clinical measurements with the scattering
coefficient, and then with the absorption coefficient, used in the
algorithm altered by .+-.15%. This is the estimated precision with
which we can predict the optical coefficients for skin of given
gestational age. The resulting variation in the bilirubin
concentrations are shown in Table 5.3. Variation in skin absorption
coefficients will directly lead to changes in the calculated
absorption coefficient that is attributed to bilirubin.
The cumulative uncertainty by which the cutaneous and serum
bilirubin concentrations are reported was calculated by the vector
sum of the individual sources of errors, and is shown in Table 5.3.
This assumes linearity of relationships around the region of
clinical interest. The error of .+-.0.516 cm.sup.-1 (or 1.88 mg/dl)
is small relative to the range of cutaneous and serum bilirubin
concentrations encountered clinically (see FIGS. 38A and 38B).
5.7 Conclusions
Based on the Monte Carlo model of cutaneous bilirubin developed in
this section, the measurements presented on neonates, and the
considerations developed in the previous sections, an algorithm was
developed that took the following into account.
Melanin in the epidermis behaves as a thin attenuation filter,
decreasing the reflected signal in a linear fashion. This is very
different from the effect that bulk tissue absorbers have on the
reflectance of a tissue.
The scattering properties of the skin influence the interpretations
of measured reflectance spectra. Therefore, the variable scattering
has to be taken into account when determining the bilirubin
concentration in skin. The maturity of the skin, from which the
scattering properties are derived, can be determined by
extrapolating the measured optical density spectra to 837 nm.
The effects of bulk tissue absorption in the dermis due to skin,
bilirubin, and blood on the measured optical density do not
accumulate linearly. For correct determination of the cutaneous
bilirubin concentration, the total absorption in the skin at chosen
wavelengths has to be determined correctly from radiative transport
theory. Only then can the absorption due to skin, blood and
bilirubin be analyzed linearly.
An algorithm was developed to determine the cutaneous bilirubin
concentration with all these light transport considerations in
mind. The different scattering properties of skin of neonates of
different gestational ages, and the different melanin and blood
content of the skin are all considered. The operation of the
algorithm was demonstrated on reflectance measurements conducted on
a clinical population. This is the first algorithm, aimed at
determining the cutaneous bilirubin concentrations by determining
the optical absorption coefficient of bilirubin in the skin.
Appendix A
Optical Interaction Parameters
A.1 Optical Coefficients
The rate at which energy is absorbed and scattered by a particle is
the energy extinction rate, W.sub.ext, of the particle, expressed
in watts. The extinction rate W.sub.ext is comprised of W.sub.a and
W.sub.s, which are the energy absorption and the energy scattering
rates of the particle.
The extinction cross section, C.sub.ext (cm.sup.2), is defined as
the ratio of W.sub.ext (W) to the incident fluence rate, I.sub.i
(W/cm.sup.2), and similarly the absorption cross section and
scattering cross section are defined: ##EQU31##
The extinction, absorption, and scattering cross sections have
dimensions of square area, and are related by:
In a medium containing a concentration .rho. of such particles per
unit volume, the extinction, absorption, and scattering
coefficients of the medium are defined as:
The extinction coefficient of the medium, .mu..sub.ext, is
sometimes referred to as the total attenuation coefficient,
.mu..sub.t, and is equal to the sum of .mu..sub.a and .mu..sub.s.
These interaction coefficients have units of inverse distance, such
as cm.sup.-1.
The light distribution in a tissue is determined by the optical
characteristics of the tissue which include its optical properties,
thickness, and geometry. For a slab of arbitrary thickness, the
problem is 1-dimensional, and optical characteristics are described
either in dimensional or non-dimensional units, as shown in table
A-1 below:
TABLE A-1 ______________________________________ Dimensional Non -
Dimensional ______________________________________ Absorption
.mu..sub.a (cm.sup.-1) Albedo ##STR1## Scattering .mu..sub.s
(cm.sup.-1) Optical depth b = (.mu..sub.a + .mu..sub.s)d Thickness
d (cm) ______________________________________
A.2 Anisotropy
The anisotropy factor, sometimes referred to as the asymmetry
parameter, g, is equal to the average cosine of the angle of
scattering .theta.. ##EQU32## where p(.theta.) is the scattering
phase function in a fixed plane, and is subject to the following
constraint to conserve photon energy: ##EQU33##
The anisotropy factor, g, is a measure of the directionality of the
scattered light, and varies from 0 for isotropically scattered
light to 1 for forwardly scattered light.
A.3 Light Transport
Combining .mu..sub.s and (1-g) as the product, .mu..sub.s (1-g),
gives the reduced scattering coefficient, also referred to as
.mu..sub.s '. The reduced scattering coefficient, is used in
diffusion theory to specify the effective light scattering that
determines light penetration into a medium [Ishimaru 1978]. The
reduced scattering coefficient is a useful parameter which can be
used to describe the effective scattering in a tissue without
uniquely solving for both .mu..sub.s and g individually in a
tissue.
In a one dimensional situation, for light, I.sub.0, traveling a
distance x in the tissue with optical interaction parameters
.mu..sub.a and .mu..sub.s, the amount of light that is neither
absorbed nor scattered as a function of x is given by:
In three dimensional space, the diffusion equation can be solved
far from a light emitting point source. The fluence rate, .phi.(r),
specified in Watts/cm.sup.2, is given by [Patterson 1990]:
##EQU34## where r is the distance from the delta function point
source, D is the diffusion constant and is given in Equation A-10,
and .mu..sub.eff is the effective coefficient and is given in
Equation A-11. ##EQU35##
Appendix B
Calculation of Optical Patch Collection Efficiency from Monte Carlo
Results
B.1 Introduction
The collection efficiency of the optical patch, or other optical
delivery and collection device with specified geometry, can be
determined by convolution of the Monte Carlo radial reflectance
profile. The calculations involved to determine the collection
efficiency are presented here for the optical patch described in
section 3. The convolution procedure presented can be applied to
any optical devices in which the collection and delivery areas are
concentric.
B.2 Convolution Procedure
The light delivered through the optical patch is delivered through
the delivery area. The Monte Carlo point source reflectance
response of the tissue has to be convolved over the whole delivery
area to determine the light collection efficiency of the optical
patch.
FIG. 42 defines the geometry of the collection and delivery areas
used in the general convolution procedure described. The delivery
area is the circular area with radius R.sub.in. Similarly, the
collection area is defined as the circular area with radius
R.sub.out as illustrated. This procedure is designed to calculate
the collection efficiency in an optical patch in which the delivery
and collection areas are two full concentric circles. The radiuses
of the delivery and collection areas, R.sub.in and R.sub.out, can
be different.
The light delivered through the optical patch equals the integral
of irradiance, E.sub.o (W/cm.sup.2), over the entire delivery area
of the optical patch. Therefore the light delivered by the optical
patch can be expressed as: ##EQU36##
The total collection efficiency of the optical patch, f, is
calculated as: ##EQU37##
To calculate the collection efficiency, f, the total light
collected, C(r), and lost, L(r), from each input radial point, r,
is determined. The quantities C(r) and L(r) are expressed in watts.
To calculate C(r) and L(r), for each value of the input radius, r,
the output radius, r', is incremented from 0 to .infin., as to sum
all the reflected light. The fraction of reflected light that is
collected depends on r, and r', as seen in the three cases
described below.
The integration parameters are illustrated in FIG. 42. The input
irradiance is can be normalized to 1 (W/cm.sup.2). The light
collected is then expressed as fractions of the delivered light
energy. In the following calculations, the reflection profile,
R(r'), gives the amount of light that is reflected in the whole
annulus with radius r', and so is specified in units of W/cm. The
total power delivered in the annulus with radius r' and thickness
.DELTA.t' is equal to the product R(r').DELTA.r'.
Case 1 (FIG. 43A): If r'<(R.sub.out -r) then, as diagramed in
FIG. 43A, all the light reflected at radius r' is collected by the
optical patch. Therefore, ##EQU38##
Case 2 (FIG. 43B): If (R.sub.out -r)<r'<(R.sub.out +r) then,
as diagramed in FIG. 43B, a fraction of the light reflected at
radius r' is collected by the optical patch. Therefore, ##EQU39##
where .phi.(r',r) is the angle shown in FIG. 43b, and is equal to:
##EQU40##
The angle .phi., in equation B-7 was derived by application of the
cosine law which states that in a triangle with sides a, b, and c,
the following relationship holds:
where .gamma. is the internal angle in the triangle that projects
side c. For derivation of Equation B-7 from B-8, .phi./2 was set as
.gamma., r was set to a, r' was set to b, and R.sub.out was equal
to c (See FIG. 43B).
The remaining light remitted in the radial range, r', that is not
collected by the optical patch is lost. Therefore: ##EQU41##
Case 3 (FIG. 43C): If r'>(R.sub.out +r) then, as diagramed in
FIG. 43C, none of the light reflected at radius r' is collected by
the optical patch. Therefore:
The total light, C(r), delivered at radius r, that is collected by
the optical patch is therefore equal to:
The total light, L(r), delivered at radius r, that is reflected
outside the optical patch and so is not collected is equal to:
The total collection efficiency, f, of the optical patch can then
be given as: ##EQU43##
The Monte Carlo data described in subsection 3.4, is used with the
geometry described above to determine the optical patch collection
efficiency, f. The next two sections describe the use of the Monte
Carlo data in implementation of a computer program to determine
f.
B.3 Monte Carlo Method and Approximations
The basis of the Monte Carlo data used in this convolution
procedure is described in subsection 3.4. The program simulates the
launching of photons with unit weight, W=1, into an absorptionless
medium. Each time a fraction of the photon weight is remitted, the
Monte Carlo program stores in a file ("photon history file") the
radial distance from the source at which the photon was remitted
(m), the fraction of the photon weight that was remitted (fraction
of 1), the pathlength travelled by the photon in the absorptionless
medium (m), the maximum depth in the medium reached by the photon
(m, not used in the convolution procedure), and the average depth
reached in the medium by the photon (m, not used in the convolution
procedure). The Monte Carlo simulation also stored the total number
of photons launched into the medium, and the scattering coefficient
used during the simulation. The distances stored in the photon
history file can subsequently be converted to centimeters (see
subsection 3.4.2 for details), or effective scattering lengths (as
is described in the convolution program in this appendix).
The photon histories stored during the Monte Carlo computer
simulations are intended to predict the reflection response of an
infinitely thick medium (See subsection 3.4 for introduction).
Monte Carlo simulates each scattering event that a photon
experiences. To get an accurate assessment of the total tissue
response to photons, many photons need to be simulated, and the
process is time consuming. This is especially true in the case of a
thick absorptionless medium, where the photon record is dropped
only by reflection or transmission of the photon, but not by
absorption. To prevent excessively long Monte Carlo simulations,
the thickness was made finite, and equal to approximately sixty
effective scattering lengths (or 300 mean scattering path lengths
(g=0.8)). With this thickness assigned to the absorptionless medium
simulated by Monte Carlo, approximately 4.5% of the photons were
transmitted through the medium, 2.5% were laterally transmitted,
and the remaining 93% were reflected. The transmission through this
medium will result in a small approximation error in the
calculation of the optical patch collection efficiency, since it
assumes an infinitely thick medium through which there is no
transmission. This error is estimated below.
FIG. 44 shows the geometry of the Monte Carlo model used. As
discussed in Section 3, the distances in the Monte Carlo model can
be converted to dimensionless units, and so a wide range of
dimensions can then be modelled from the same Monte Carlo results.
The dimensions in FIG. 44 correspond to typical optical properties
of .sub.a of 1 cm.sup.-1 and .sub.s ' of 20 cm.sup.-1.
In a medium in which .sub.s '=20 cm.sup.-1 then an absorption
coefficient, .sub.a =1 cm.sup.-1, corresponds to: 1/20=0.05
effective scattering lengths. In a worst case scenario, if the 7%
transmitted light in the Monte Carlo model had an unscattered path
in the medium, then after absorption the amount of light that was
transmitted corresponds to:
(0.07) * e.sup.(-0.05*60) =0.0035 fraction of the light that was
input into the medium. This calculation assumes 60 effective
scattering lengths for the depth and radius of the medium modelled
by Monte Carlo, which is worse than the real case.
If this light was actually reflected from the lower surface of the
medium, rather than being transmitted, then after absorption on the
return trip before remission from the upper surface, the fraction
of the input light that is remitted can be estimated as:
0.0035* e.sup.(-0.05*60) =1.73.times.10.sup.-4 fraction of the
light input into the medium.
The optical patch collection efficiency, f, is calculated as (from
equation B-3): ##EQU44##
With the optical properties defined above, the approximate
reflection of the tissue is approximately 40% (from equation 3-28).
Therefore, the term (collected+lost) in the denominator of equation
B-3 is equal to 0.4. The collection efficiency, f, is approximately
equal to 0.6 (from Equation 3-21). From equation B-3, the fraction
of the light input by the patch that is lost can be solved to equal
0.24, and the fraction that is lost equals 0.16.
In a worst case scenario, the light that was transmitted in the
absorptionless case actually rebounded from the lower surface (see
FIG. 44), and remitted from the upper surface after absorption, as
discussed. Also, as a worst case, if this light was remitted from
the upper surface such that it was not collected by the optical
patch, then the f would be: ##EQU45##
This implies a 0.04% error in the calculation of f due to the
approximation of an infinite medium. This error will vary with
optical properties, but 0.04% is a conservative estimate since it
assumes worst cases.
B.4 Computer Implementation of Convolution Procedure
The collection fraction, f, is determined as the fraction of light
that is collected divided by the sum of collected and lost light
(see Equation B-3). The lost light refers to light that was
remitted beyond the collection area of the optical patch. To
determine the collected and the lost light, the profile of
reflected light has to be determined. This profile of reflected
light is then used in the convolution procedure (R(r') in equations
B-4 through B-11). In the computer program application of the
convolution procedure, the reflection profile is made discrete, and
placed in an array called Refwtotalab, as explained below.
The photon histories file contains the location of remission of
each photon, r.sub.-- em, the fractional weight of the photon
remitted, w, and the pathlength of the photon travel in the
absorptionless medium (see subsection 3.4 for more complete
discussion). The distances expressed in the, in m, are converted to
average effective scattering lengths, by multiplication by the
effective scattering coefficient, .sub.s '.sub.0 used in the Monte
Carlo simulation during generation of the photon histories file.
For example:
The photon weight remitted for each photon is then calculated, as
in equation 3-18. Each photon weight remitted is added to the
appropriate element of the array Refwtotalab[index], where index is
assigned to the radius of photon remission, r.sub.-- em, by the
programming statement:
where delta.sub.-- r is the resolution with which the reflection
profile is made discrete. Delta.sub.-- r is expressed in the same
units as r.sub.-- em, either m or effective scattering lengths.
All index values greater than a set number, indexmax, are assigned
as indexmax+1. This allows for the limiting of the number of
discrete elements in the array Refwtotalab, without the loss of
resolution at the radii of interest.
When all the remitted photons are added to the appropriate
Refwtotalab array elements, the the total light reflected is
accounted for in the sum of the Refwtotalab elements, as shown
below: ##EQU46##
The light that is reflected and collected by the optical patch, and
the light that is reflected but not collected (lost), are counted
individually in convolution procedure. They are used to determine
the collection efficiency, f, as in Equation B-3. An example of a
Pascal program implementation of the convolution procedure using
Monte Carlo data is presented below.
B.3 Computer Implementation of Monte Carlo Convolution program
MctrackscalRr
__________________________________________________________________________
{Program to calculate optical patch collection efficiency from
absorptionless Monte Carlo photon histories} {Iyad Saidi, Laser
Biology Research Laboratory, UT-M.D. Anderson Cancer Center}
{subprograms used sane contains arithmetic functions} uses sane var
{variables used} r.sub.-- em: real {radial distance from source at
which photons remitted} refwnoabs: real {weight of photon remitted
with no absorption taken in to account} refwabs: real {weight of
photon remitted after absorption taken into account} L: real
{Pathlength of photon in absorptionless medium} delta.sub.-- r:
real {radial interval in which r.sub.-- em is discretized}
refwabstotal: real {sum of photon weights after absorption} musg:
real {.sub.s ' specified} mua: real {.sub.a specified} photosin:
real {number of photons input to absorptionless Monte Carlo
simulation} musgfile: real {s' specified when absorptionless Monte
Carlo run to generate photohistory file, (.sub.s '.sub.0 in text}
Rin: real {Radius of delivery circular area of optical patch} Rout:
real {Radius of collection circular area of optical patch}
fraction: real {fraction of delivered light that is collected in
case 2 situation} collected: real {Variable to sum collected light
input at radius r, (equivelant to C(r)} lost: real {Variable to sum
lost light input at radius r, (equivelant to L(r)} totalcollected:
real {Sum of collected light (equivelant to integral of C(r)}
totallost: real {Sum of lost light (equivelant to integral of L(r)}
dummy: real {read from photon history file but not used} i: integer
{index to keep track of photon histories read} indexmax: integer
{max. number of radial descretizations} i.sub.-- r: integer
{discrete radius of delivery annulus (r)} i.sub.-- rprime: integer
{discrete radius of collection annulus (r')} i.sub.-- Rin: integer
{discrete radius of delivery area of patch (Rin)} i.sub.-- Rout:
integer {discrete radius of collection area of patch (Rout)} index:
integer {index used to discretize reflection profile R(r)}
filename: string {name of file which contains photon histories}
junk: string {string read but not used} source: text {source file
alias} refwtotalab: array[0 . . . 51]of real {Array containing
photon remission profile after absorption} {Subroutine to find
inverse cosine} function Arccos (x: extended): extended begin
Arccos := 2 * Arctan(sqrt((1 - x) / (1 + x))) {spurious
divide-by-zero may arise} end {begining of procedure} begin {read
in reduced scattering coefficient desired} writeln('what is s(1-g)
in inverse cm') readln(musg) {read in absorption coefficient
desired} writeln('what is a in inverse cm') readln(mua) mua: = mua
/ (musg) {mua in units of mean effective scattering lengths}
{Specify dimension of optical patch} Rin := 1.05 {Radius in which
there are input fibers (mm)} Rin := Rin / 10 {cm} Rout := 1.05
{Radius in which there are output fibers (mm)} Rout := Rout / 10
{cm} (open file which contains Monte Carlo photon histories at
reflection} filename := oldfilename ('which file has the tracks
data from Monte Carlo') reset(source, filename) {read in the number
of photons run, and the reduced scattering coefficient with which
it was run} readln(source, photosin, musgfile) readln(source, junk)
{set number of photons read = 0} i := 0 indexmas := 25 {set arrays
= } for index := 0 to (indexmax + 1) do begin Refwtotalab[index] :=
0 end {chose rbucket size =Max radius encountered in patch of
interest so that resolution is not wasted, (Rin + Rout) is the
maximum possible encountered distance in patch to be collected in
dimensionless units of effective scattering lengths} delta.sub.-- r
:= (Rin + Rout) * musg / (indexmax - 2) I.sub.-- Rout :=
Num2integer(Rout * musg / delta.sub.-- r) {discrete form of
distance of patch collection radius, Rout} I.sub.-- Rin :=
num2integer(Rin * musg / delta.sub.-- r) {discrete form of distance
of patch delivery radius, Rin} {set photon counts to zero, for
absorptionless and absorbed cases} refwabstotal := 0 {input photon
reflections from photon files} while not eof(source) do begin
{count number of photon histories recorded} i := i + 1 {read:
radius of reflection, weight reflected, pathlength of travel
maximum depth reached, and average depth in phantom using m for
distances} readln(source, r.sub.-- em, Refwnoabs, L, dummy, dummy)
{convert m .fwdarw. cm .fwdarw. effective scattering lengths}
r.sub.-- em := r.sub.-- em * musgfile * 0.0001 L := L * musgfile *
0.0001 {sum reflected light, in absorptionless and absorbed case}
refwabs := (refwnoabs * exp(-mua * L) refwabstotal := refwabstotal
+ refwabs {categorize r.sub.-- em at which photons reflected in
discrete boxes, (indices), then sum reflection within each radius
index} index := round((r.sub.-- em - (delta.sub.-- r / 2)) /
delta.sub.-- r) if index < indexmax then index := indexmax + 1
Refwtotalab[index] := Refwtotalab[index] + Refwabs end
close(source) {Convolution to find optical path collection
efficiencies} totalcollected := 0 totallost := 0 {integrate total
over all input radiuses} for i.sub.-- r := 0 to i.sub.-- Rin do
begin collected := 0 {the light collected from this radial} lost :=
0 {case 1, full circles collected} for i.sub.-- rprime := 0 to
(i.sub.-- Rout - i.sub.-- r) do begin index := i.sub.-- rprime if
index < indexmax + 1 then index := indexmax + 1 collected :=
collected + Refwtotalab[index] end {case 2, fraction of circles
collected} for i.sub.-- rprime := 0 to (i.sub.-- Rout - i.sub.-- r
+ 1) to (i.sub.-- Rout + i.sub.-- r) do begin index := i.sub.--
rprime if index < indexmax + 1 then index := indexmax + 1
fraction := Arccos((sqr(i.sub.-- rprime) + sqr(i.sub.-- r) -
sqr(i.sub.-- Rin)) / (2 * i.sub.-- r * i.sub.-- rprime)) / (pi) if
(i.sub.-- r = 0) or (i.sub.-- rprime = 0) then fraction := 0
collected := collected + (Refwtotalab[index] * fraction) lost :=
lost + (1 - fraction) * (Refwtotalab[index]) end {case 3, All light
is lost} for i.sub.-- rprime := (i.sub.-- Rout + i.sub.-- r + 1) to
indexmax + 1 to {add remaining escaping fraction} begin index :=
i.sub.-- rprime if index < indexmax + 1 then index := indexmax +
1 lost := lost + (Refwtotalab[index]) end {input area is * 2pi R}
collected := collected * 2 * pi * i.sub.-- r lost := lost * 2 * pi
* i.sub.-- r totalcollected := totalcollected + collected totallost
:= totallost + lost end {end the adding of i.sub.-- r} {write out
results} writeln('fraction collected = ', totalcollected /
(totalcollected + totallost)) end.
__________________________________________________________________________
Appendix C
Effect of Skin Thickness on Reflectance Measurements
C.1 Introduction
The neonates' skin thickness may vary between individuals and
sites, as discussed in Section 4. FIG. 31 shows the thickness of
the skin measured on the 20 in vitro neonatal skin samples
discussed in Section 2. The algorithms presented in accordance with
this invention were developed for infinite media, since the skin is
optically thick. The effect of the skin thickness variation on the
measured light reflection is studied in this appendix, and the
potential errors in bilirubin estimation are analyzed.
Model of Skin Thickness Effect
C.2.1 Monte Carlo Model
As discussed in Section 4, the hypodermis, a fatty collagenous
layer, lies below the dermis. Absorptionless Monte Carlo computer
simulations were run, similar to the Monte Carlo simulations
discussed in Section 3. The pathlength in each one of ten layers in
the skin was stored for the remitted photons. The photon reflection
profiles were analyzed varying optical properties in the skin. The
optical properties of the individual layers were set at those of
dermis, or hypodermis. The optical properties of dermis were
estimated from optical measurements, and from the literature
[Cheong 1991]. The scattering coefficient in the hypodermis is
about half that of the dermis. The number of layers with dermal
optical properties was varied depending on the desired thickness of
the skin simulated. The true reflection and collection efficiency
of the optical patch was calculated for each of the simulated skin
thicknesses.
The thickness of the dermis above the hypodermis was varied between
600 and 1200 nm, which are the expected range of skin thicknesses
of viable neonates (>24 weeks gestational age).
C.2.2 Results
As the thickness of the skin was decreased, the true reflectance of
the tissue decreased while the fraction of reflected light
collected by the optical patch increased. Consequently the measured
reflectance was found to drop by less than the drop in the true
reflection of the tissue. The effect of skin thickness and optical
patch diameter on the measured reflection is illustrated in FIG.
45, for thirty week gestational age dermal optical properties at
650 nm. In this figure the measured reflectance of skin of finite
thickness overlying hypodermis divided by measured reflectance for
skin of infinite thickness is shown as a function of skin
thickness. The decrease in skin reflectance measured with the 2.1
mm optical patch is less than 10% for the thinnest skin expected
(.apprxeq.600 .mu.m). The effect skin thickness has on the
reflectance measured with the optical patch increases with
wavelength, since at the longer wavelengths, the tissue is
optically thinner. FIG. 46 shows the fraction of measured
reflectance of finite thickness skin relative to infinite thickness
skin for the wavelengths 460, 585, 650, and 750 nm. At 460 and 585
nm, the variation in reflectance of very thin skin (.apprxeq.600
.mu.m) and very thick skin (.apprxeq.1200 .mu.m) is less than
3%.
The fraction of measured reflectance of finite thickness skin
relative to infinite thickness skin for the 460-nm light is:
##EQU47## and for 585-nm light is: ##EQU48## where t is the
thickness in .mu.m.
C.2.3 Discussion
The measured reflectance does not drop as fast as the true total
reflectance, because the addition of an absorbing layer beneath the
skin would affect the photons that have penetrated deeply. These
deep photons, on average, have a higher probability of remittance
outside the collection area of the optical patch than do the more
shallow penetrating photons. Therefore, the absorbing layer beneath
the skin will not affect the photons that are remitted into the
optical patch as much as it would affect, on average, all the
remitted photons. This phenomenon will be of increased relevance
with optical patches with smaller delivery and collection areas. As
shown in this figure, the reflectance measurements performed
between 650 and 750 nm, which are used to determine the skin
maturity by extrapolation to 837 nm, are affected by skin
thickness. However, an extreme variation in thickness between
600-nm thick and 1200-nm thick, still has a less then 10% variation
in extrapolated reflectance at 837 nm. This compares to variation
of 150% in the measured reflectance at 837 nm due to changes with
gestational age, as seen from FIG. 20.
C.2.4 Conclusion
In conclusion, the thickness of the skin presents a potential
source of error in the reflectance spectra measurements at the skin
surface. Variation in the skin thickness may alter the reflectance
measurements in the 650-750 nm range by up to 10%, which in turn
will affect the interpretation of the skin maturity. Variation in
the skin thickness will play a small role in readings in the
400-600 nm range (<3% variation) where blood and bilirubin
absorbances are read. Finally, the existence of a hypodermis
consisting of collagen fibers and fat beneath the dermis, and
measurement of the reflectance with an optical patch rather than
measurement of total reflectance, will both decrease the effect
skin thickness has on the measured reflectance.
C.3 Partial Correction of Skin Thickness Error
The optical absorption at 460 and 585 nm are determined from the
reflectance measurements, as explained in Section 3. At these two
wavelengths, the reflectance measured from skin of finite thickness
is less than that predicted for an infinitely thick medium, as
explained above. The effect that finite skin thickness has on the
measured reflectance can be corrected for approximately in the
iteration procedure used to determine the absorbance. This
correction is performed by lowering the predicted reflectance
calculated during the iteration procedure, as to account for the
finite skin thickness. This is illustrated in FIG. 47. The
predicted reflectance, M, is multiplied by a constant, c, before it
is compared to the actual measured reflectance. The constant, c is
selected based on the estimated maturity of the skin, and is equal
to the fraction of measured reflectance of finite thickness skin
relative to infinite thickness skin, as presented in section C.2.2.
Equation 4-18 in Section 4 relates skin thickness (in m) to
gestational maturity (in weeks). It is rewritten here:
To determine the relationship between gestational maturity and the
correction factor, c, Equation C-3 can be combined with Equations
C-1 and C-2 to yield:
for 460-nm light, and:
for 585-nm light.
The adjustment in the iteration procedure described above will
correct for the fact that skin is of finite thickness, but will not
account for the variation of skin thicknesses for a given estimated
gestational maturity. Reflectance measurements between 650 and 750
nm are not corrected in the manner above, since the correlation of
837-nm reflectance to gestational age is performed with uncorrected
measurements. Therefore, this correlation also accounts for any
increase in skin thickness associated with gestational age in
addition to changes in scattering profiles.
APPENDIX D
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