U.S. patent application number 09/789427 was filed with the patent office on 2001-07-26 for three-dimensional reconstruction of intrabody organs.
Invention is credited to Reisfeld, Daniel.
Application Number | 20010009974 09/789427 |
Document ID | / |
Family ID | 22400876 |
Filed Date | 2001-07-26 |
United States Patent
Application |
20010009974 |
Kind Code |
A1 |
Reisfeld, Daniel |
July 26, 2001 |
Three-dimensional reconstruction of intrabody organs
Abstract
A method of reconstructing a map of a volume, including
determining coordinates of a plurality of locations on a surface of
the volume having a configuration, generating a grid of points
defining a reconstruction surface in 3D space in proximity to the
determined locations, for each of the points on the grid, defining
a respective vector, dependent on a displacement between one or
more of the points on the grid and one or more of the locations,
and adjusting the reconstruction surface by moving substantially
each of the points on the grid responsive to the respective vector,
so that the reconstruction surface is deformed to resemble the
configuration of the surface.
Inventors: |
Reisfeld, Daniel; (Haifa,
IL) |
Correspondence
Address: |
Philip S. Johnson, Esq.
Johnson & Johnson
One Johnson & Johnson Plaza
New Brunswick
NJ
08933-7003
US
|
Family ID: |
22400876 |
Appl. No.: |
09/789427 |
Filed: |
February 21, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09789427 |
Feb 21, 2001 |
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09122137 |
Jul 24, 1998 |
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6226542 |
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Current U.S.
Class: |
600/407 |
Current CPC
Class: |
A61B 5/282 20210101;
A61B 5/341 20210101; G06T 2210/41 20130101; A61B 2562/17 20170801;
G06T 17/20 20130101 |
Class at
Publication: |
600/407 |
International
Class: |
A61B 005/05 |
Claims
What is claimed is:
1. A method of constructing a map of a body organ having a volume
comprising: determining coordinates of a plurality of locations
having a configuration on a surface of the volume; generating a
grid of points defining a reconstruction surface in 3D space in
proximity to the determined locations; for each of the points on
the grid, defining a respective vector, dependent on a displacement
between one or more of the points on the grid and one or more of
the locations; and adjusting the reconstruction surface by moving
substantially each of the points on the grid responsive to the
respective vector, so that the reconstruction surface is deformed
to resemble the configuration of the surface.
2. A method according to claim 1, wherein generating the grid
comprises acquiring an image of the volume and defining the
reconstruction surface such that it resembles the image of the
volume.
3. A method according to claim 1, wherein adjusting the surface
comprises a rough adjustment stage and a flexible matching
stage.
4. A method according to claim 3, wherein the rough adjustment
stage comprises moving each point on the grid toward a respective
weighted center of mass of the determined locations, wherein
locations closer to the point on the grid are given larger
weight.
5. A method according to claim 4, wherein moving each point
comprises defining, for each of the points on the grid, a
respective rough adjustment vector which comprises a weighted sum
of vectors from the point to each of the determined locations and
moving the points a distance proportional to the respective
vector.
6. A method according to claim 3, wherein the flexible matching
stage comprises selecting a grid point to be associated
respectively with each of the determined locations.
7. A method according to claim 6, wherein the flexible matching
stage comprises moving the selected grid points toward their
respective determined locations.
8. A method according to claim 7, wherein the flexible matching
stage comprises defining a displacement function which comprises a
weighted sum of vectors, each vector connecting a location and its
associated point.
9. A method according to claim 7, wherein the flexible matching
stage comprises moving the grid points according to the
displacement function so as to smooth the surface.
10. A method according to claim 1, wherein determining the
coordinates comprises positioning a catheter tip at the plurality
of locations.
11. A method according to claim 10, wherein positioning the
catheter tip comprises positioning the catheter at a plurality of
locations in a chamber of the heart.
12. A method according to claim 1, and comprising acquiring a
signal indicative of a value of physiological activity at
substantially each of the plurality of locations.
13. A method according to claim 1, wherein the volume is in motion,
and wherein determining the coordinates comprises determining a
correction factor responsive to the motion.
14. A method according to claim 13, wherein the motion comprises
cyclic motion, and wherein determining the correction factor
comprises determining a factor responsive to a cycle frequency of
the motion.
15. A method according to claim 1, and comprising estimating a
measure of the volume responsive to the reconstructed surface by
choosing a point inside the grid and calculating the volumes of
tetrahedrons defined by the chosen point and groups of three points
on the grid which cover the entire grid surface.
16. Apparatus for constructing a map of a body organ having volume
from coordinates of a plurality of determined locations having a
configuration on a surface of the volume, comprising: a processor,
which receives the coordinates and generates a grid of points
defining a reconstruction surface in 3D space in proximity to the
determined locations, and which defines a respective vector for
each of the points on the grid, dependent on a displacement between
one or more of the points on the grid and one or more of the
locations, and which adjusts the reconstruction surface by moving
each of the points on the grid responsive to the respective vector,
so that the reconstruction surface is deformed to resemble the
configuration of the surface of the volume.
17. Apparatus as in claim 16, and comprising a display screen for
displaying the adjusted surface.
18. Apparatus as in claim 16, and comprising an imaging device for
acquiring an image of the volume, wherein the processor defines the
grid initially such that it resembles the image of the volume.
18. Apparatus according to claim 16, and comprising a probe, which
is brought into engagement with the surface to determine the
locations thereon.
19. Apparatus according to claim 18, wherein the probe comprises a
position sensor which indicates the position of a tip of the
probe.
20. Apparatus according to claim 18, wherein the probe comprises a
functional portion for acquiring a value of a physiological
activity at the plurality of locations.
21. Apparatus according to claim 19, and comprising a reference
catheter for registering the determined locations relative to a
frame of reference associated with the volume.
22. A method of displaying values of a parameter which varies over
a surface of a portion of the human body, comprising: determining a
value of the parameter at each of a plurality of points on the
surface; and rendering an image of the surface to a display with a
different degree of transparency in different areas of the surface,
responsive in each of the areas to the value of the parameter at
one or more points in the area.
23. A method according to claim 22, wherein determining the value
comprises sampling a plurality of points and creating a map of the
surface responsive thereto, and wherein rendering the image
comprises rendering a graphic representation of the map.
24. A method according to claim 22, wherein rendering the image
comprises rendering one or more of the areas having a low measure
of reliability relative to another one or more of the areas with a
relatively greater degree of transparency.
25. A method according to claim 23, wherein the plurality of points
comprises sampled points and interpolated points, and further
comprising the value comprises determining a measure of reliability
of the map in each of the areas; wherein determining the measure of
reliability comprises assigning measures of reliability to the
interpolated points according to their respective distance from a
closest sampled point.
Description
FIELD OF THE INVENTION
[0001] The present invention relates generally to systems and
methods for mapping, and specifically to methods of mapping of
intrabody organs.
BACKGROUND OF THE INVENTION
[0002] Cardiac mapping is used to locate aberrant electrical
pathways and currents within the heart, as well as mechanical and
other aspects of cardiac activity. Various methods and devices have
been described for mapping the heart. Such methods and device are
described, for example, in U.S. Pat. Nos. 5,471,982 and 5,391,199
and in PCT patent publications WO94/06349, WO96/05768 and
WO97/24981. U.S. Pat. No. 5,391,199, for example, describes a
catheter including both electrodes for sensing cardiac electrical
activity and miniature coils for determining the position of the
catheter relative to an externally-applied magnetic field. Using
this catheter a cardiologist may collect a set of sampled points
within a short period of time, by determining the electrical
activity at a plurality of locations and determining the spatial
coordinates of the locations.
[0003] In order to allow the surgeon to appreciate the determined
data, a map, preferably a three dimensional (3D) map, including the
sampled points is produced. U.S. Pat. No. 5,391,199 suggests
superimposing the map on an image of the heart. The positions of
the locations are determined with respect to a frame of reference
of the image. However, it is not always desirable to acquire an
image, nor is it generally possible to acquire an image in which
the positions of the locations can be found with sufficient
accuracy.
[0004] Various methods are known in the art for reconstructing a 3D
map of a cavity or volume using the known position coordinates of a
plurality of locations on the surface of the cavity or volume. Some
methods include triangulation, in which the map is formed of a
plurality of triangles which connect the sampled points. In some
cases a convex hull or an alpha-hull of the points is constructed
to form the mesh, and thereafter the constructed mesh is shrunk
down to fit on the sampled points within the hull. Triangulation
methods do not provide a smooth surface and therefore require
additional stages of smoothing.
[0005] Another method which has been suggested is forming a
bounding ellipsoid which encloses the sampled points. The sampled
points are projected onto the ellipsoid, and the projected points
are connected by a triangulation method. The triangles are
thereafter moved with the sampled points back to their original
locations, forming a crude piecewise linear approximation of the
sampled surface. However, this method may reconstruct only surfaces
which have a star shape, i.e., a straight line connecting a center
of the reconstructed mesh to any point on the surface does not
intersect the surface. In most cases heart chambers do not have a
star shape.
[0006] In addition, reconstruction methods known in the art require
a relatively large number of sampled locations to achieve a
suitable reconstructed map. These methods were developed, for
example, to work with CT and MRI imaging systems which provide
large numbers of points, and therefore generally work properly only
on large numbers of points. In contrast, determining the data at
the locations using an invasive catheter is a time-consuming
process which should be kept as short as possible, especially when
dealing with a human heart. Therefore, reconstruction methods which
require a large number of determined locations are not
suitable.
SUMMARY OF THE INVENTION
[0007] It is an object of the present invention to provide an
improved method for creating a map of a 3D volume or cavity, based
on the positions of points on a surface of the volume or
cavity.
[0008] It is an object of some aspects of the present invention to
provide methods and apparatus for generating a map of a volume in
the human body from a plurality of sampled points, regardless of
the shape of the volume.
[0009] It is another object of some aspects of the present
invention to provide a simple, rapid method for reconstructing a 3D
map of a volume in the human body from a plurality of sampled
points, preferably using fewer sampled points than is feasible
using methods known the art.
[0010] It is another object of preferred embodiments of the present
invention to provide a method for reconstructing a 3D map of a
volume in the human body from a plurality of sampled points,
without assuming any topological relationship between the
points.
[0011] It is another object of some aspects of the present
invention to provide a simple method for reconstructing a 3D map of
a volume in movement.
[0012] It is another object of some aspects of the present
invention to provide a simple method for reconstructing a 3D map of
a volume in the human body from a plurality of sampled points
independent of the sampling order.
[0013] It is another object of some aspects of the present
invention to provide a quick method for reconstructing a 3D map of
a volume in the human body from a plurality of sampled points, such
that the method may be used in interactive procedures.
[0014] It is another object of some aspects of the present
invention to provide a method for reconstructing a smooth 3D map of
a volume in the human body from a plurality of sampled points.
[0015] In preferred embodiments of the present invention, a
processor reconstructs a 3D map of a volume or cavity in a
patient's body (hereinafter referred to as the volume), from a
plurality of sampled points on the volume whose position
coordinates have been determined. In contrast to prior art
reconstruction methods in which a large number of sampled points
are used, the preferred embodiments of the present invention are
directed to reconstruction of a surface based on a limited number
of sampled points. The number of sampled points is generally less
than 200 points and may be less than 50 points. Preferably, ten to
twenty sampled points are sufficient in order to perform a
preliminary reconstruction of the surface to a satisfactory
quality.
[0016] An initial, generally arbitrary, closed 3D curved surface
(also referred to herein for brevity as a curve) is defined in a
reconstruction space in the volume of the sampled points. The
closed curve is roughly adjusted to a shape which resembles a
reconstruction of the sampled points. Thereafter, a flexible
matching stage is preferably repeatedly performed once or more to
bring the closed curve to accurately resemble the shape of the
actual volume being reconstructed. Preferably, the 3D surface is
rendered to a video display or other screen for viewing by a
physician or other user of the map.
[0017] In preferred embodiments of the present invention, the
initial closed curved surface encompasses substantially all the
sampled points or is interior to substantially all the sampled
points. However, it is noted that any curve in the vicinity of the
sampled points is suitable. Preferably, the closed 3D curved
surface comprises an ellipsoid, or any other simple closed curve.
Alternatively, a non-closed curve may be used, for example, when it
is desired to reconstruct a single wall rather than the entire
volume.
[0018] A grid of a desired density is defined on the curve, and
adjustment of the curve is performed by adjusting the grid points.
The grid preferably divides the curved surface into quadrilaterals
or any other polygons such that the grid evenly defines points on
the curve. Preferably, the grid density is sufficient such that
there are generally more grid points than sampled points in any
arbitrary vicinity. Further preferably, the grid density is
adjustable according to a desired compromise between reconstruction
accuracy and speed.
[0019] In some preferred embodiments of the present invention,
external information is used to choose an initial closed curve
which is more closely related to the reconstructed volume, for
example, using the image of the volume, as described above. Thus,
the reconstruction procedure may produce a more accurate
reconstruction in less time. Alternatively or additionally, a
database of closed curves suitable for various volumes of the body
is stored in a memory, and the curve to be used is chosen according
to the specific procedure. In a further preferred embodiment of the
present invention, a map of a reconstructed volume in a patient is
used as a beginning curve for subsequent mapping procedures
performed at later times on the same volume.
[0020] Preferably, the rough adjustment of the closed curve is
performed in a single iteration, most preferably by calculating for
each grid point an adjustment point, and moving the grid point a
fraction of the distance to the adjustment point. Preferably, the
grid point is moved about 50-80% of the distance between its
original point and the adjustment point, more preferably about
75%.
[0021] The adjustment point is preferably determined by taking a
weighted sum over substantially all the sampled points. Preferably,
the weights are inversely related to the distances from the
adjusted grid point to the sampled points, referred to herein as
grid distances. In a preferred embodiment of the present invention,
each weight is defined as the reciprocal of the sum of a small
constant plus the grid distance, raised to a predetermined power,
so that sampled points close to the grid point are given a larger
weight. Preferably, the power is approximately between 4 to 9, most
preferably 8. The small constant is preferably smaller than the
magnitude of the smallest grid distance, and is preferably of the
size of the accuracy of the determination of the coordinates of the
sampled points. The small constant is used to prevent division by
zero when a grid-point is on a sampled point.
[0022] In some preferred embodiments of the present invention, the
weights also include a factor which is indicative of the density of
points in the vicinity of their corresponding point. Preferably,
the weight is multiplied by a density value between zero and one,
indicative of the density, such that isolated sampled points
influence the sum more than sampled points in a dense area.
Preferably, the influence of the points is thus substantially
independent of the density of points in their vicinity.
[0023] In a preferred embodiment of the present invention, the
flexible matching step is performed by associating each sampled
point with a corresponding grid-point, such that each sampled point
is associated with the grid point which is closest to it. A
movement vector is calculated for each of the associated and
non-associated grid-points. Preferably, the movement vectors are
calculated based on vectors from the associated grid points to
their respective sampled points. Further preferably, the sampled
points influence the value of the movement vector for a specific
point according to their proximity to the specific point. In
addition, the function by which the movement vectors are calculated
is preferably smooth and does not include complicated calculations.
Preferably, the function is a weighted sum of the vectors from the
associated grid points to their respective sampled points. The grid
points are then moved according to their respective movement
vectors.
[0024] Additionally or alternatively, the associated grid points
are moved toward their corresponding sampled points by a percentage
of the distance between them. Those grid points which are not
associated with a sampled point are moved a distance which is
determined by interpolation between the distances which surrounding
points on the grid are moved. Preferably, the resulting grid is
smoothed using a suitable smoothing transformation. Preferably, the
process of associating and moving is repeated two or more times to
allow finer adjustment of the closed curve.
[0025] In a preferred embodiment of the present invention, a user
can adjust the number of times the flexible matching step is
repeated according to a desired compromise between image quality
and speed. Alternatively or additionally, a quick reconstruction is
first provided to the user, and thereafter the calculation is
repeated to receive a finer reconstruction. Preferably, the weights
of the weighted sum used in the flexible matching stage are
adjusted according to the number of times the matching is to be
performed. Alternatively or additionally, the weights are
determined for each flexible matching step according to its place
in the sequential order of the flexible matching steps.
[0026] Preferably, the distances used for the weights and/or for
interpolation are Euclidean geometrical distances between the
points. The Euclidean distance is easily computed and causes points
on opposite walls of the volume to mutually repel, so that the
walls do not intersect. Alternatively, other distances, such as the
distance along the original or adjusted grid, may be used. In a
preferred embodiment of the present invention, during the first
flexible matching step the distance used is the distance along the
original grid while subsequent flexible matching steps use the
Euclidean distance.
[0027] In some preferred embodiments of the present invention, a
smoothing process is applied to the reconstructed surface,
preferably by applying a surface convolution with a Gaussian-like
kernel. The smoothing process provides a better approximation of
the surface and allows easier performance of calculations based on
the reconstructed surface. However, applying the surface
convolution results in some shrinkage of the surface, and therefore
an affine transformation is preferably performed on the smoothed
surface. The affine transformation is preferably chosen according
to those sampled points which are external to the reconstructed
surface. The chosen affine transformation preferably minimizes the
mean square distance of the external points to the surface.
[0028] Preferably, when the reconstruction is finished, each
sampled point substantially coincides with a grid point. In some
preferred embodiments of the present invention, a final exact
matching stage is performed. Each sampled point is associated with
a closest grid point, and the associated grid point is moved onto
the sampled point. The rest of the grid points are preferably not
moved. Generally, most of the sampled points are by this stage very
close to the reconstructed surface, and therefore the smoothness of
the surface is substantially not affected. However, some outlier
sampled points, i.e., sampled points which do not belong to the
surface, may cause substantial changes to the surface. Preferably,
the user may determine whether to move the surface onto points that
are distanced from the surface by more than a predetermined maximum
distance. Alternatively or additionally, the entire exact matching
step is optional and is applied only according to a user
request.
[0029] Further alternatively or additionally, the grid points are
brought to a fixed distance from the sampled points. Leaving such a
fixed distance may be desired, for example, when the sampled
coordinates are of locations close to a distal tip of a sampling
catheter rather than at the distal tip itself.
[0030] In preferred embodiments of the present invention, data
regarding the sampled points are acquired by positioning a catheter
within the volume which is to be reconstructed, for example, within
a chamber of the heart. The catheter is positioned with a distal
end thereof in contact with each of the sampled points in turn, and
the coordinates of the points and, optionally, values of one or
more physiological parameters are sensed at a distal end of the
catheter. Preferably, the catheter comprises a coordinate sensor
close to its distal end, which outputs signals indicative of the
coordinates of the tip of the catheter. Preferably, the coordinate
sensor determines the position by transmitting and receiving
electromagnetic waves, as described, for example, in PCT
publications GB93/01736, WO94/04938, WO97/24983 and WO96/05768, or
in U.S. Pat. No. 5,391,199, commonly owned by the present assignee
and which are all incorporated herein by reference.
[0031] In some preferred embodiments of the present invention, the
reconstructed volume is in movement, for example, due to beating of
the heart. In such embodiments, the sampled points are preferably
registered with a reference frame fixed to the heart. Preferably, a
reference catheter is fixed in the heart, and the sampled points
are determined together with the position of the reference catheter
which is used to register the points, as described, for example, in
the above-mentioned U.S. Pat. No. 5,391,199 and PCT publication
WO96/05768.
[0032] Alternatively or additionally, when at least part of the
movement is a cyclic movement, as in the heart, acquisition of the
sampled points is synchronized to a specific time point of the
cycle. Preferably, when the sampled volume is in the heart, an ECG
signal is received and is used to synchronize the acquisition of
the sampled points. For example, the sampled points may be acquired
at end diastole. Further alternatively or additionally, the
coordinates of each of the sampled points are determined together
with an indication of the time point relative to the cyclic
movement in which the coordinates were acquired. Preferably, the
indication includes the relative time from the beginning of the
cycle and the frequency of the cyclic movement. According to the
frequency and the relative time, the determined coordinates are
corrected to end diastole, or any other point in the cyclic
movement.
[0033] In some preferred embodiments of the present invention, for
each sampled point a plurality of coordinates are determined at
different time points of the cyclic movement. In one of these
preferred embodiments, each sampled point has two coordinates which
define the range of movement of the point. Preferably, if the
plurality of coordinates of different points are associated with
different cycle frequencies, the coordinates are transformed so as
to correspond to a set of coordinates in a single-frequency cyclic
movement. Further preferably, the coordinates are processed so as
to reduce or substantially eliminate any contribution due to
movement other than the specific (cardiac) cyclic movement, such as
movement of the chest due to respiration. Reconstruction is
performed for a plurality of configurations of the volume at
different time points of the cyclic movement. Preferably, a first
reconstruction is performed as described above to form an anchor
reconstruction surface, and reconstruction of surfaces for other
time points of the cycle are performed relative to the anchor
reconstruction surface.
[0034] Preferably, for each further time point of the cyclic
movement, the anchor surface is adjusted according to the
coordinates of the sampled points at the further time point
relative to the coordinates of the sampled points of the anchor
surface. Preferably, the anchor surface is adjusted by a quadratic
transformation which minimizes a mean square error, the error
representing the distances between the sampled points of the
further time point and the adjusted surface. Alternatively or
additionally, an affine transformation is used instead of the
quadratic transformation. Further alternatively or additionally, a
simple transformation is used for surfaces having relatively few
sampled points, while surfaces with a relatively large number of
sampled points a quadratic transformation is used. The simple
transformation may be an affine transformation, a scaling and
rotation transformation, a rotation transformation, or any other
suitable transformation.
[0035] Preferably, the adjustment of the surface for the further
time points includes, after the transformation, one or more,
preferably two, flexible matching steps and/or an exact matching
stage.
[0036] Alternatively or additionally, the reconstruction is
performed separately for each of the further time points. Further
alternatively or additionally, a first reconstruction of the
surfaces for the further time points is performed relative to the
anchor surface, and afterwards a more accurate reconstructed is
performed for each time point independently.
[0037] In some preferred embodiments of the present invention,
dedicated graphics hardware which is designed to manipulate
polygons is used to perform the reconstruction stages described
above.
[0038] In some preferred embodiments of the present invention, one
or more physiological parameters are acquired at each sampled
point. The physiological parameters for the heart may comprise a
measure of cardiac electrical activity, for example, and/or may
comprise any other type of local information relating to the heart,
as described in the PCT patent publication WO97/24981, also owned
by the present assignee and further incorporated herein by
reference. The one or more physiological parameters may be either
scalars or vectors and may comprise, for example, a voltage,
temperature, pressure, or any other desired value.
[0039] Preferably, after the volume is reconstructed based on the
coordinates, values of the physiological parameter are determined
for each of the grid points based on interpolation of the parameter
value at surrounding sampled points. Preferably, the interpolation
of the physiological parameter is performed in a manner
proportional to the aggregate interpolation of the coordinates.
Alternatively, the physiological parameters are interpolated
according to the geometrical distance between the points on the
grid. Alternatively or additionally, the physiological parameters
are interpolated in a manner similar to the flexible matching step
described hereinabove.
[0040] The reconstructed surface may be displayed in movement,
and/or a physician may request a display of a specific time point
of the cycle. Preferably, the physiological parameter is displayed
on the reconstructed surface based on a predefined color scale. In
a preferred embodiment of the present invention, the reliability of
reconstruction of regions of the reconstructed surface is indicated
on the displayed surface. Preferably, regions which are beneath a
user-defined threshold are displayed as semi-transparent, using
known methods such as .alpha.-blending. Preferably, the reliability
at any grid point is determined according to its proximity to
sampled points. Those points on the grid which are beyond a
predetermined distance from the nearest sampled point are less
reliable.
[0041] In some preferred embodiments of the present invention,
acquired images such as LV-grams and fluoroscopic images are used
together with the sampled points to enhance the speed and/or
accuracy of the reconstruction. Preferably, the processor performs
an object recognition procedure on the image to determine the shape
of the closed 3D curved surface to use in constructing the initial
grid of the reconstruction. Alternatively or additionally, the
image is used by the physician to select areas in which it is most
desired to receive sampled points.
[0042] In some preferred embodiments of the present invention, the
physician may define points, lines, or areas on the grid which must
remain fixed and are not to be adjusted. Alternatively or
additionally, some points may be acquired as interior points which
are not to be on the map since they are not on a surface of the
volume. The reconstruction procedure is performed accordingly so
that the closed curve is not moved too close to the interior
points.
[0043] In some preferred embodiments of the present invention, the
reconstruction surface is used to determine an accurate estimate of
the volume of the cavity. The surface is divided by the grid points
into quadrilaterals, and each quadrilateral is further divided into
two triangles. Based on these triangles the volume defined by the
surface is estimated. Alternatively, the volume is calculated using
a volumetric representation. Other measurements, such as geodesic
surface measurements on the surface, may also be performed using
the reconstructed surface.
[0044] It is noted that some of the stages described above may be
ignored in some preferred embodiments of the invention, in order to
save processing time and speed up the reconstruction procedure.
[0045] There is therefore provided in accordance with a preferred
embodiment of the present invention, a method of reconstructing a
map of a volume, including determining coordinates of a plurality
of locations on a surface of the volume having a configuration,
generating a grid of points defining a reconstruction surface in 3D
space in proximity to the determined locations, for each of the
points on the grid, defining a respective vector, dependent on a
displacement between one or more of the points on the grid and one
or more of the locations, and adjusting the reconstruction surface
by moving substantially each of the points on the grid responsive
to the respective vector, so that the reconstruction surface is
deformed to resemble the configuration of the surface.
[0046] Preferably, the method includes displaying the
reconstruction surface.
[0047] Preferably, generating the grid includes generating a grid
such that the reconstruction surface encompasses substantially all
of the determined locations or is interior to substantially all of
the determined locations.
[0048] Preferably, generating the grid includes defining an
ellipsoid.
[0049] Preferably, the reconstruction surface is defined and
adjusted substantially independently of any assumption regarding a
topology of the volume.
[0050] Further preferably, the reconstruction surface is defined
and adjusted substantially without reference to any point within
the volume.
[0051] Alternatively or additionally, generating the grid includes
acquiring an image of the volume and defining the reconstruction
surface such that it resembles the image of the volume.
[0052] Further alternatively or additionally, generating the grid
includes choosing a grid from a memory library according to at
least one characteristic of the volume.
[0053] Preferably, adjusting the surface includes a rough
adjustment stage and a flexible matching stage.
[0054] Preferably, the rough adjustment stage includes moving each
point on the grid toward a respective weighted center of mass of
the determined locations, and locations closer to the point on the
grid are given larger weight.
[0055] Preferably, moving each point in the rough adjustment stage
includes defining, for each of the points on the grid, a respective
rough adjustment vector which includes a weighted sum of vectors
from the point to each of the determined locations and moving the
points a distance proportional to the respective vector.
[0056] Preferably, defining the rough adjustment vector includes
calculating a weight for each of the summed vectors that is
generally inversely proportional to a magnitude of the summed
vector raised to a predetermined power.
[0057] Preferably, the weight includes an inverse of a sum of a
constant and the magnitude of the vector raised to a power between
4 and 10.
[0058] Preferably, the constant is smaller than a precision of the
location determination.
[0059] Preferably, moving each point includes moving each point
toward a respective target point by a distance between 50 and 90%
of the distance between the point and the target point.
[0060] Preferably, the flexible matching stage includes selecting a
grid point is to be associated respectively with each of the
determined locations.
[0061] Preferably, selecting the grid point includes finding for
each determined location a point on the grid that is substantially
closest thereto.
[0062] Further preferably, the flexible matching stage includes
moving the selected grid points toward their respective determined
locations.
[0063] Preferably, moving the selected grid points includes moving
the grid points substantially onto their respective, determined
locations.
[0064] Preferably, the flexible matching stage includes moving grid
points that were not selected by an amount dependent on the
movements of surrounding grid points.
[0065] Preferably, moving the grid points that were not selected
includes moving the grid points by an amount dependent
substantially only on the movements of surrounding selected grid
points.
[0066] Preferably, moving the grid points includes calculating a
movement of a grid point that was not selected based on the
movements of the surrounding selected grid points and distances
from these surrounding grid points.
[0067] Preferably, calculating the movement of the grid point
includes interpolating between the movements of surrounding grid
points.
[0068] Preferably, the distances include geometrical distances.
Alternatively or additionally, the distances include a length of
the reconstruction surface between the grid points.
[0069] Preferably, the flexible matching stage includes defining a
displacement function which includes a weighted sum of vectors,
each vector connecting a location and its associated point.
[0070] Preferably, the flexible matching stage includes moving the
grid points according to the displacement function so as to smooth
the surface.
[0071] Preferably, determining the coordinates includes positioning
a catheter tip at the plurality of locations.
[0072] Preferably, positioning the catheter tip includes
positioning the catheter at a plurality of locations in a chamber
of the heart.
[0073] Preferably, determining the coordinates includes positioning
a catheter tip at the plurality of locations.
[0074] Preferably, determining the coordinates includes
transmitting and receiving non-ionizing waves.
[0075] Preferably, determining the coordinates includes positioning
at the plurality of locations a device which generates signals
indicative of the position of the device.
[0076] Preferably, the device generates signals indicative of the
six degrees of position and orientation of the device.
[0077] Preferably, determining the coordinates includes receiving
the coordinates from an external source.
[0078] Preferably, the method includes acquiring a signal
indicative of a value of physiological activity at substantially
each of the plurality of locations.
[0079] Preferably, acquiring the signal includes acquiring a signal
indicative of a value of electrical activity at the location.
[0080] Preferably, the method includes estimating a value of the
physiological activity at the adjusted grid points.
[0081] Preferably, estimating the value of the physiological
activity includes estimating based on an acquired value of the
physiological activity at a location in a vicinity of the adjusted
grid points.
[0082] Preferably, estimating based on the acquired value includes
interpolating the value responsive to deformation of the
reconstruction surface.
[0083] Preferably, determining coordinates of a plurality of
locations includes determining coordinates of less than 200
locations, more preferably of less than 50 locations, and most
preferably of less than 20 locations.
[0084] Preferably, the volume is in motion, and determining the
coordinates includes determining a correction factor responsive to
the motion.
[0085] Preferably, the motion includes cyclic motion, and
determining the correction factor includes determining a factor
responsive to a cycle frequency of the motion.
[0086] Preferably, determining the factor includes filtering out
motion at a frequency substantially different from the cycle
frequency.
[0087] Preferably, the motion includes cyclic motion, and
determining the coordinates includes determining the coordinates at
a predetermined phase of the cyclic motion.
[0088] Preferably, determining the coordinates at the predetermined
phase includes determining the coordinates in a plurality of time
points and adjusting the coordinates relative to the cyclic
movement.
[0089] Preferably, adjusting the coordinates includes determining a
rate of the cyclic movement together with the coordinates for
substantially each coordinate determination.
[0090] Preferably, generating the grid and adjusting the
reconstruction surface are performed separately with respect to the
coordinates determined in each phase of the cyclic motion.
[0091] Alternatively or additionally, generating and adjusting are
performed for the coordinates of a plurality of phases of the
cyclic motion so as to form a motion map of the volume.
[0092] Preferably, generating the grid and adjusting the
reconstruction surface are performed for a first group of
coordinates determined in a first phase of the cyclic motion, and
the reconstructed surface of the first group is adjusted to form a
reconstructed surface in one or more additional phases.
[0093] Preferably, the method includes smoothing the reconstructed
surface.
[0094] Preferably, the method includes applying an affine
transformation to the reconstructed surface.
[0095] Preferably, the method includes a final stage in which each
determined location is associated with a respective grid point, and
the associated grid points are moved onto the determined locations
while non-associated grid points are substantially not moved.
[0096] Preferably, the method includes estimating a measure of the
volume responsive to the reconstructed surface.
[0097] Preferably, estimating the measure of the volume includes
choosing an arbitrary point inside the grid and calculating the
volumes of tetrahedrons defined by the arbitrary point and groups
of three points on the grid which cover the entire grid
surface.
[0098] There is further provided in accordance with a preferred
embodiment of the present invention, apparatus for reconstructing a
map of a volume from coordinates of a plurality of determined
locations on a surface of the volume having a configuration,
including a processor, which receives the coordinates and generates
a grid of points defining a reconstruction surface in 3D space in
proximity to the determined locations, and which defines a
respective vector for each of the points on the grid, dependent on
a displacement between one or more of the points on the grid and
one or more of the locations, and which adjusts the reconstruction
surface by moving each of the points on the grid responsive to the
respective vector, so that the reconstruction surface is deformed
to resemble the configuration of the surface of the volume.
[0099] Preferably, the apparatus includes a display screen for
displaying the adjusted surface.
[0100] Preferably, the processor analyzes the adjusted surface to
determine a characteristic of the volume.
[0101] Preferably, the apparatus includes a memory for storing the
adjusted surface.
[0102] Preferably, the grid initially encompasses substantially all
of the determined locations.
[0103] Preferably, the apparatus includes an imaging device for
acquiring an image of the volume, and the processor defines the
grid initially such that it resembles the image of the volume.
[0104] Preferably, the apparatus includes a memory library
including a plurality of closed curves, and the processor defines
the grid initially by choosing a closed curve from the memory
library according to at least one characteristic of the volume.
[0105] Preferably, the processor generates and defines the
reconstruction surface substantially independently of any
assumption regarding a topology of the volume.
[0106] Preferably, the processor generates and defines the
reconstruction surface substantially without reference to any point
within the volume.
[0107] Preferably, the processor forms the adjusted grid in two
stages: a rough adjustment stage and a flexible matching stage.
[0108] Preferably, in the rough adjustment stage, the processor
moves each point on the grid toward a respective weighted center of
mass of the determined locations, and locations closer to the point
on the grid are given larger weight.
[0109] Preferably, the processor calculates the center of mass
using a weight that is substantially proportional for each location
to the inverse of the sum of a small constant and the distance
between the point and the location raised to a power between 4 and
10.
[0110] Preferably, the constant is smaller than a precision of the
location determination.
[0111] Preferably, in the flexible matching stage, the processor
selects a respective grid point to associate with each of the
determined locations.
[0112] Preferably, the selected grid point for each determined
location includes a point on the grid that is closest to the
location.
[0113] Preferably, in the flexible matching stage, the processor
moves the selected grid points toward their respective, associated
locations.
[0114] Preferably, the processor moves the selected grid points
onto the associated locations.
[0115] Preferably, the processor moves non-selected grid points by
an amount dependent on the movements of surrounding grid
points.
[0116] Preferably, the amount of movement of the non-selected grid
points is dependent on the movements of surrounding selected grid
points.
[0117] Preferably, the amount of movement of each of non-selected
grid points is calculated by the processor based on the distances
from the surrounding selected grid points to the non-selected grid
point.
[0118] Preferably, the amount of movement of the non-associated
grid points is calculated by the processor based on an
interpolation of the movements of surrounding selected grid
points.
[0119] Preferably, the distances include geometrical distances.
Preferably, the apparatus includes a probe, which is brought into
engagement with the surface to determine the locations thereon.
[0120] Further preferably, the probe includes a position sensor
which indicates the position of a tip of the probe.
[0121] Preferably, the sensor includes at least one coil.
[0122] Preferably, the sensor generates signals indicative of
position and orientation of the sensor.
[0123] Alternatively or additionally, the probe includes a
functional portion for acquiring a value of a physiological
activity at the plurality of locations.
[0124] Preferably, the functional portion includes an
electrode.
[0125] Preferably, the processor estimates a value of the
physiological activity at the adjusted grid points.
[0126] Preferably, the processor estimates the value of the
physiological activity based on the acquired values of the
physiological activity at points surrounding the adjusted grid
points.
[0127] Preferably, the processor estimates the value by
interpolation from the acquired values responsive to deformation of
the reconstruction surface.
[0128] Preferably, the apparatus includes a reference catheter for
registering the determined locations relative to a frame of
reference associated with the volume.
[0129] Preferably, the apparatus includes an ECG monitor for gating
the operation of the probe so as to determine the points at a fixed
phase of a cyclic movement of the volume.
[0130] There is further provided in accordance with a preferred
embodiment of the present invention, a method of displaying values
of a parameter which varies over a surface, including determining a
value of the parameter at each of a plurality of points on the
surface, and rendering an image of the surface to a display with a
different degree of transparency in different areas of the surface,
responsive in each of the areas to the value of the parameter at
one or more points in the area.
[0131] Preferably, determining the value includes sampling a
plurality of points and creating a map of the surface responsive
thereto, and rendering the image includes rendering a graphic
representation of the map.
[0132] Preferably, creating the map includes creating a
three-dimensional map.
[0133] Preferably, determining the value includes determining a
measure of reliability of the map in each of the areas.
[0134] Preferably, rendering the image includes rending one or more
of the areas having a low measure of reliability relative to
another one or more of the areas with a relatively greater degree
of transparency.
[0135] Preferably, determining the measure of reliability includes
determining a density of the sampled points.
[0136] Preferably, rendering the image includes defining a color
scale and displaying a color associated with the value, at each of
the plurality of points.
[0137] Preferably, the plurality of points includes sampled points
and interpolated points, and determining the measure of reliability
includes assigning a high reliability measure to the sampled
points.
[0138] Preferably, determining the measure of reliability includes
assigning measures of reliability to the interpolated points
according to their respective distance from a closest sampled
point.
BRIEF DESCRIPTION OF THE DRAWINGS
[0139] The present invention will be more fully understood from the
following detailed description of the preferred embodiments
thereof, taken together with the drawings in which:
[0140] FIG. 1 is a schematic, perspective view of a heart mapping
system, in accordance with a preferred embodiment of the present
invention;
[0141] FIG. 2 shows a mapping catheter within a heart of a patient,
in accordance with a preferred embodiment of the present
invention;
[0142] FIG. 3 is a flow chart illustrating a method of point
sampling and map reconstruction, in accordance with a preferred
embodiment of the present invention;
[0143] FIG. 4 is a flow chart illustrating a reconstruction
procedure, in accordance with a preferred embodiment of the present
invention;
[0144] FIGS. 5A-5E are simplified, two dimensional graphs
illustrating reconstruction of a map from sampled points, in
accordance with a preferred embodiment of the present
invention;
[0145] FIG. 6 is a schematic illustration of a displayed
reconstructed heart volume, in accordance with a preferred
embodiment of the present invention;
[0146] FIG. 7 is an illustration of a volume estimation method, in
accordance with another preferred embodiment of the present
invention; and
[0147] FIG. 8 is an illustration of a reconstruction procedure, in
accordance with another preferred embodiment of the present
invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0148] FIG. 1 shows a mapping system 18 for mapping of a volume in
a patient's body, in accordance with a preferred embodiment of the
present invention. System 18 comprises an elongate probe,
preferably a catheter 20, for insertion into the human body. A
distal end 22 of catheter 20 includes a functional portion 24 for
performing diagnostic and/or therapeutic functions, adjacent to a
distal tip 26. Functional portion 24 preferably comprises
electrodes (not shown in the figure) for performing
electrophysiological measurements, as described, for example, in
U.S. Pat. No. 5,391,199 or in PCT publication WO97/24983, which are
incorporated herein by reference. Alternatively or additionally,
functional portion 24 may include other diagnostic apparatus for
recording parameter values at points within the body. Such
apparatus may include a chemical sensor, a temperature sensor, a
pressure sensor and/or any other desired sensor. Functional portion
24 may determine for each point a single value of the parameter, or
alternatively a plurality of values dependent on the time of their
acquisition. Functional portion 24 may also include therapeutic
apparatus, as is known in the art.
[0149] Distal end 22 of catheter 20 further includes a device 28
that generates signals used to determine the position and,
preferably, orientation of the catheter within the body. Device 28
is preferably adjacent to functional portion 24, in a fixed
relation with tip 26. Device 28 preferably comprises three
non-concentric coils, such as described in PCT patent publication
WO96/05768, whose disclosure is incorporated herein by reference.
This device enables continuous generation of six dimensions of
position and orientation information with respect to an
externally-applied magnetic field. Alternatively, device 28
comprises other position and/or coordinate sensors as described in
U.S. Pat. Nos. 5,391,199, 5,443,489 and PCT publication WO94/04938,
which are incorporated herein by reference. Further alternatively
or additionally, tip 26 is marked with a marker whose position can
be determined from outside of the body, for example, a radio-opaque
marker for use with a fluoroscope.
[0150] Catheter 20 preferably includes a handle 30, having controls
32 which are used by a surgeon to steer distal end 22 of the
catheter in a desired direction, so as to position and/or orient it
as desired. Catheter 20 preferably comprises a steering mechanism
in distal end 22, as is known in the art, so that repositioning of
tip 26 is facilitated.
[0151] Catheter 20 is coupled, via an extension cable 21, to a
console 34 which enables the user to observe and regulate the
functions of catheter 20. Console 34 preferably includes a computer
36, keyboard 38, signal processing circuits 40, which are typically
inside the computer, and display 42. Signal processing circuits 40
typically receive, amplify, filter and digitize signals from
catheter 20, including signals generated by position signal
generating device 28, whereupon these digitized signals are
received and used by computer 36 to compute the position and
orientation of the catheter. Alternatively, appropriate circuitry
may be associated with the catheter itself so that circuits 40
receive signals that are already amplified, filtered and/or
digitized. Preferably, computer 36 includes a memory for storing
positions and determined parameters of the points. Computer 36
preferably also includes dedicated graphic hardware for polygon
manipulation, which allows performing reconstruction stages
described hereinbelow using fast computer graphic techniques.
[0152] Preferably, system 18 also includes an ECG monitor 73,
coupled to receive signals from one or more body surface electrodes
52 and to convey the signals to computer 36. Alternatively, the ECG
monitoring function may be performed by circuits 40.
[0153] FIG. 2 shows a distal portion of mapping catheter 20 within
a heart 70 of a patient, in accordance with a preferred embodiment
of the present invention. Catheter 20 is inserted into heart 70 and
tip 26 is brought into contact with a plurality of locations, such
as locations 75 and 77 on an inner surface 72 of heart 70. Surface
72 bounds the volume to be reconstructed, and it is locations on
this surface which are to be sampled. At each of the plurality of
locations, the coordinates of tip 26 are determined by device 28,
preferably together with physiological information determined by
functional portion 24. The determined coordinates and, optionally,
physiological information form a local data point. The local data
points from a plurality of locations are used for producing a map
of heart 70, or of a portion of the heart.
[0154] At least one reference catheter 78 is preferably inserted
into heart 70 and is placed in a fixed position relative to the
heart. By comparing the positions of catheters 20 and 78, the
position of tip 26 is accurately determined relative to the heart,
irrespective of heart motion. Alternatively, any other suitable
method may be used to compensate for movement of heart 70.
[0155] Preferably, the coordinates of tip 26 at the plurality of
locations are determined at a common time-point in the cardiac
cycle, preferably at end-diastole. Alternatively or additionally,
each determined position is recorded together with a time-point,
preferably relative to a predetermined time-point in the cardiac
cycle, and together with indication of the current heart rate. The
relative time-point and the rate of the cycle are used to correct
for the movement of the heart. Thus, it is possible to determine
positions of a large number of points, simply, in a limited time
period.
[0156] Further alternatively or additionally, the position of tip
26 is determined at each location at two or more time-points in the
cardiac cycle, such that for each location, a range of positions
are determined. Thus, a geometric map of the plurality of locations
may comprise a plurality of "snapshots" of heart 70, each snapshot
associated with a different phase of the cardiac cycle. The cardiac
cycle is preferably determined using ECG monitor 73, according to
physiological readings from functional portion 24, or according to
movements of reference catheter 78. Preferably, each position is
determined together with the heart rate at the time of
determination. A frequency and phase shift transformation is
preferably applied to the plurality of positions at each location
to bring the positions to a state as if they were determined at
common time-points with respect to a common predetermined heart
rate.
[0157] Preferably, the transformation applied to the positions also
serves to reduce or eliminate the effects of any movement of the
heart that is not due to the cardiac cycle, particularly chest
movement due to respiration or other movements of the patient.
These effects are removed by defining a cyclic trajectory of the
points associated with each location, and then filtering out of the
trajectory frequencies of motion other than frequencies associated
with the heart rate. Preferably, any frequencies whose
corresponding wavelengths do not evenly divide the cardiac cycle
length, as determined from the ECG, are filtered out. The result
for each location is a modified trajectory, including a corrected
end-diastolic point, which is then used in reconstructing the map
of the heart, as described hereinbelow.
[0158] Preferably, at each location at which tip 26 is positioned,
it is verified that catheter 20 is in contact with the surface,
using any suitable method, for example, as described in PCT
publication WO97/24981, which is incorporated herein by
reference.
[0159] FIG. 3 is a flow chart illustrating the process of point
sampling and reconstruction of a map, in accordance with a
preferred embodiment of the present invention. As described above,
catheter 20 is brought into contact with surface 72 of heart 70,
and signals are received from the catheter to form a local data
point characteristic of the location of tip 26. The local data
point preferably includes coordinates of the point at a plurality
of time points and one or more values, associated with the point,
of at least one physiological parameter. Preferably, as mentioned
above, the local data point includes an indication of the heart
rate and time point in the heart cycle for each determined
coordinate. The parameter values may be associated with specific
time points or may be associated generally with the point.
[0160] Preferably, the contact between tip 26 and surface 72 is
verified and the point is added to the map only if there is
sufficient contact between the tip and the surface. In a preferred
embodiment of the present invention, points for which proper
contact does not exist are added to a database of interior points.
These points are interior to the reconstructed surface and indicate
areas on the map which are not part of the reconstructed surface.
Alternatively or additionally, the user may indicate sampled points
which are not to be used as part of the reconstructed surface, for
example because they are outstandingly outside of the area of the
other sampled points. Tip 26 is then moved to an additional
location on surface 72 and data are likewise determined regarding
the additional point. This procedure is repeated for a plurality of
sampled points until data are determined for a sufficient number of
points to make the map, or for a predetermined amount of time.
Preferably, computer 36 counts the number of sampled points and
compares the number of points to a predetermined required minimum
number of points. Preferably, the predetermined number of points is
between about ten to twenty points for fast procedures and is up to
100 points for longer procedures. Alternatively or additionally,
the physician notifies computer 36 when a sufficient number of
points have been sampled.
[0161] A map of heart 70 or of a volume within the heart is
reconstructed, as described below, and the physician decides
whether the map includes sufficient detail and appears to be
accurate. If the map is not sufficient, more points are acquired
and the map is accordingly updated or is again reconstructed. The
reconstructed map is thereafter used for analysis of the
functioning of heart 70, and the physician may decide on a required
treatment accordingly.
[0162] FIG. 4 is a flow chart illustrating a reconstruction
procedure, in accordance with a preferred embodiment of the present
invention. Reconstruction is initially performed for positions
determined at an anchor time point (t.sub.0) of the heart cycle,
such as end diastole. In a first stage of the initial
reconstruction, a grid enclosing the sampled points is constructed.
Thereafter, a stage of model distortion is applied to the grid, in
which the grid is roughly adjusted to the shape defined by the
sampled points. Subsequently, a preferably iterative stage of
flexible matching is carried out finely adjusting the grid points
according to the coordinates of the sampled points. Final
adjustment is preferably applied to the grid including smoothing,
an affine transformation and/or an exact matching stage which
brings the grid to include substantially all the sampled points.
The parameter values associated with the sampled points are
preferably interpolated to all the grid points and the grid is
subsequently displayed. This procedure is described in greater
detail hereinbelow with reference to the figures that follow.
[0163] FIGS. 5A-5E are simplified, two-dimensional graphs
illustrating the reconstruction procedure for a single time-point,
in accordance with a preferred embodiment of the present invention.
For clarity of illustration, the figures and the following
description refer to a simplified, two dimensional example. The
extension of the principles illustrated herein to 3D reconstruction
will be clear to those skilled in the art. Points S.sub.i are
sampled points on the surface of the volume to be reconstructed,
whose coordinates were received during the above-described sampling
process.
[0164] As shown in FIG. 5A, in the first stage, an initial grid 90
is defined in a vicinity of the sampled points, preferably
enclosing the sampled points. Alternatively, grid 90 may be
interior to the sampled points or pass between the points.
Preferably, grid 90 comprises a number of points substantially
greater than the number of sampled points. The density of the
points is preferably sufficient to produce a map of sufficient
accuracy for any required medical procedure. In a preferred
embodiment of the present invention, the physician can adjust the
density of points on the grid according to a desired compromise
between reconstruction speed and accuracy. Preferably, grid 90 has
an ellipsoidal shape or any other simple closed shape.
[0165] Alternatively or additionally, grid 90 has a shape based on
known characteristics of the volume on whose surface the sampled
points are located, for example, a shape determined by processing
an LV-gram or other fluoroscopic or ultrasound image of the heart.
In a preferred embodiment of the present invention, computer 36
contains a data-base of initial grids according to commonly-sampled
volumes. The physician indicates, preferably via keyboard 38, which
volume is being sampled and initial grid 90 is chosen accordingly.
The chosen grid may be initially aligned with the sample points
using any method known in the art, for example as described in Paul
J. Besl and Neil D. McKay, "A method for registration of 3-D
shapes," IEEE Transactions on Pattern Analysis and Machine
Intelligence, 14(2):239-258, February 1992, which is incorporated
herein by reference. The initial grid may alternatively be chosen
from the grid library using geometric hashing or alignment, as
described, for example, in Haim J. Wolfson, "Model-based object
recognition by geometric hashing," in: O. Faugeras, ed., Computer
Vision-ECCV90 (First European Conference on Computer Vision,
Antibes, France, Apr. 23-27, 1990), Springer, Berlin, 1990,
526-536, or in P. Huttenlocher and S. Ullman, "Recognizing solid
objects by alignment with an image," International Journal of
Computer Vision, 5: 195-212, 1990, which are incorporated herein by
reference. After the initial alignment, the method of the present
invention proceeds, preferably as shown in FIG. 4 and described
further hereinbelow.
[0166] As shown in FIG. 5B, grid 90 is transformed to a grid 92 of
points G', which is a rough adjustment toward the structure of the
sampled volume. For each point Gj on grid 90, an adjustment vector
{right arrow over (V)}.sub.j is constructed, and point Gj is
replaced by a corresponding point Gj' on grid 92, which is
displaced by {right arrow over (V)}.sub.j from point Gj on grid 90.
Adjustment vector {right arrow over (V)}.sub.j is preferably a
weighted sum of vectors {right arrow over (V)}.sub.ji from Gj to
the sampled points S.sub.i, as shown in FIG. 5A. Preferably, the
weights of vectors {right arrow over (V)}.sub.ji in the sum are
strongly inversely dependent on the magnitude of the vectors.
Preferably, the weights are inversely dependent on the magnitude
raised to a power (k), wherein k preferably ranges between 4 and
10, and is most preferably either between 6 and 8. In a preferred
embodiment of the present invention, adjustment vectors {right
arrow over (V)}.sub.j are calculated according to equation (1): 1 V
j = C f i V ij r j k + 1 r j k + , r j = V ij ( 1 )
[0167] In equation (1), epsilon is a small scalar, preferably,
smaller than the magnitude of the smallest vector which is not
zero, and is preferably of the size of the accuracy of the
determination of the sampled points, for example, about 10.sup.-6.
Epsilon is used to prevent division by zero when the grid point is
on a sampled point, and therefore the magnitude of the vector is
zero. C.sub.f is a constant factor between 0.1 and 1, preferably
between 0.5 and 0.9 most preferably about 0.75, which is adjusted
to determine how closely the points G.sub.j' will approach points
S.sub.i in the rough adjustment.
[0168] In a preferred embodiment, the influence of a sampled point
Si on grid point Gj, takes into account not only the distance
between the sampled point Si and Gj, as shown above in equation (1)
but also the density of sampled points S in the vicinity of Si.
Hence, the weighting factor applied to each sampled point, 2 1 r j
6 + ,
[0169] is multiplied by a density value .quadrature..sub.i, which
preferably takes on values between 0 and 1. Preferably,
.delta..sub.i is as defined in equation (2): 3 i = 1 j 1 ( ; S j -
S i r; 2 + 1 ) ( 2 )
[0170] The more points there are in the vicinity of S, the smaller
value .delta. takes on and the less influence each point has.
Preferably, the sum of influences of a plurality of points in a
close vicinity is the same as the influence of a single isolated
point, which preferably has a density value .delta. of about 1.
[0171] FIG. 5C illustrates a first part of a flexible matching
step, in which each of sampled points S.sub.i is associated with a
grid point Gj from roughly adjusted grid 92. The associated grid
points are moved toward their respective sampled points, while the
rest of the G' points on the roughly adjusted grid are moved
according to interpolation of the movements of neighboring points
on grid 92, as described further hereinbelow. Preferably, each
sampled point S.sub.i is associated with the closest grid point.
For example, the closest grid point to S.sub.1 is G.sub.1', and
these points are therefore associated. Preferably, computer 36
creates a memory list in which these pairs of points are listed.
For clarity of this explanation, the associated points are marked
by dashed ovals 96 in FIG. 5C.
[0172] Preferably, a transformation function f, which moves the
associated grid points toward their respective sampled points, is
generated. The non-associated grid points are also moved according
to function f. Function f is preferably easily calculated, and
transforms the grid to a smooth form. Preferably, function f is a
weighted sum of the distances between the associated pairs of
sampled and grid points, such that pairs of associated points close
to the grid point influence its displacement more than pairs of
associated points far from the grid point. Function f is preferably
as given in equation (3) below, with w.sub.i(Gj) dependent on the
distances between the grid point Gj and the associated grid points
Gi, preferably as defined in equation (4). Alternatively,
w.sub.i(Gj) is dependent on the distance between the grid point Gj
and the sampled points Si, as in equation (1). In the flexible
matching stage, k is preferably smaller than the power law in the
rough adjustment stage in order to generate a smoother grid
surface. Preferably, k in the flexible matching stage is between 2
and 6 and is most preferably 4. Preferably, k is an even number in
order to simplify the calculations. Although the equations below
are stated for convenience in scalar notation, it will be
understood that S.sub.i, G.sub.i and f(G.sub.j) are vector
quantities, as in equation (1) above: 4 f ( G j ) = i w i ( G j ) (
S i - G i ) w i ( G j ) ( 3 ) w i ( G j ) = 1 ; G j - S i r; k + C
C > 0 ( 4 )
[0173] The constant C determines how close the associated grid
points are moved toward their associated sampled points. For very
small values of C, the associated grid points G.sub.i are moved
substantially onto the sampled points S.sub.i. Preferably, C is
between 0.3 and 0.7, more preferably about 0.5. Alternatively or
additionally, C is changed according to the number of times the
flexible matching is to be performed. Further alternatively or
additionally, in the first flexible matching step, C is relatively
large, while in subsequent flexible matching steps C is gradually
reduced.
[0174] The distance definition used in equations (2), (3) and (4)
is preferably the Euclidean distance in R.sup.3, due to its
simplicity in calculation and the fact that it causes points on
opposite walls of the reconstructed volume to repel one
another.
[0175] In an alternative preferred embodiment of the present
invention, the grid points which have an associated sampled point
are moved toward their associated sampled points by a portion of
the distance between them. Preferably, the points are moved a
percentage of the distance between the associated pair. For
example, in FIG. 5C the points are moved about 2/3 of the distance.
Alternatively, the grid points are moved by any other amount
dependent on the distance between the associated pair.
[0176] As shown in FIG. 5D, those grid points G'.sub.k which are
not associated with sampled points S.sub.i are then moved according
to a movement vector {right arrow over (V)}.sub.k which is
dependent on the movements of the grid points G'.sub.l surrounding
the point. Preferably, the non-associated points G'.sub.k are moved
a distance which is a linear interpolation of the movements of the
surrounding points G'.sub.l. Preferably, the distance between the
grid points is determined as the geometrical distance between the
points as they are on the present adjusted grid. For example, the
geometrical distance between G'.sub.15 and G'.sub.16 is indicated
by X.sub.2, and may be calculated according to the coordinates of
the two points. Alternatively or additionally, the distance used is
the grid-distance {tilde over (X)}.sub.2along the present adjusted
grid, the grid-distance {tilde over (L)}.sub.2 along the original
grid, or the geometrical distance L.sub.2on the original grid. In a
preferred embodiment of the present invention, in a first flexible
matching step, the distance used is the grid-distance--either
l.sub.2 or {tilde over (X)}.sub.2--while in subsequent flexible
matching steps the distance used is the geometrical distance
X.sub.2.
[0177] For example, as shown in FIG. 5D, point G'.sub.15 is moved a
distance defined by a vector, which is a weighted sum of vectors 5
V 14 r ,
[0178] and 6 V 16 r
[0179] of grid points G'.sub.14, and G'.sub.16, respectively.
Preferably, 7 V 15 r
[0180] is as described in equation (2) below, in which d.sub.1 is a
selected type of distance between G.sub.15 and G.sub.14, and may
include X.sub.1, {tilde over (X)}.sub.1, l.sub.1 or any other
suitable distance definition. Likewise, d.sub.2 is a selected type
of distance between G.sub.15 and G.sub.16 and may include X.sub.2,
{tilde over (X)}.sub.2, l.sub.2, or any other distance definition.
Preferably, in the first flexible matching step illustrated in FIG.
5D, d.sub.1 and d.sub.2 are taken as X.sub.1 and X.sub.2
respectively. 8 V 15 ' = d 2 d 1 + d 2 V 14 ' + d 1 d 1 + d 2 V 16
' ( 5 )
[0181] Although equation (8) illustrates a first-order linear
interpolation, it will be understood that higher-order and
non-linear interpolation methods may also be used.
[0182] Preferably, during the flexible matching stage, flexible
matching steps are repeated a few times (N.sub.0 times, as shown in
FIG. 4). Each time, grid points are associated with the sampled
points, and the associated and non-associated grid points are moved
accordingly.
[0183] The rough adjustment and flexible matching tend to cause the
grid to become non-uniform. Therefore, during a final adjustment
stage the grid is preferably smoothed, for example, by applying a
surface convolution with a Gaussian-like kernel. Preferably, the
kernel is a 3.times.3 Gaussian kernel, and is applied to the grid a
plurality of times, preferably between five and ten times.
Alternatively, a larger kernel may be used in which case it may be
applied to the grid fewer times, most preferably only once. The
surface convolution, however, generally causes shrinkage of the
surface, and therefore a simple transformation, preferably an
affine transformation, is applied to the grid to cancel the
shrinkage and improve the matching of the grid to the sampled
points. The affine transformation is preferably chosen as the
transformation which minimizes the mean square distance between
sampled points outside of the grid and a surface defined by the
grid. This choice of the transformation causes substantially all
the sampled points to be on or inside the surface defined by the
grid. This choice is in accordance with the anatomical structure of
the heart in which outliers, i.e., points not on the sampled
surface, are generally inside the sampled surface, i.e. inside a
cardiac chamber rather than on the myocardial wall. Thus, the
reconstructed grid is properly reconstructed by ignoring outliers
which otherwise may deform the grid incorrectly.
[0184] To conclude the final adjustment stage, the user may
optionally request an exact matching stage in which the grid
surface is deformed to include substantially all the sampled
points. Preferably, for each sampled point not on the grid surface
as a result of prior stages, a closest grid point is chosen and
moved to the position of the sampled point. The rest of the grid
points are preferably not moved. Preferably, internal points which
are beyond a certain distance from the grid surface are not moved
in this stage and are regarded as outliers. It is noted that
external points are not generally distanced from the grid surface
due to the affine transformation described above.
[0185] Alternatively or additionally, a last flexible matching step
is performed in which the associated grid points are moved onto the
sampled points, as shown in FIG. 5E. Curved line 100 in FIG. 5E
represents the final grid configuration and comprises an accurate
approximation of the sampled volume.
[0186] Alternatively, the flexible matching is performed in one
step, and the associated points from the rough adjustment grid are
immediately moved onto the sampled points. In a preferred
embodiment of the present invention, computer 36 first produces an
approximate map, in which the flexible matching is performed in one
step. The approximate map is used by the physician to decide if
more sampled points are needed. Once the physician decided that no
more points are needed, computer 36 reconstructs a more accurate
map in which the flexible matching is performed a plurality of
times. Meanwhile, the physician may use the approximate map in
order to save time. In further preferred embodiments, the first
reconstructed map is produced with a relatively low density of
points on the grid, while later reconstructions use a more dense
grid.
[0187] Referring back to FIG. 4, when the sampled points include
data from more than one time point, the reconstructed grid of the
anchor time point (hereinafter referred to as the anchor grid) is
preferably used to quickly reconstruct the grid for other time
points t.sub.i. For each of the other time points, a simple
transformation is performed on the anchor grid to bring the grid
close to the form of the sampled points of time t.sub.i. The simple
transformation is preferably a quadratic transformation or an
affine transformation. Alternatively, the transformation comprises
a rotation and/or scaling transformation. In some preferred
embodiments of the present invention, the transformation is chosen
according to the number of sampled points. Preferably, when there
are a relatively large number of sampled points, a quadratic
transformation is applied, while for fewer sampled points, simpler
transformations are employed.
[0188] Flexible matching is then preferably performed on the
transformed grid one or more times (N.sub.T), preferably fewer
times than were required in reconstruction of the anchor-time grid
(N.sub.T>N.sub.0), most preferably twice. Final adjustments are
then preferably applied to the grid, and the resulting grid at time
t.sub.i may be displayed. The parameter value may also be
interpolated separately for time t.sub.i, substantially as
described above with respect to the anchor grid. When
reconstruction for all of the time points is concluded, the
reconstructed grids may be displayed in sequence as a function of
time, or in any other manner. Preferably, the reconstruction
process continues while the anchor grid is displayed, so that a
physician may use the reconstructed data without delay.
[0189] Preferably, as noted hereinabove, each data point includes
at least one physiological parameter, such as an indicator of the
electrical activity in the heart, measured using functional portion
24 of catheter 20. After the map is constructed, as described
above, the points on the grid, G.sub.1, G'.sub.4, G'.sub.7, etc.,
that were associated with sampled points S.sub.1, S.sub.2, S.sub.6,
etc., are assigned the physiological parameter value of their
respective sampled points. The non-associated grid points receive
parameter values by interpolation between the values of the
parameters of neighboring associated grid points in a manner
similar to that described above. Alternatively or additionally, the
non-associated grid points receive parameter values in a manner
similar to the way they received their coordinates in flexible
matching.
[0190] Further alternatively or additionally, the non-associated
grid points are given parameter values using a zero-order-hold
filling in method. Starting from the sampled points, all the
surrounding grid points are given the same parameter value as the
sampled point has, propagating outward until another grid point
with a different parameter value is encountered. Thereafter, a
Gaussian smoothing process is preferably applied to the parameter
values. Thus, parameter values are given in a very simple method to
all the grid points substantially without forfeiting visual
clarity.
[0191] Thus, a 3D map is reconstructed showing both the geometrical
shape of the heart chamber and local electrical parameters or other
physiological parameters as a function of position in the heart.
The local parameters may include electrogram amplitude, activation
time, direction and/or amplitude of the electrical conduction
vector, or other parameters, and may be displayed using pseudocolor
or other means of graphic realization, as is known in the art.
Preferably, a predefined color scale is associated with the
parameter, setting a first color, e.g., blue, for high values of
the parameter, and a second color, e.g., red, for low values of the
parameter.
[0192] FIG. 6 is a schematic illustration of a displayed
reconstructed heart volume 130, in accordance with a preferred
embodiment of the present invention. A plurality of sampled points
134 are used to reconstruct a surface 132 of volume 130. A grid
(not shown) is adjusted as described above to form surface 132.
Preferably, each point on the grid receives a reliability value
indicative of the accuracy of the determination. Further
preferably, the reliability value is a function of the distance
from the grid point to the closest sampled point on surface 132
and/or of a density of sampled points 134 in a vicinity of the grid
point. Preferably, areas of surface 132 covered by less-reliable
grid points, such as an area 140, are displayed as
semi-transparent, preferably using .quadrature.-blending. Due to
the transparency, points 136 on an inner surface of volume 130 are
displayed, being seen through volume 130. Preferably, the user may
define the predetermined distance and/or sample density defining
less-reliable points. Alternatively or additionally, different
levels of semi-transparency are used together with a multi-level
reliability scale.
[0193] FIG. 7 is a schematic illustration of a volume estimation
method, in accordance with a preferred embodiment of the present
invention. In some cases it is desired to estimate the volume
encompassed by one or more reconstructed surfaces, for example, to
compare the volume of a heart chamber at different time-points of
the heart cycle. In FIG. 7 the reconstructed grid surface is
represented, for clarity, by a ball 150. The surface of ball 150 is
partitioned into quadrilaterals by the grid points, and these
quadrilaterals are used for volume estimation. An arbitrary point
O, in a vicinity of the surface, preferably within the volume, most
preferably close to the center of mass of ball 150, is chosen, thus
defining a pyramid 152 for each quadrilateral on the surface of
ball 150. An estimate of the sum of the volumes of pyramids 152
accurately represents the volume of ball 150.
[0194] Preferably, each quadrilateral is divided into two
triangles, and the volume is estimated by summing the volumes of
tetrahedrons defined by these triangles as bases and vertex O apex.
Let A.sub.m, B.sub.m, C.sub.m, denote the vertices of the m-th
triangle arranged clockwise, so that the normals of the triangles
point outward from the surface of ball 150. The volume V of ball
150 is estimated by equation (6): 9 V = 1 6 m ( B m - A m ) .times.
( C m - A m ) ( O - A m ) ( 6 )
[0195] FIG. 8 is an illustration of a reconstruction procedure, in
accordance with another preferred embodiment of the present
invention. In this preferred embodiment the sampled points are
known to be on a single, open surface, rather than surrounding a 3D
volume, and therefore the beginning grid may comprise an open
plane, rather than a closed curve. Catheter 20 is brought into
contact with a plurality of locations on an inner wall 76 of heart
70, and the coordinates of these locations are determined to give
sampled points 120. Preferably, a physician indicates to console 34
the direction from which catheter 20 contacts surface 76. Computer
36 accordingly generates an initial grid 122, which includes a
plurality of grid points 124, such that all the grid points are
preferably on one side of the sampled points. The adjustment
procedure is performed substantially as described above, bringing
grid points 124 to maximally resemble surface 76.
[0196] In a preferred embodiment of the present invention, the
adjustment procedure may be performed step-by-step on display 42,
allowing the physician to interrupt and direct the procedure if
necessary.
[0197] It is noted that although the above description assumes that
the data regarding the sampled points are acquired by the system
which performs the reconstruction, the reconstruction procedure may
also be performed on points received from any source, such as from
a different computer, a library database or an imaging system.
Furthermore, although preferred embodiments are described herein
with reference to mapping of the heart, it will be appreciated that
the principles and methods of the present invention may similarly
be applied to 3D reconstruction of other physiological structure
and cavities, as well as in non-medical areas of 3D image
reconstruction.
[0198] It will thus be appreciated that the preferred embodiments
of the invention described above are cited by way of example, and
the full scope of the invention is limited only by the claims which
follow.
* * * * *