Monoplane 3D reconstruction of mapping ablation catheters: a feasibility study
P Fallavollita, PhD
School of Computing, Queen�s University, Kingston, Ontario, Canada
Abstract
Purpose: Radiofrequency (RF) catheter ablation has
transformed treatment for arrhythmias and has become firstline therapy for
some tachycardias. The precise localization of the arrhythmogenic site and the
positioning of the RF catheter over that site are problematic: they can impair
the efficiency of the procedure and are time consuming (several hours). This
study evaluates the feasibility of using only single plane Carm images in
order to estimate the 3D coordinates of RF catheter electrodes in a cardiac
phase.
Materials and methods: The method makes use of a
priori 3D model of the RF mapping catheter assuming rigid body motion
equations in order to estimate the 3D locations of the catheter tipelectrodes
in single view Carm fluoroscopy images. Validation is performed on both
synthetic and clinical data using computer simulation models. The authors'
monoplane reconstruction algorithm is applied to a 3D helix mimicking the shape
of a catheter and undergoing solely rigid motion. Similarly, the authors test
the feasibility of recovering nonrigid motion by applying their method on true
3D coordinates of 13 ventricular markers from a sheep�s ventricle.
Results: The results of this study showed that the
proposed monoplane algorithm recovers rigid motion adequately when using the
spatial positions of a catheter in six consecutive Carm image frames yielding
maximum 3D root mean squares errors of 4.3 mm. On the other hand, the suggested
algorithm did not recover nonrigid motion precisely as suggested by a maximum
3D root mean square value of 8 mm.
Conclusion: Since RF catheter electrodes are rigid
structures, the authors conclude that there is promise in recovering the 3D
coordinates of the electrodes when making use of only single view images.
Future work will involve adding nonrigid motion equations to their algorithm,
which will then be applied to actual clinical data. � 2010 Biomedical
Imaging and Intervention Journal. All rights reserved.
Keywords: 3D reconstruction; monoplane; Carm fluoroscopy;
catheter ablation; cardiac arrhythmias
Introduction
In 2005, the incidence of sudden cardiac death (SCD) in
the United States was about 290,000 cases per year [1]. Left ventricular dysfunction,
such as ventricular tachycardia (VT), is currently the best available predictor
for SCD [2]. Severe disorders of the heart rhythm that can cause sudden cardiac
death or morbidity, can be treated by radiofrequency (RF) catheter ablation,
which consists of inserting a catheter inside the heart, near the area from
which the abnormal cardiac electrical activity originates, and delivering RF
current through the catheter tip so as to ablate this arrhythmogenic area [3].
The precise localization of the arrhythmogenic site and positioning of the RF
catheter at that site are problematic: they can impair the efficacy of the
procedure, which can last many hours, especially for complex arrhythmias [3].
To shorten the duration of RF catheter ablation and increase its efficiency,
commercial systems that provide a 3D color display of the cardiac electrical
activation sequence during the arrhythmia have been proposed. These systems
incorporate basket electrode arrays (Constellation, EPT Inc.), catheters
with a balloon electrode array (Ensite 3000, Endocardial Solutions Inc.)
and catheters with magnetic position detectors (CARTO XP, Biosense
Webster Inc.). Lastly, a complete navigation and registration framework is
available (CartoMerge, Biosense Webster Inc.).
The CARTO XP ablation mapping and navigation system
provides realtime data on 3D, colorcoded maps of the electrical activity of
the heart. The CARTO XP system makes possible precise, realtime
tracking of catheter location by using magnetic fields. The mapping catheter
resembles a standard deflectable ablation catheter with a 4mm tip and proximal
2mm ring electrodes. The location sensors lie adjacent to the tip electrode,
totally embedded within the catheter. The three location sensors are located
orthogonally to each other. A locator pad is placed beneath the operating table
and includes three coils that generate low magnetic fields, which decay as a
function of the distance from their sources. When the catheter is moved within
this magnetic field, signals received by the sensors are transmitted along the
catheter shaft to the main processing unit so as to track its position in 3D.
This approach enables tracking of the catheter independent of fluoroscopy [4].
The EnSite 3000 system provides electrophysiologists
with a realtime, virtual image of the electrical activity of the heart without
contacting the heart�s surface. The electrode array consists of a small balloon
around which are woven 64 insulated wires with a single break in their
insulation, producing 64 unipolar electrodes. This array is mounted at the end
of a catheter, which is introduced in the cardiac chamber to be investigated.
When placed in the chamber, the small balloon is partially inflated. The
balloon does not fill the chamber and the electrodes do not make contact with
the cardiac wall (which is why this approach is called noncontact). A
multichannel amplifier and computer workstation processes the raw farfield
electrographic data and displays 3D anatomical information [5].
Simultaneous mapping of multiple points is performed using
a 64lead basket Constellation catheter that can be deployed
percutaneously. Current designs of basket arrays consist of a series of equally
spaced electrodes mounted on eight flexible splines. Each spline contains eight
1.5 mm electrodes with 3mm spacing. The catheter is introduced percutaneously
through a sheath into the chamber. By pulling back the sheath, the splines
deploy and are apposed against the endocardium. The basket catheter is
connected via amplifiers to the mapping system. The signals are filtered from
30 to 400 Hz. Detection of local activation is performed for each
electrogram and 2D isochronal maps are generated but with no 3D display of the
anatomy [5].
All these systems are costly [6]. The first two can map
the cardiac activation sequence using data recorded during a single beat
whereas the CARTO system relies on data recorded pointbypoint during
numerous beats, which implies that the arrhythmia must remain stable during the
procedure.
Recently, the authors have proposed a more affordable
fluoroscopic navigation system by obtaining local activation times from a
roving mapping catheter, when treating VT, whose positions are computed from
biplane fluoroscopic projections, and by superimposing the isochronal map
depicting the cardiac electrical activation sequence over the fluoroscopic
image of the heart [3]. As biplane Carm fluoroscopes are not commonly
available in hospitals, the authors attempted to estimate the depth of the
tipelectrode of a mapping catheter using only a single image. The final
results yielded depth estimations of about 10 mm. Due to this large error,
continued research on estimating the 3D coordinates of the tip electrode using
only a singleview fluoroscopic sequence is primordial.
The focus of this paper establishes two significant
modifications to the previous work. First, the authors will consider a full
perspective camera model instead of orthographic projection so as to create a
more precise 3D geometry of the mapping catheter and the electrodes in it.
Second, they propose to use a priori 3D information of the mapping
ablation catheter positions in order to estimate its depth on Carm fluoroscopy
images using only singleplane image sequences. The authors will exploit the
spatiotemporal information in the Carm images to compensate for the unknown
zvalue of the tipelectrode. This intuition of exploiting multiple singleview
images should lead to a more precise depth estimate of the catheter. The
authors emphasize that this work is a feasibility study and, therefore,
computer simulations depicting both rigid and nonrigid movement of the
catheter will be used for assessment of their proposed methodology. Lastly, to
their knowledge, this analysis is a first of its kind for singleview 3D
reconstruction and depth estimation for the purpose of assisting catheter
ablation procedures.
Methodology
Full perspective camera model
Figure 1 shows the full perspective camera model that will
be used for the 3D reconstruction problem [7]. If the authors define a 3D point
P_{world}= [X Y Z 1]^{T} in the world coordinate system,
then its 2D projection in an image, m= [u v 1]^{T}, is achieved
by constructing a projection matrix:
_{}�������������� (1)
The intrinsic matrix of size [3x3], contains the pixel
coordinates of the image center, also known as the principal point (u_{o},
v_{o}), the scaling factor k, which defines the number of
pixels per unit distance in image coordinates, and the focal length f of
the camera (in meters). The extrinsic matrix of size [3x4] is identified by the
transformation needed to align the world coordinate system to the camera
coordinate system. This means that a translation vector, t, and a
rotation matrix, R, need to be found in order to align the corresponding
axis of the two reference frames. Lastly, image resolution (usually mm/pixel)
is calculated from the imaging intensifier size divided by the actual size of
the image in pixels.
Orthographic and weak perspective camera model
An
orthographic camera is one that uses parallel projection to generate a 2D image
of a 3D object. The image plane is perpendicular to the viewing direction.
Parallel projections are less realistic than full perspective projections,
however, they have the advantage that parallel lines remain parallel in the
projection, and distances are not distorted by perspective foreshortening. The
parallel projection matrix is given by:
_{}���������� (2)
The weak perspective camera is
an approximation of the full perspective camera, with individual depth points Z_{i}
replaced by an average depth Z_{avg}. The authors define the
average depth, Z_{avg} as being located at the centroid of the
cloud of 3D points in the world coordinate system. The weak perspective
projection matrix is given by:
_{}�������� (3)
A priori 3D monoplane algorithm
The authors first suppose that they have at their disposal
a set of n 3D ablation catheter electrode points (X0_{n}, Y0_{n},
Z0_{n}) at time t = 0 obtained from biplane fluoroscopic
data. They also suppose that this first time instant reflects the diastolic
cardiac phase. In this phase, the ventricles are filled with blood and the
heart motion is at its smallest allowing for a more accurate 3D representation.
The a priori coordinates are expressed in the camera reference frame in
order to have a Zdirection corresponding to catheter electrode depth.
The authors also have at their disposal the Carm fluoroscope gantry
parameters, which can be extracted from the image header DICOM files. These
parameters enable them to construct a projection matrix for a specific viewing
angle by using the full perspective camera model. They can now solve for the 3D
displacements (dx_{i,i+1}, dy_{i,i+1}, dz_{i,i+1})
between consecutive Carm image frames beginning with the first image i=1.
Expanding equation (1) and using an additional fluoroscopy image frame i
=2, they obtain their first two equations as follows:
_{}������ (4)
Both equations describe the pixel coordinates in the
second image (u_{2}, v_{2}) and the twelve coefficients m_{i=1:12}
are the values of the projection matrix. By adding an additional
fluoroscopy image frame at time i = 3, we obtain two new equations with
three additional unknowns in 3D:
_{}��������� (5)
The previous four equations take into account the spatial
positions of a projected 3D world point on the acquired Carm images. As the
authors have four equations with six unknowns, they can extract two additional
equations based on the fact that the Euclidean distances in pixels, d,
between catheter electrode points in two consecutive images are known. It is to
note that the distance between 3D points is not the same as the distance
between their projected image points. Thus, they consider orthogonal projection
estimations in this case and deem that this approximation is suitable enough
for the proposed analysis. The authors arrive at the following two equations:
_{}����������������������������� (6)
They can now solve for the 3D displacements. A LevenbergMarquardt
optimization scheme [8] can be used here in order to solve for the unknown
displacements. For the optimization scheme, initial approximations are a
requirement to initialize the process. Hence, a suitable approximation for the
displacements dx and dy can be obtained if the authors consider a
parallel back projection of the 2D image points into the world coordinate
system. As for the displacements dz, if they assume that the average
depth of the catheter electrodes remains relatively constant in consecutive
time frames (i.e. weak perspective camera model), then they can calculate the
average depth of the 3D points (X0, Y0, Z0) in the second image (t
= 1). This mean depth should be the same at time instants i =2, 3, etc.,
signifying that depths dz will be set to zero for the optimization
scheme. However, for the sake of a more exhaustive analysis, they will also
consider depth displacements dz �
[15] millimeters as well.
Single view algorithm motivation
A rationale use of the authors' algorithm would be to
acquire biplane information at the beginning of the procedure and track
catheter positions from monoplane fluoroscopy images during successive heart
chamber mapping. They realize that they can select nonconsecutive image frames
as well, however, an accurate 3D reconstruction is only representative by
taking into account all image frames. This does not diminish the overall effort
of determining if and when the singleview algorithm fails and at what time
instants it happens. For example, if the algorithm proves that singleplane
reconstruction can be achieved reliably in the first 5 time instants and then
fails, nothing impedes the authors to reperform twoview reconstruction at
that specific time in order to compensate for the failed results.
Evaluation
To validate the authors' proposed monoplane algorithm,
they performed first rigid and nonrigid synthetic experimentation of
structures. Authors in [9] modeled a cardiac intravascular (IVUS) transducer as
a helix, and since a radiofrequency mapping catheter has the same tubular
characteristics as the IVUS transducer, they represented it by a helix as well.
They created a 3D helix in space and applied only rigid movement to it in a
temporal fashion. The 3D points were reprojected in singleview 2D images.
They also had at their disposal, 13 ventricle markers of a sheep with their
temporal 3D coordinates as ground truth. These markers represent well the
inherent nonrigid movement of the heart and should depict accurately the true
movement of the heart. They projected these 3D markers on singleplane
synthetic images as well and ran their monoplane algorithm.
Results and discussion
Computer simulations: rigid motion
The authors created a 3D helix containing 30 coordinate
points so as to model the shape of a catheter. Then, they defined a biplane
Carm gantry setup that represented the posterior/anterior (PA) and left
lateral (LAT) views of the heart. The focal length of the fluoroscopic system
was set to a typical value of 100 cm and the helix location was set to 50 cm
along the focal axis. The primary angles were equal to (90˚, 0˚),
respectively, for the PA and LAT views, whereas the secondary angles were equal
to (0˚, 0˚) for both views, respectively. The image sizes were set to
[512x512] pixels and the Carm intensifier size was chosen to be [178x178] mm.
This allowed for a resolution 0.347 mm/pixel. They could now calculate two
projection matrices and projected the 3D helix points on a first set of biplane
images. These biplane images represent a first time instant at t=0.
Subsequent biplane images were calculated by applying rigid movement on the 3D
helix coordinates using the following rigid motion equation:
_{}������������������������� (7)
The 3D angles were set to [θ, Φ, φ] � [0.5˚, 0.5˚, 0.5˚] and the
3D translations were set to [Tx, Ty, Tz] �
[1, 1, 1] mm each. This accounted for average 2D interframe helix displacements
in the images of (6.82, 6.03) pixels in the left lateral view and (4.97,
7.12) pixels for the posterior/anterior views. These average displacements
depict well a standard 15 fps acquisition rate for a typical Carm procedure. A
new set of biplane images and 3D helix points are obtained at t=1. In a
similar fashion, equation (7) is reapplied to produce subsequent biplane data.
Excluding the a priori biplane set at t=0, a total of five
biplane datasets are generated. For good measure, they added error of up to 2
mm in coordinates. They tested their singleplane algorithm from three to six
consecutive time instants (i.e. using three to six consecutive monoplane
images). Figure 2 shows an example of the 2D projections of the helix using the
specified gantry settings. The displacement between each image frame for the
left lateral view was on average 6.5 pixels, whereas the displacement
between each image frame for the posterior/anterior view was 5 and 7 pixels,
respectively. Using orthographic projections for the approximations of dx
and dy to solve their monoplane equations, they obtain approximations in
the range of [1.72.4] millimeters using the intensifier size and image size
values.
Table 1 shows the simulation results for rigid motion
analysis on a helix. They observe that as the number of images used to optimize
their monoplane equations increases, the overall reconstruction results
deteriorate. This is expected as the uncertainty of landmark positions
increases temporally in a singleview framework. The initial depth
approximation dz plays a role in the convergence process. If they select
an initial depth approximation of dz = 1 mm, which is actually the true
simulated displacements from their computer simulations, then they obtain lower
3D root mean square errors (RMS) between optimized and true 3D coordinates.
Depth initial estimates dz �
[1,2,3] mm produce RMS values less than 3 mm when using three consecutive
monoplane images. The RMS values are accumulated values across the number of
images used for the monoplane algorithm. The PA view simulations produce better
results probably due to the projected helix points being distributed with no
coplanarity in the images. On average, they are at most 2.074 mm from the true
displacements when considering six consecutive images using approximate depth
displacements of dz � [1,2,3] mm. However, there is a
tradeoff with the accumulated 3D RMS errors being at most 8 mm when using the
LAT view and six consecutive images. As expected, if initial depth estimates
are far away from the true ground truth values, results deteriorate as seen
when using dz � [4, 5] mm.
Left ventricle simulations: non rigid motion
The clinical data for the ventricle of a sheep was
obtained from [10]. Figure 3 represents the 2D projections of six consecutive
real time instants of the contracting ventricle using the previous gantry
parameters for the helix simulations. They perform monoplane reconstruction
across the six image frames for this type of nonrigid motion of the ventricle.
Figure 4 shows the results obtained on the left ventricle
data. The accuracy of depth determination will decrease if more than six Carm
images are used in their optimization scheme. In other words, monoplane
reconstruction can still be achieved but with a higher RMS value. In such a
case, the authors can compensate for this error by getting additional 3D
information of the catheter at that particular time instant and then reperform
monoplane reconstruction and depth estimation in subsequent images using their
equations. A priori information could also be obtained by CT for
example, and the authors can easily obtain 3D coordinates of the catheter at
the diastolic and systolic cardiac phases. Thus, using a Carm fluoroscope and
assuming 15 frames per second acquisition rate, they normally would have close
to ten monoplane image frames representing the cardiac cycle. If they assume
the 1^{st} frame would represent diastole and the last systole, they
can estimate depth for the middle Carm images by using the two a priori
3D representations obtained from CT, instead of using only a single a priori
model as suggested in this paper. This protocol might alleviate failure to
correctly estimate depth. The average 3D RMS increased from 2.5 mm to 5 mm
when tracking 13 crystals across six images and using an initial guess of dz
= 1 mm. Authors in [11], have demonstrated that point correspondence can be
completed temporally to provide the minimal information required for robust 3D
structure estimation using a total of 12 landmark points. From their monoplane
analysis and Figure 4, they determine that a minimum of six tracked points
begin yielding stable 3D RMS values. Worst case results show that when using a
more realistic depth initial guess of dz = 2 mm, 3D RMS errors for the
13 crystals was about 8 mm with six consecutive Carm images.
Here, 8 mm is a 3D accumulated error for all landmark
points tracked across six consecutive singleview Carm images. This means, it
is the sum of all 3D errors for the 13 landmarks across the six images. In
consequence, from prior work [3], the authors had estimated depth to within 1
cm of the true value using only 1 landmark, that is, the tip electrode on a
single image. The algorithm does better; about 20%, as estimated depth to
within 0.8 cm for 12 electrodes and for six images. Nevertheless, the accepted
clinical threshold is set to 2 mm. Depending on the Carm acquisition frame
rate, six consecutive images probably depicts half of a cardiac cycle (i.e.
between diastolic and systolic phases). This leads to the belief that
additional constraints need to be added to the equations for future analysis, if
the inherent nonrigid motion of the cardiac structures be recovered in its
totality. This is determined by simply comparing the recovered 3D rigid RMS
values in Table 1 as being more accurate than the nonrigid 3D values from
Figure 4.
Future work
The proposed algorithm and computer simulations
demonstrated that rigid movements can indeed be recovered; hence to the
reconstruction of rigid objects can certainly be attempted, such as catheter
electrodes, across a monoplane sequence. Furthermore, the monoplane
reconstruction procedure can be extended to clinical instruments such as
arrhythmia ablation catheter tips as they are rigid objects as well.
Conclusion
A new algorithm to estimate the depth of the mapping
catheter tip was presented. The methodology exploits the spatiotemporal
information of rigid structures in order to estimate their depth in the focal
direction of the Carm fluoroscope. Several conclusions can be made from the
present work: (i) only Carm images are used to detect 3D catheter positions
with no added cost from expensive 3D mapping technologies, (ii) a 3D a
priori model of the catheter is required at a first time instant to
estimate subsequent depth positions at later image frames, (iii) a minimum of
three consecutive Carm fluoroscopy images are required to solve for rigid
motion and interframe displacements of the mapping catheter, (iv) a minimum of
six image points are required during the tracking phase in order to observe
algorithm convergence and minimization of 3D RMS, and (v) nonrigid motion was
not recovered as observed in the final reconstruction results when compared to
the rigid simulations. This feasibility study provided results that were an
improvement to those in the simple biplane projection method developed in [3]
when using only a single image. The global objective remains to provide
interventional assistance for cardiac ablation procedures. By exploiting
spatial and projective information using only singleplane images, the authors
aim to decrease overall intervention time and still maintain highlevel
accuracy when predicting the depth position of the mapping catheter. The
ambition is to depict the ablation catheter electrodes in 3D accurately between
the diastolic and systolic cardiac phases that, in turn, can help the
interventionist during the ablation procedure. Future work will focus on adding
nonrigid constraints to the monoplane equation, which capture the inherent
shape of the rigid electrodes and not only their positions.
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Received 18 August 2009; received in revised form 20 October
2009, accepted 13 November 2009
Correspondence: School of Computing, Queen�s University, Kingston, Ontario, Canada. Tel.: (613) 5336000 ext 78234; Fax: (613) 5336513; Email: pascal@cs.queensu.ca (Pascal Fallavollita).
Please cite as: Fallavollita P,
Monoplane 3D reconstruction of mapping ablation catheters: a feasibility study, Biomed Imaging Interv J 2010; 6(2):e17
<URL: http://www.biij.org/2010/2/e17/>
