Andrew J. Pullan

An Anatomically Based Model of Transient Coronary Blood Flow in the Heart

An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier--Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum. These equations are coupled to a pressure-radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment. The two step Lax--Wendroff finite difference method is used to numerically solve these equations. The flow through bifurcations, where three vessel segments join, is governed by the equations of conservation of mass and momentum. The solution to these simultaneous equations is calculated using the multidimensional Newton--Raphson method. Simulations of blood flow through a geometric model of the coronary network are presented demonstrating phy...

Cardiac Microstructure: Implications for Electrical Propagation and Defibrillation in the Heart

Abstract— Our understanding of the electrophysiological properties of the heart is incomplete. We have investigated two issues that are fundamental to advancing that understanding. First, there has been widespread debate over the mechanisms by which an externally applied shock can influence a sufficient volume of heart tissue to terminate cardiac fibrillation. Second, it has been uncertain whether cardiac tissue should be viewed as an electrically orthotropic structure, or whether its electrical properties are, in fact, isotropic in the plane orthogonal to myofiber direction. In the present study, a computer model that incorporates a detailed three-dimensional representation of cardiac muscular architecture is used to investigate these issues. We describe a bidomain model of electrical propagation solved in a discontinuous domain that accurately represents the microstructure of a transmural block of rat left ventricle. From analysis of the model results, we conclude that (1) the laminar organization of myocytes determines unique electrical properties in three microstructurally defined directions at any point in the ventricular wall of the heart, and (2) interlaminar clefts between layers of cardiomyocytes provide a substrate for bulk activation of the ventricles during defibrillation.

Geometric Modeling of the Human Torso Using Cubic Hermite Elements

We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high-order (bicubic Hermite) surface elements. These elements preserve derivative (C1) continuity across element boundaries and permit smooth anatomically accurate surfaces to be obtained with relatively few elements. These elements are fitted to the data with a new nonlinear fitting procedure that minimizes the error in the fit while maintainingC1 continuity with nonlinear constraints. Nonlinear Sobelov smoothing is also incorporated into this fitting scheme. The structures fitted along with their corresponding root meansquared error, number of elements used, and number of degrees of freedom (df) per variable are: epicardium (0.91 mm, 40 elements, 142 df), left lung (1.66 mm, 80 elements, 309 df), right lung (1.69 mm, 80 elements, 309 df), skeletal muscle surface (1.67 mm, 264 elements, 1,010 df), fat layer (1.79 mm, 264 elements, 1,010 df), and the skin layer (1.43 mm, 264 elements, 1,010 df). The fitted surfaces are assembled into a combined finite element/boundary element model of the torso in which the exterior surfaces of the heart and lungs are modeled with two-dimensional boundary elements and the layers of the skeletal muscle, fat, and skin are modeled with finite elements. The skeletal muscle and fat layers are modeled with bicubic Hermite linear elements and are obtained by joining the adjacent surface elements for each layer. Applications for the torso model include the forward and inverse problems of electrocardiography, defibrillation studies, radiation dosage studies, and heat transfer studies.

Generation of an Anatomically Based Three-Dimensional Model of the Conducting Airways

AbstractAn anatomically accurate model of the conducting airways is essential for adequately simulating gas mixing, particle deposition, heat and water transfer, and fluid distribution. We have extended a two-dimensional tree-growing algorithm to three dimensions for generation of a host-shape dependent three-dimensional conducting airway model. Terminal branches in the model are both length limited and volume-supplied limited. A limit is imposed on the maximum possible branch angle between a daughter and parent branch. Comparison of the resulting model with morphometric data shows that the algorithm produces branching and length ratios, path lengths, numbers of branches, and branching angles very close to those from the experimental data. The correlation between statistics from the generated model and those from morphometric studies suggests that the conducting airway structure can be described adequately using a “supply and demand” algorithm. The resulting model is a computational mesh that can be used for simulating transport phenomena.

Origin and propagation of human gastric slow-wave activity defined by high-resolution mapping

Slow waves coordinate gastric motility, and abnormal slow-wave activity is thought to contribute to motility disorders. The current understanding of normal human gastric slow-wave activity is based on extrapolation from data derived from sparse electrode recordings and is therefore potentially incomplete. This study employed high-resolution (HR) mapping to reevaluate human gastric slow-wave activity. HR mapping was performed in 12 patients with normal stomachs undergoing upper abdominal surgery, using flexible printed circuit board (PCB) arrays (interelectrode distance 7.6 mm). Up to six PCBs (192 electrodes; 93 cm(2)) were used simultaneously. Slow-wave activity was characterized by spatiotemporal mapping, and regional frequencies, amplitudes, and velocities were defined and compared. Slow-wave activity in the pacemaker region (mid to upper corpus, greater curvature) was of greater amplitude (mean 0.57 mV) and higher velocity (8.0 mm/s) than the corpus (0.25 mV, 3.0 mm/s) (P < 0.001) and displayed isotropic propagation. A marked transition to higher amplitude and velocity activity occurred in the antrum (0.52 mV, 5.9 mm/s) (P < 0.001). Multiple (3-4) wavefronts were found to propagate simultaneously in the organoaxial direction. Frequencies were consistent between regions (2.83 +/- 0.35 cycles per min). HR mapping has provided a more complete understanding of normal human gastric slow-wave activity. The pacemaker region is associated with high-amplitude, high-velocity activity, and multiple wavefronts propagate simultaneously. These data provide a baseline for future HR mapping studies in disease states and will inform noninvasive diagnostic strategies.

Abnormal initiation and conduction of slow-wave activity in gastroparesis, defined by high-resolution electrical mapping.

BACKGROUND & AIMS Interstitial cells of Cajal (ICC) generate slow waves. Disrupted ICC networks and gastric dysrhythmias are each associated with gastroparesis. However, there are no data on the initiation and propagation of slow waves in gastroparesis because research tools have lacked spatial resolution. We applied high-resolution electrical mapping to quantify and classify gastroparesis slow-wave abnormalities in spatiotemporal detail. METHODS Serosal high-resolution mapping was performed using flexible arrays (256 electrodes; 36 cm(2)) at stimulator implantation in 12 patients with diabetic or idiopathic gastroparesis. Data were analyzed by isochronal mapping, velocity and amplitude field mapping, and propagation animation. ICC numbers were determined from gastric biopsy specimens. RESULTS Mean ICC counts were reduced in patients with gastroparesis (2.3 vs 5.4 bodies/field; P < .001). Slow-wave abnormalities were detected by high-resolution mapping in 11 of 12 patients. Several new patterns were observed and classified as abnormal initiation (10/12; stable ectopic pacemakers or diffuse focal events; median, 3.3 cycles/min; range, 2.1-5.7 cycles/min) or abnormal conduction (7/10; reduced velocities or conduction blocks; median, 2.9 cycles/min; range, 2.1-3.6 cycles/min). Circumferential conduction emerged during aberrant initiation or incomplete block and was associated with velocity elevation (7.3 vs 2.9 mm s(-1); P = .002) and increased amplitudes beyond a low base value (415 vs 170 μV; P = .002). CONCLUSIONS High-resolution mapping revealed new categories of abnormal human slow-wave activity. Abnormalities of slow-wave initiation and conduction occur in gastroparesis, often at normal frequency, which could be missed by tests that lack spatial resolution. Irregular initiation, aberrant conduction, and low amplitude activity could contribute to the pathogenesis of gastroparesis.

Noninvasive electrical imaging of the heart: theory and model development.

AbstractThe aim of this work is to begin quantifying the performance of a recently developed activation imaging algorithm of Huiskamp and Greensite [IEEE Trans. Biomed. Eng. 44:433–446]. We present here the modeling and computational issues associated with this process. First, we present a practical construction of the appropriate transfer matrix relating an activation sequence to body surface potentials from a general boundary value problem point of view. This approach makes explicit the role of different Greens functions and elucidates features (such as the anisotropic versus isotropic distinction) not readily apparent from alternative formulations. A new analytic solution is then developed to test the numerical implementation associated with the transfer matrix formulation presented here and convergence results for both potentials and normal currents are given. Next, details of the construction of a generic porcine model using a nontraditional data-fitting procedure are presented. The computational performance of this model is carefully examined to obtain a mesh of an appropriate resolution to use in inverse calculations. Finally, as a test of the entire approach, we illustrate the activation inverse procedure by reconstructing a known activation sequence from simulated data. For the example presented, which involved two ectopic focii with large amounts of Gaussian noise (100 μV rms) present in the torso signals, the reconstructed activation sequence had a similarity index of 0.880 when compared to the input source.

High-resolution mapping of in vivo gastrointestinal slow wave activity using flexible printed circuit board electrodes: methodology and validation.

High-resolution, multi-electrode mapping is providing valuable new insights into the origin, propagation, and abnormalities of gastrointestinal (GI) slow wave activity. Construction of high-resolution mapping arrays has previously been a costly and time-consuming endeavor, and existing arrays are not well suited for human research as they cannot be reliably and repeatedly sterilized. The design and fabrication of a new flexible printed circuit board (PCB) multi-electrode array that is suitable for GI mapping is presented, together with its in vivo validation in a porcine model. A modified methodology for characterizing slow waves and forming spatiotemporal activation maps showing slow waves propagation is also demonstrated. The validation study found that flexible PCB electrode arrays are able to reliably record gastric slow wave activity with signal quality near that achieved by traditional epoxy resin-embedded silver electrode arrays. Flexible PCB electrode arrays provide a clinically viable alternative to previously published devices for the high-resolution mapping of GI slow wave activity. PCBs may be mass-produced at low cost, and are easily sterilized and potentially disposable, making them ideally suited to intra-operative human use.

Generation of an anatomically based geometric coronary model.

AbstractA discrete anatomically accurate finite element model of the largest six generations of the coronary arterial network is developed. Using a previously developed anatomically accurate model of ventricular geometry the boundaries of the coronary mesh are defined from measured epicardial coronaries. Network topology is then generated stochastically from published anatomical data. Spatial information is added to this topological data using an avoidance algorithm accounting for global network geometry and optimal local branch angle properties. The generated vessel lengths, radii and connectivity are consistent with the published studies and a relativity even spatial distribution of vessels within the ventricular mesh is achieved. The local finite element coordinates of the coronary nodes within the ventricular mesh are calculated such that the coronary geometry can be recalculated within a deformed ventricular mesh.

Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology

Two predominant source formulations for the inverse problem of electrocardiology currently exist. They involve the reconstruction of epicardial potentials or myocardial activation times from noninvasively recorded torso surface potentials. Each of these formulations have their advantages, however, they have not been systematically compared against each other. We present results from a simulation study which compared a number of epicardial potential formulations (Tikhonov, truncated singular value decomposition (TSVD), Greensite-Tikhonov and Greensite-TSVD), and a myocardial activation time formulation for the inverse problem of electrocardiology. A number of different methods were also used to determine the appropriate level of regularization (optimal, L-curve, zero-crossing, and composite residual and smoothing operator) to apply to each formulation. The simulation study was conducted using an anatomically based boundary element porcine model with a variety of cardiac sources. Varying levels of geometric error were introduced to the system and solutions were computed using each of the inverse algorithms. Results show that under pure Gaussian noise potential-based methods performed best at low noise levels while the activation-based method was less effected by higher noise levels. In the presence of correlated geometric error, the activation-based method out performed the potential methods, with the Greensite-Tikhonov method being the most favored potential-based method when using the L-curve or zero-crossing method to determine the regularization parameter.