Adarsh Krishnamurthy

Patient-specific models of cardiac biomechanics

Patient-specific models of cardiac function have the potential to improve diagnosis and management of heart disease by integrating medical images with heterogeneous clinical measurements subject to constraints imposed by physical first principles and prior experimental knowledge. We describe new methods for creating three-dimensional patient-specific models of ventricular biomechanics in the failing heart. Three-dimensional bi-ventricular geometry is segmented from cardiac CT images at end-diastole from patients with heart failure. Human myofiber and sheet architecture is modeled using eigenvectors computed from diffusion tensor MR images from an isolated, fixed human organ-donor heart and transformed to the patient-specific geometric model using large deformation diffeomorphic mapping. Semi-automated methods were developed for optimizing the passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Material properties of active cardiac muscle contraction were optimized to match ventricular pressures measured by cardiac catheterization, and parameters of a lumped-parameter closed-loop model of the circulation were estimated with a circulatory adaptation algorithm making use of information derived from echocardiography. These components were then integrated to create a multi-scale model of the patient-specific heart. These methods were tested in five heart failure patients from the San Diego Veterans Affairs Medical Center who gave informed consent. The simulation results showed good agreement with measured echocardiographic and global functional parameters such as ejection fraction and peak cavity pressures.

Patient-Specific Modeling of Dyssynchronous Heart Failure: A Case Study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.

An Atlas-Based Geometry Pipeline for Cardiac Hermite Model Construction and Diffusion Tensor Reorientation

Here we present a novel atlas-based geometry pipeline for constructing three-dimensional cubic Hermite finite element meshes of the whole human heart from tomographic patient image data. To build the cardiac atlas, two superior atria, two inferior ventricles as well as the aorta and the pulmonary trunk are first segmented, and epicardial and endocardial boundary surfaces are extracted and smoothed. Critical points and skeletons (or central-line paths) are identified, following the cardiac topology. The surface model and the path tree are used to construct a hexahedral control mesh via a skeleton-based sweeping method. Derivative parameters are computed from the control mesh, defining cubic Hermite finite elements. The thickness of the atria and the ventricles is obtained using segmented epicardial boundaries or via offsetting from the endocardial surfaces in regions where the image resolution is insufficient. We also develop a robust optical flow approach to deform the constructed atlas and align it with the image from a second patient. This registration method is fully-automatic, and avoids manual operations required by segmentation and path extraction. Moreover, we demonstrate that this method can also be used to deformably map diffusion tensor MRI data with patient geometries to include fiber and sheet orientations in the finite element model.

Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces

This paper presents a new unified and optimized method for evaluating and displaying trimmed NURBS surfaces using the Graphics Processing Unit (GPU). Trimmed NURBS surfaces, the de facto standard in commercial mechanical CAD modeling packages, are currently being tessellated into triangles before being sent to the graphics card for display since there is no native hardware support for NURBS. Other GPU-based NURBS evaluation and display methods either approximated the NURBS patches with lower degree patches or relied on specific hard-coded programs for evaluating NURBS surfaces of different degrees. Our method uses a unified GPU fragment program to evaluate the surface point coordinates of any arbitrary degree NURBS patch directly, from the control points and knot vectors stored as textures in graphics memory. This evaluated surface is trimmed during display using a dynamically generated trim-texture calculated via alpha blending. The display also incorporates dynamic Level of Detail (LOD) for real-time interaction at different resolutions of the NURBS surfaces. Different data representations and access patterns are compared for efficiency and the optimized evaluation method is chosen. Our GPU evaluation and rendering speeds are more than 40 times faster than evaluation using the CPU.

Direct evaluation of NURBS curves and surfaces on the GPU

This paper presents a new method to evaluate and display trimmed NURBS surfaces using the Graphics Processing Unit (GPU). Trimmed NURBS surfaces, the de facto standard in commercial 3D CAD modeling packages, are currently tessellated into triangles before being sent to the graphics card for display since there is no native hardware support for NURBS. Previous GPU-based NURBS display methods relied on first approximating the NURBS patches with lower degree Bezier patches before evaluation. Our method uses a GPU fragment program to evaluate the surface point coordinates of the original NURBS patch directly, from the control points and knot vectors stored as textures in graphics memory. This evaluated surface is trimmed during display using a dynamically generated trim-texture calculated via alpha blending. The implementation incorporates dynamic Level of Detail (LOD) for real-time interaction at different resolutions of the NURBS surfaces. We obtain rendering speeds at least one order of magnitude faster than evaluation using the CPU.

Novel role for vinculin in ventricular myocyte mechanics and dysfunction.

Vinculin (Vcl) plays a key structural role in ventricular myocytes that, when disrupted, can lead to contractile dysfunction and dilated cardiomyopathy. To investigate the role of Vcl in myocyte and myocardial function, cardiomyocyte-specific Vcl knockout mice (cVclKO) and littermate control wild-type mice were studied with transmission electron microscopy (TEM) and in vivo magnetic resonance imaging (MRI) tagging before the onset of global ventricular dysfunction. MRI revealed significantly decreased systolic strains transverse to the myofiber axis in vivo, but no changes along the muscle fibers or in fiber tension in papillary muscles from heterozygous global Vcl null mice. Myofilament lattice spacing from TEM was significantly greater in cVclKO versus wild-type hearts fixed in the unloaded state. AFM in Vcl heterozygous null mouse myocytes showed a significant decrease in membrane cortical stiffness. A multiscale computational model of ventricular mechanics incorporating cross-bridge geometry and lattice mechanics showed that increased transverse systolic stiffness due to increased lattice spacing may explain the systolic wall strains associated with Vcl deficiency, before the onset of ventricular dysfunction. Loss of cardiac myocyte Vcl may decrease systolic transverse strains in vivo by decreasing membrane cortical tension, which decreases transverse compression of the lattice thereby increasing interfilament spacing and stress transverse to the myofibers.

Performing Efficient NURBS Modeling Operations on the GPU

We present algorithms for evaluating and performing modeling operations on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for retessellation. Our GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates. We also extend our surface-surface intersection algorithm to evaluate self-intersections in NURBS surfaces.

Direct immersogeometric fluid flow analysis using B-rep CAD models

Immersogeometric analysis that directly uses the B-rep CAD model is proposed.A GPU-accelerated point membership classification is performed.Distribution of the surface quadrature points is crucial for accuracy.The quadrature error near the trim curves is relatively insignificant.The methodology is found effective on a 3D benchmark and an industrial problem. We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsches method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep.

Computing the Hausdorff distance between NURBS surfaces using numerical iteration on the GPU

We present a GPU algorithm for computing the directed Hausdorff distance between two NURBS surfaces. The algorithm is based on sampling of one surface, and performing numerical iterations on the GPU to compute the minimal distance from each sample to the other surface. An error analysis for the Hausdorff distance computations is performed, based on bounds on the NURBS surfaces. We compare a CUDA implementation of our algorithm to existing methods, demonstrating that the new method addresses limitations of previous hierarchical culling methods such as the sensitivity to the position of the inputs.

A multiscale model for the study of cardiac biomechanics in single-ventricle surgeries: A clinical case

Complex congenital heart disease characterized by the underdevelopment of one ventricular chamber (single ventricle (SV) circulation) is normally treated with a three-stage surgical repair. This study aims at developing a multiscale computational framework able to couple a patient-specific three-dimensional finite-element model of the SV to a patient-specific lumped parameter (LP) model of the whole circulation, in a closed-loop fashion. A sequential approach was carried out: (i) cardiocirculatory parameters were estimated by using a fully LP model; (ii) ventricular material parameters and unloaded geometry were identified by means of the stand-alone, three-dimensional model of the SV; and (iii) the three-dimensional model of SV was coupled to the LP model of the circulation, thus closing the loop and creating a multiscale model. Once the patient-specific multiscale model was set using pre-operative clinical data, the virtual surgery was performed, and the post-operative conditions were simulated. This approach allows the analysis of local information on ventricular function as well as global parameters of the cardiovascular system. This methodology is generally applicable to patients suffering from SV disease for surgical planning at different stages of treatment. As an example, a clinical case from stage 1 to stage 2 is considered here.