arXiv subjects

Aishwarya Pawar

Publications and source records attributed to Aishwarya Pawar.

5 recordsLinked to original sources

arXiv2026

Novel Dynamics in Models of Angiogenesis with p-Laplacian diffusion

Ischemic heart diseases represent the leading cause of mortality worldwide. Revascularization, the process to restore blood flow in blockages, shows promise. To this end, mathematical models for angiogenesis, the process by which new blood vessels form from existing ones, have been extremely well investigated. In the current work, we consider a classical two species model for angiogenesis, consisting of cell and VEGF populations. However, we assume the cells move according to p-Laplacian diffusion, which could be both ``fast" ($1 2$), in addition to normal diffusion ($p=2$). We first show that the system is well posed in a weak sense when $p>\frac{3}{2}$, for sufficiently small initial data. Next, we show that the p-Laplacian can lead to several novel dynamics not reported earlier; these include increased cellular proliferation via bi-modal and multi spike solutions, gain of regularity, prevention of finite time blow-up, cell depletion via finite time extinction, and Turing patterns. We discuss applications of these results for cardiac health via a digital twins framework.

math.AP↗

arXiv2026

Procedural Volumetric Modeling of Plant Branching Structures for Finite Element Analysis

Precision agriculture, smart breeding, and agricultural robotics require accurate and automated plant modeling. These models provide high-fidelity three-dimensional (3D) representations of plant architecture. They provide the geometric foundation for simulations of water and nutrient transport, light interception, structural loading, and crop lodging. Unlike static plant modeling pipelines, procedural modeling frameworks not only generate accurate 3D plant geometries but also support the generative modeling of crop diversity and the dynamic modeling of plant growth. While terrestrial laser scanning, LiDAR, photogrammetry, and neural reconstruction-based approaches have made 3D plant reconstruction possible, the resulting data are typically in the form of point clouds, which cannot be directly utilized for high-fidelity simulations. We present an automated volumetric procedural modeling framework for plant branching structures that generates analysis-suitable hexahedral meshes from input skeletons or 3D point clouds. The input skeleton is first converted into a rooted graph representation that captures the plant branching topology. Each graph edge is then represented by a smooth centerline B-spline curve, around which a cylindrical tensor-product B-spline volume is constructed. At each junction, incident B-spline volume control lattices are joined using blending operations. The resulting volumetric parameterization is evaluated to generate a smooth and conforming hexahedral mesh of the whole plant. We demonstrate the framework on three diverse plant datasets, namely mung bean, tomato, and walnut trees, generating meshes with both uniform and spatially varying branch radii. The framework also supports dynamic mesh generation suitable for modeling plant growth by locally updating newly added branches without reconstructing the full plant geometry.

cs.GR↗

arXiv2025

VALVEFIT: An analysis-suitable B-spline-based surface fitting framework for patient-specific modeling of tricuspid valves

Patient-specific computational modeling of the tricuspid valve (TV) is vital for the clinical assessment of heart valve diseases. However, this process is hindered by limitations inherent in the medical image data, such as noise and sparsity, as well as by complex valve dynamics. We present VALVEFIT, a novel GPU-accelerated and differentiable B-spline surface fitting framework that enables rapid reconstruction of smooth, analysis-suitable geometry from point clouds obtained via medical image segmentation. We start with an idealized TV B-spline template surface and optimize its control point positions to fit segmented point clouds via an innovative loss function, balancing shape fidelity and mesh regularization. Novel regularization terms are introduced to ensure that the surface remains smooth, regular, and intersection-free during large deformations. We demonstrate the robustness and validate the accuracy of the framework by first applying it to simulation-derived point clouds that serve as the ground truth. We further show its robustness across different point cloud densities and noise levels. Finally, we demonstrate the performance of the framework toward fitting point clouds obtained from real patients at different stages of valve motion. An isogeometric biomechanical valve simulation is then performed on the fitted surfaces to show their direct applicability toward analysis. VALVEFIT enables automated patient-specific modeling with minimal manual intervention, paving the way for the future development of direct image-to-analysis platforms for clinical applications.

math.OC↗

arXiv2022

PDE-constrained shape registration to characterize biological growth and morphogenesis from imaging data

We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then split into growth and elastic contributions. The growth tensor captures addition of mass, i.e. growth, and evolves according to a constitutive equation which is usually a function of the elastic deformation. Stress is generated in the material due to the elastic component of the deformation alone. The result of the registration is obtained by minimizing a total energy functional which includes: a distance measure reflecting similarity between the shapes, and the total elastic energy accounting for the growth of the tissue. We apply the proposed shape registration framework to study zebrafish embryo epiboly process and tissue expansion during skin reconstruction surgery. We anticipate that our PDE-constrained shape registration method will improve our understanding of biological and medical problems in which tissues undergo extreme deformations over time.

physics.bio-ph↗

arXiv2017

Adaptive FEM-based nonrigid image registration using truncated hierarchical B-splines

We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework minimizes an energy functional using an FEM-based method and thus involves solving a large system of linear equations. This framework is carried out on a set of successively refined grids. However, due to the increased number of control points during subdivision, large linear systems are generated which are generally demanding to solve. Instead of using uniform subdivision, an adaptive local refinement scheme is carried out, only refining the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency. The performance of the proposed method is demonstrated on 2D synthetic and medical images.

math.NA↗