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We introduce a diffusion-based cross-domain image translator in the absence of paired training data. Unlike GAN-based methods, our approach integrates diffusion models to learn the image translation process, allowing for more coverable…
Digital twins (DTs) are redefining healthcare by paving the way for more personalized, proactive, and intelligent medical interventions. As the shift toward personalized care intensifies, there is a growing need for an individual's virtual…
Tumor shape is a key factor that affects tumor growth and metastasis. This paper proposes a topological feature computed by persistent homology to characterize tumor progression from digital pathology and radiology images and examines its…
We investigate the dynamics of a nonlinear system modeling tumor growth with drug application. The tumor is viewed as a mixture consisting of proliferating, quiescent and dead cells as well as a nutrient in the presence of a drug. The…
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed in [A. Hawkins-Daruud, K.G. van der Zee, J.T. Oden, Numerical simulation of a thermodynamically consistent…
Magnetic resonance imaging (MRI) is a vital diagnostic tool, but its inherently long acquisition times reduce clinical efficiency and patient comfort. Recent advancements in deep learning, particularly diffusion models, have improved…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the…
Most cancers in humans are large, measuring centimeters in diameter, composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division.…
Recent progress in microdissection and in DNA sequencing has enabled subsampling of multi-focal cancers in organs such as the liver in several hundred spots, helping to determine the pattern of mutations in each of these spots. This has led…
Digital pathology is not only one of the most promising fields of diagnostic medicine, but at the same time a hot topic for fundamental research. Digital pathology is not just the transfer of histopathological slides into digital…
Quantitative computed tomography (QCT) plays a crucial role in assessing bone strength and fracture risk by enabling volumetric analysis of bone density distribution in the proximal femur. However, deploying automated segmentation models in…
Radioembolization is a localized liver cancer treatment that delivers radioactive microspheres (30 micron) to tumors via a catheter inserted in the hepatic arterial tree. The goal is to maximize therapeutic efficacy while minimizing damage…
Image enhancement improves visual quality and helps reveal details that are hard to see in the original image. In medical imaging, it can support clinical decision-making, but current models often over-edit. This can distort organs, create…
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during…
The Diffusion Probabilistic Model (DPM) has recently gained popularity in the field of computer vision, thanks to its image generation applications, such as Imagen, Latent Diffusion Models, and Stable Diffusion, which have demonstrated…
This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…
Deep learning (DL) models for disease classification or segmentation from medical images are increasingly trained using transfer learning (TL) from unrelated natural world images. However, shortcomings and utility of TL for specialized…
We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a…
Cancer is a complex disease driven by dynamic regulatory shifts that cannot be fully captured by individual molecular profiling. We employ a data-driven approach to construct a coarse-grained dynamic network model based on hallmark…