A5050535603- Mathematical Biology Tumor Growth
- Advanced Numerical Analysis Techniques
- Advanced Numerical Methods in Computational Mathematics
- Advanced Mathematical Modeling in Engineering
- Solidification and crystal growth phenomena
- Cellular Mechanics and Interactions
- Numerical methods in engineering
- Radiomics and Machine Learning in Medical Imaging
- Prostate Cancer Treatment and Research
- Prostate Cancer Diagnosis and Treatment
- Fluid Dynamics and Turbulent Flows
- Fluid Dynamics and Thin Films
- Blood properties and coagulation
- Lattice Boltzmann Simulation Studies
- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Heat Transfer
- Micro and Nano Robotics
- Composite Structure Analysis and Optimization
- Cancer Genomics and Diagnostics
- MRI in cancer diagnosis
- Rheology and Fluid Dynamics Studies
- Ultrasound and Cavitation Phenomena
- Cancer Cells and Metastasis
- Tribology and Lubrication Engineering
- Angiogenesis and VEGF in Cancer
Purdue University West Lafayette
2017-2024
Center for Cancer Research
2019-2024
Purdue University Institute for Cancer Research
2024
Weatherford (Switzerland)
2024
Median SCP (Spain)
2024
University of Florida
2024
University of California, Merced
2021-2023
University of Castilla-La Mancha
2022
Universidade da Coruña
2009-2020
Weldon City Schools
2020
We present a mathematical model for vascular tumor growth. use phase fields to cellular growth and reaction-diffusion equations the dynamics of angiogenic factors nutrients. The naturally predicts shift from avascular at realistic scales. Our computations indicate that negative regulation Delta-like ligand 4 signaling pathway slows down by producing larger density non-functional capillaries. results show good quantitative agreement with experiments.
Significance Benign prostatic hyperplasia (BPH) is a common disease in aging men that causes the prostate to enlarge progressively. Men with larger prostates tend harbor tumors more favorable features. The underlying mechanisms explain this interaction between BPH and cancer (PCa) are largely unknown. Here, we propose may mechanically impede PCa growth by producing increasingly intense mechanical stresses over time, which known slow down tumor dynamics. To explore hypothesis, ran qualitative...
We present the application of a class deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. explain how incorporate momentum balance constitutive relations into PINN, explore detail linear elasticity, illustrate its extension nonlinear problems through an example that showcases von~Mises elastoplasticity. While common PINN algorithms are based on training one neural network (DNN), we propose multi-network model results more accurate...
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of thermodynamic transition from a fluid state to crystalline state. resulting phase field crystal model describes variety spatially localized structures, in addition different extended periodic structures. location these structures temperature versus mean order parameter plane is determined using combination numerical continuation one dimension and direct simulation two three...
Significance We perform a tissue-scale, personalized computer simulation of prostate cancer (PCa) growth in patient, based on prostatic anatomy extracted from medical images. To do so, we propose mathematical model for the PCa. The includes an equation reference biomarker PCa: prostate-specific antigen (PSA). Hence, can link results our to data that urologists easily interpret. Our reproduces features tumor observed experiments and clinical practice. It also captures known shift pattern PCa,...
SUMMARY Tumor angiogenesis, the growth of new capillaries from preexisting ones promoted by starvation and hypoxia cancerous cell, creates complex biological patterns. These patterns are captured a hybrid model that involves high‐order partial differential equations coupled with mobile, agent‐based components. The continuous rely on phase‐field method to describe intricate interfaces between vasculature host tissue. discrete posed cellular scale treat tip endothelial cells as mobile agents....
Cancerous tumours have the ability to recruit new blood vessels through a process called angiogenesis. By stimulating vascular growth, get connected circulatory system, receive nutrients and open way colonize distant organs. Tumour-induced networks become unstable in absence of tumour angiogenic factors (TAFs). They may undergo alternating stages regression regrowth. Following phase-field methodology, we propose model angiogenesis that reproduces aforementioned features highlights importance...
Abstract Active surveillance (AS) is a suitable management option for newly diagnosed prostate cancer, which usually presents low to intermediate clinical risk. Patients enrolled in AS have their tumor monitored via longitudinal multiparametric MRI (mpMRI), PSA tests, and biopsies. Hence, treatment prescribed when these tests identify progression higher-risk cancer. However, current protocols rely on detecting through direct observation according population-based monitoring strategies. This...
The phase-field crystal model (PFC model) resolves systems on atomic length scales and diffusive time lies in between standard modeling atomistic methods. More recently a hyperbolic or modified PFC was introduced to describe fast (propagative) slow (diffusive) dynamics. We present finite-element method for solving the equation, introducing an unconditionally stable integration algorithm. A spatial discretization is used with traditional ${\mathcal{C}}^{0}$-continuous Lagrange elements...