Research Interests

Mathematical Modeling of Complex Biological Systems and Their Numerical Simulations
Ordinary and Partial Differential Equations
Finite Element Methods, Discontinuous Galerkin Methods
Image Processing
Machine and Deep Learning
Uncertainty Quantification

Publications

P. Kumar, M. Lacroix, P. Dupre, J. Arslan, L. Fenou, B. Orsetti, L. Le Cam, D. Racoceanu, O. Radulescu. Deciphering Oxygen Distribution and Hypoxia Profiles in the Tumor Microenvironment: A Data‐Driven Mechanistic Modeling Approach, Physics in Medicine & Biology, 2024, 69 125023. DOI: https://doi.org/10.1088/1361‑6560/ad524a.
J. Arslan, M. Ounissi , H. Luo, M. Lacroix, P. Dupré, P. Kumar, A. Hodgkinson, S. Dandou, R. Larive, C. Pignodel, L. Le Cam, O. Radulescu, and D. Racoceanu. Efficient 3D reconstruction of whole slide images in melanoma, Medical Imaging 2023: Digital and Computational Pathology, 12471, 463-475, 2023. DOI: https://doi.org/10.1117/12.2657473.
P. Kumar, C. Surulescu, and A. Zhigun. Multiphase modelling of glioma pseudopalisading under acidosis. Mathematics in Engineering, 2022, 4(6): 1-28. DOI: https://doi.org/10.3934/mine.2022049 .
P. Kumar, J. Li, and C. Surulescu. Multiscale modeling of glioma pseudopalisades: contributions from the tumor microenvironment. Journal of Mathematical Biology, 82: 49, 2021. DOI: https://doi.org/10.1007/s00285-021-01599-x .
P. Kumar, and C. Surulescu. A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis. Symmetry, 12: 1870, 2020. DOI: https://doi.org/10.3390/sym12111870.

PhD Thesis

P. Kumar. Mathematical Modeling of Glioma Patterns as a Consequence of Acidosis and Hypoxia. PhD Thesis, Technische Universitat Kaiserslautern, 2021. DOI: https://doi.org/10.26204/KLUEDO/6573.

Conferences/Workshops

P. Kumar, P. Andrey. “PlantCPM: A Wall-Mechanistic Cellular Potts Model for Plant Morphogenesis”, Plant Computational Biology Workshop, Lyon, France, September 07–11, 2026 (Poster Presentation).
P. Kumar, F. Crauste, F. Clément, C. Audebert. “Deciphering Spatiotemporal Dynamics of Oocyte Selection during Ovarian Development: A 3D Multiscale Agent-Based Model”, European Conference on Mathematical and Theoretical Biology (ECMTB 2026), Multiscale and Multiphysics Modelling, Graz, Austria, July 13–17, 2026 (Presentation).
P. Kumar, C. Audebert, F. Clément, F. Crauste. “Multiscale Modeling of Ovarian Development: Mechanisms Underlying the Selection of Future Oocytes”, Journées Math Bio Santé (JMBS), Montpellier, France, November 05–07, 2025 (Presentation).
P. Kumar, K. Sadreddini, M. Hamadache, M. Lacroix, P. Dupré, B. Orsetti, L. Fenou, L. Le Cam, D. Racoceanu, O. Radulescu. “Extending Tumor Hypoxia Modeling from 2D to 3D: A Mechanistic, Data-Driven Approach Informed by 2D Histopathology”, CompSysBio2025: Advanced Lecture Course on Computational Systems Biology, Aussois, France, October 05–10, 2025 (Poster Presentation).
P. Kumar, J. Arslan, A. Hodgkinson, H. Luo, S. Dandou, M. Lacroix, P. Dupré, C. Pignodel, R M Larive, L. Le Cam, D. Racoceanu, O. Radulescu. “Estimating spatial distribution of oxygen and hypoxia in tumor microenvironment: a mechanistic approach”, CanceropoleGSO, Montpellier, November 30‐Decembre 02, 2022 (Presentation).
P. Kumar, J. Arslan, A. Hodgkinson, H. Luo, S. Dandou, M. Lacroix, P. Dupré, C. Pignodel, R M Larive, L. Le Cam, D. Racoceanu, O. Radulescu. “Data driven mechanistic modeling of oxygen distribution and hypoxia profile in tumor microenvironment”, COMPSYSCAN2022, Lyon, October 17‐18, 2022 (Presentation).
D. Fettahoglu, C. Choufani, P. Kumar, A. Castro, T. Lorca, O. Radulescu.“Stochasticity of Meiotic Entryin Xenopus Oocytes”, International Conference in Systems Biology, Berlin, October 08‐12, 2022 (Joint Poster).
J. Arslan, P. Kumar, Hodgkinson,A;Luo,H;Dupré,P;Dandou,S;Pignodel,C;Larive,R;Lacroix,M;LeCam,L;Radulescu,O; Racoceanu, D. “3D reconstruction and mathematical modelling of whole slide images to elucidate resistance to the targeted therapy in melanoma”, International Conference in Systems Biology, Berlin, October 08‐12, 2022 (Joint Poster).
Annual Meeting of the International Physics of Living Systems (iPoLS) Network, Montpellier, May 31 – June 3, 2022 (Participation).
P. Kumar. A Multiscale Model for Pseudopalisading in Glioblastoma, Workshop on Mathematical Modeling of Cell Migration, Kaiserslautern, January 08-09, 2020 (Presentation).
LMS Research School: PDEs in Mathematical Biology: Modelling and Analysis, Edinburgh, 29 April – 3 May 2019. (Participation).
P. Kumar. Uncertainty Quantification for the Input Data Involved in the Mathematical Models for Tumor Growth, International Conference on Advances In Scientific Computing, Chennai, November 28-30, 2016 (Paper Presentation).

Recent Results

A computational framework to predict hypoxia [1]):

Evolution of glioma, acidity, endothelial cells(ECs) and vascular endothelial growth factor(VEGF) during the hypoxia induced angiogenesis of glioma pseudopalisading cells (model and results published in [5]):