Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2501.13774

A mathematical model of CAR-T cell therapy in combination with chemotherapy for malignant gliomas

Dmitry Sinelshchikov·Juan Belmonte-Beitia·Matteo Italia
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the dynamics and interactions between combined chemotherapy and chimeric antigen receptor (CAR-T) cells therapy and malignant gliomas (MG). MG is one of the most common primary brain tumor, with high resistance to therapy and unfavorable prognosis. Here, we develop a mathematical model that describes the application of chemo- and CAR-T cell therapies and the dynamics of sensitive and resistant populations of tumor cells. This model is a five-dimensional dynamical system with impulsive inputs corresponding to clinical administration of chemo- and immunotherapy. We provide a proof of non-negativeness of solutions of the proposed model for non-negative initial data. We demonstrate that if we apply both therapies only once, the trajectories will be attracted to an invariant surface that corresponds to the tumor carrying capacity. On the other hand, if we apply both treatments constantly, we find regions of the parameter where the tumor is eradicated. Moreover, we study applications of different combinations of the above treatments in order to find an optimal combination at the population level. To this aim, we generate a population of $10^{4}$ virtual patients with the model parameters uniformly distributed in the medically relevant ranges and perform \emph{in silico} trials with different combinations of treatments. We obtain optimal protocols for several different relations of tumor growth rates between sensitive and drug resistant cells. We demonstrate that the tumor growth rate, efficacy of chemotherapy, and tumor immunosuppression are the parameters that mostly impact survival time in \emph{in silico} trials. We believe that our results provide new theoretical insights to guide the design of clinical trials for MG therapies.

Explore related subjects

math.DS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Dmitry Sinelshchikov, Juan Belmonte-Beitia, Matteo Italia. 2025-06-03. A mathematical model of CAR-T cell therapy in combination with chemotherapy for malignant gliomas. https://doi.org/10.1063/5.0260252

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Pivoting technique for the circle homeomorphism group

We adapt Gou{ë}zel's pivoting technique to the circle homeomorphism group. As an application, we give different proofs of Gilabert Vio's probabilistic Tits alternative and Malicet's exponential synchronization.

math.DS↗
arXiv2026

Asymmetry of a class of Mellin transforms

We introduce the quantity $μ_η$, defined for every complex $s$ in the critical strip, as a transformation of the Mellin transform associated to the functions $η$. We establish a sufficient condition on $η$ under which $μ_η(s)$ and $μ_η(1-s)$ cannot both vanish outside the critical line. An application is given to the case in which $η$ is the fractional part function, and the zeros of $μ_η$ coincide with the zeros of the Riemann zeta function.

math.DS↗
arXiv2026

Infinite Set of Resonances in the Linear Damped Oscillator Subject to Harmonic Forcing with Non-standard Frequency Modulation

It is shown that harmonic signals incorporating a type of weak non-standard frequency modulation (wNSFM) have interesting spectral properties, namely, time-dependent bandwidths that become increasingly broader with increasing time. As such, they represent a class of signals with frequency-time coupling in their spectra. Specifically, the weakly damped oscillator exhibits always two transient resonance captures involving two distinct harmonics possessing relatively high amplitudes over finite time intervals, while the overall response decays as $~t^{-1/2}$ as $t\rightarrow\infty$. Considering the undamped oscillator, it possesses two types of resonances, referred to as simple and non-simple resonances. Simple resonances correspond to finite-amplitude steady-state responses caused by two sustained resonance captures, in the form of two distinct modulated quasi-periodic responses, which, however are "activated" at different time instances. The necessary and sufficient conditions for non-simple resonances are given in the form of a theorem which predicts the existence of resonant harmonics and specifies the special phase conditions that the resonant harmonics must satisfy for constructive interference; the resulting undamped non-simple resonance grows unboundedly as $~t^{-1/2}$ as $t\rightarrow\infty$, in contrast to the classical resonance growth of the linear resonator with unmodulated harmonic excitation whose response grows as $~t$ as $t\rightarrow\infty$. These resonant responses are persistent to changes in the parameters of the wNSFM. Our results reveal interesting infinite sets of resonances in linear SDOF resonators under frequency-modulated excitations.

math.DS↗