Here we put forward a mathematical model describing the response of low-grade (WHO grade II) oligodendrogliomas (LGO) to temozolomide (TMZ). The model describes the longitudinal volumetric dynamics of tumor response to TMZ of a cohort of 11 LGO patients treated with TMZ. After finding patient-specific parameters, different therapeutic strategies were tried computationally on the ‘in-silico twins’ of those patients. Chemotherapy schedules with larger-than-standard rest periods between consecutive cycles had either the same or better long-term efficacy than the standard 28-day cycles. The results were confirmed in a large trial of 2000 virtual patients. These long-cycle schemes would also have reduced toxicity and defer the appearance of resistances. On the basis of those results, a combination scheme consisting of five induction TMZ cycles given monthly plus 12 maintenance cycles given every three months was found to provide substantial survival benefits for the in-silico twins of the 11 LGO patients (median 5.69 years, range: 0.67 to 68.45 years) and in a large virtual trial including 2000 patients. We used 220 sets of experiments in-silico to show that a clinical trial incorporating 100 patients per arm (standard intensive treatment versus 5 + 12 scheme) could demonstrate the superiority of the novel scheme after a follow-up period of 10 years. Thus, the proposed treatment plan could be the basis for a standardized TMZ treatment for LGO patients with survival benefits. We developed a mathematical model describing the longitudinal volumetric growth data of grade II oligodendroglioma patients and their response to temozolomide. The model was used to explore alternative therapeutic protocols for the in-silico twins of the patients and in virtual clinical trials. The simulations show that enlarging the time interval between chemotherapy cycles would maintain the therapeutic efficacy, while limiting toxicity and deferring the development of resistance. This may allow for improved drug-exposure by administering a larger number of cycles for longer treatment periods. A scheme based on this idea consisting of an induction phase (5 consecutive cycles, 1 per month) and a maintenance phase (12 cycles given in three-months intervals) led to substantial survival benefits in-silico. The computational results suggest that a clinical trial enrolling 100 patients per arm (standard intensive therapy versus 5+12 novel scheme) could prove the effectiveness of the proposed approach after a follow-up period of 10 years.

Low-grade gliomas (LGGs) are brain tumors characterized by their slow growth and infiltrative nature. Treatment options for these tumors are surgery, radiation therapy and chemotherapy. The optimal use of radiation therapy and chemotherapy is still under study. In this paper, we construct a mathematical model of LGG response to combinations of chemotherapy, specifically to the alkylating agent temozolomide and radiation therapy. Patient-specific parameters were obtained from longitudinal imaging data of the response of real LGG patients. Computer simulations showed that concurrent cycles of radiation therapy and temozolomide could provide the best therapeutic efficacy in-silico for the patients included in the study. The patient cohort was extended computationally to a set of 3000 virtual patients. This virtual cohort was subject to an in-silico trial in which matching the doses of radiotherapy to those of temozolomide in the first five days of each cycle improved overall survival over concomitant radio-chemotherapy according to RTOG 0424. Thus, the proposed treatment schedule could be investigated in a clinical setting to improve combination treatments in LGGs with substantial survival benefits.

Low-grade gliomas are primary brain tumors that arise from glial cells and are usually treated with temozolomide (TMZ) as a chemotherapeutic option. They are often incurable, but patients have a prolonged survival. One of the shortcomings of the treatment is that patients eventually develop drug resistance. Recent findings show that persisters, cells that enter a dormancy state to resist treatment, play an important role in the development of resistance to TMZ. In this study we constructed a mathematical model of low-grade glioma response to TMZ incorporating a persister population. The model was able to describe the volumetric longitudinal dynamics, observed in routine FLAIR 3D sequences, of low-grade glioma patients acquiring TMZ resistance. We used the model to explore different TMZ administration protocols, first on virtual clones of real patients and afterwards on virtual patients preserving the relationships between parameters of real patients. In silico clinical trials showed that resistance development was deferred by protocols in which individual doses are administered after rest periods, rather than the 28-days cycle standard protocol. This led to median survival gains in virtual patients of more than 15 months when using resting periods between two and three weeks and agreed with recent experimental observations in animal models. Additionally, we tested adaptive variations of these new protocols, what showed a potential reduction in toxicity, but no survival gain. Our computational results highlight the need of further clinical trials that could obtain better results from treatment with TMZ in low grade gliomas.

The use of mathematical models for personalization of cancer therapies and raising hypothesis of potential clinical impact is an emerging topic in the interface between mathematics and oncology. Here we put forward a mathematical model describing the response of low-grade (WHO grade II) oligodendrogliomas (LGO) to temozolomide (TMZ). The model described the longitudinal volumetric dynamics of tumor response to TMZ of a cohort of 11 LGO patients treated with TMZ. After finding patient-specific parameters, different therapeutical strategies were tried computationally on the ‘in-silico twins’ of those patients. Chemotherapy schedules with larger-than-standard rest periods between consecutive cycles had either the same or better long-term efficacy than the standard 28-day cycles. The results were confirmed in a large virtual clinical trial including 2000 patients. These long-cycle schemes would also have reduced toxicity and defer the appearance of resistances. On the basis of those results, a combination scheme consisting of five induction TMZ cycles given monthly plus 12 maintenance cycles given every three months was found to provide substantial survival benefits for the in-silico twins of the 11 LGO patients (median 5.69 years, range: 0.67 to 68.45 years) and in a large virtual trial including 2000 patients. This scheme could be useful for defining a standardized TMZ treatment for LGO patients with survival benefits. Author summary: A mathematical model described the longitudinal volumetric growth data of grade II oligodendrogliomas patients and their response to temozolomide. The model was used to explore alternative therapeutical protocols for the in-silico twins of the patients and in virtual clinical trials. The simulations show that enlarging the time interval between chemotherapy cycles would maintain the therapeutical efficacy, while limiting toxicity and defering the development of resistances. This may allow for improved drug-exposure by administering a larger number of cycles for longer treatment periods. A scheme based on this idea consisting of an induction phase (5 consecutive cycles, 1 per month) and a maintenance phase (12 cycles given in three-months intervals) led to substantial survival benefits in-silico.

Modeling diabetic illness with random perturbations is the goal of this work. The proposed model consists of three classes: the pre-diabetic population, the diabetic population with complications, and the diabetic population without complications. We examined the suggested problem to determine at least one unique solution within the positive feasible region. The stationary distribution of this model was also explored, and the non-negative $C^2$-Lyapunov function was used to create an adequate condition for the persistence of one stationary ergodic distribution. For this model, the existence and uniqueness of the solution were also established. Additionally, the stochastic non-standard finite difference (NSFD) scheme was developed for the model. The consistency and stability of the scheme were analyzed, showing that it is consistent and stable in the mean-square sense. The underlying system admits a unique endemic equilibrium point. Finally, a test problem was studied by using a numerical technique, varying the noise levels, and maintaining the same parameter values. The outcomes for each stated class were numerically simulated in order to validate our proposed approach.