Applied mathematics and nonlinear sciences in the war on cancer

Pérez-Garcı́a, Vı́ctor M.; Fitzpatrick, Susan M.; Pérez-Romasanta, Luis A.; Pešić, Milica; Schucht, Philippe; Arana, Estanislao; Sánchez-Gómez, Pilar

doi:10.21042/amns.2016.2.00036

Cited by 38 publications

(20 citation statements)

References 84 publications

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“…Furthermore, mathematical models can range wildly in their complexity, which may result in either highly unrealistic or mathematically and computationally untractable models. There have been numerous reviews of the growing literature on mathematical oncology in the past 15 years [15,[23][24][25][26]. However, none of these reviews exclusively and extensively cover mathematical models for prostate cancer.…”

Section: Mathematical Models For Prostate Cancermentioning

confidence: 99%

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

et al. 2020

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We review and synthesize key findings and limitations of mathematical models for prostate cancer, both from theoretical work and data-validated approaches, especially concerning clinical applications. Our focus is on models of prostate cancer dynamics under treatment, particularly with a view toward optimizing hormone-based treatment schedules and estimating the onset of treatment resistance under various assumptions. Population models suggest that intermittent or adaptive therapy is more beneficial to delay cancer relapse as compared to the standard continuous therapy if treatment resistance comes at a competitive cost for cancer cells. Another consensus among existing work is that the standard biomarker for cancer growth, prostate-specific antigen, may not always correlate well with cancer progression. Instead, its doubling rate appears to be a better indicator of tumor growth. Much of the existing work utilizes simple ordinary differential equations due to difficulty in collecting spatial data and due to the early success of using prostate-specific antigen in mathematical modeling. However, a shift toward more complex and realistic models is taking place, which leaves many of the theoretical and mathematical questions unexplored. Furthermore, as adaptive therapy displays better potential than existing treatment protocols, an increasing number of studies incorporate this treatment into modeling efforts. Although existing modeling work has explored and yielded useful insights on the treatment of prostate cancer, the road to clinical application is still elusive. Among the pertinent issues needed to be addressed to bridge the gap from modeling work to clinical application are (1) real-time data validation and model identification, (2) sensitivity analysis and uncertainty quantification for model prediction, and (3) optimal treatment/schedule while considering drug properties, interactions, and toxicity. To address these issues, we suggest in-depth studies on various aspects of the parameters in dynamical models such as the evolution of parameters over time. We hope this review will assist future attempts at studying prostate cancer.Prostate cancer (PCa) is the leading cause of cancer in US men (behind non-melanoma skin cancers), as well as the second leading cause of cancer-related mortality in men. The American Cancer Society estimates that in 2020, 191,930 Americans will be diagnosed with prostate cancer, with approximately 21.5% of all new cancer cases in men. The average five-year survival rate for all cases of prostate cancer is about 99%, which is a 31% point higher than in the 1970s [1]. However, once cancer metastasizes, the five-year survival rate drops to 30%, an increase of 10 percentage-point compared to the 1970s [2]. While the incidence of prostate cancer in the US is decreasing (see Figure 1), one possible cause is doctors' discouragement of early PCa diagnosis due to the fear of overtreating cancer. Globally, the incidence of prostate cancer is increasing, especially among developing nations [3].

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Section: Mathematical Models For Prostate Cancermentioning

confidence: 99%

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

et al. 2020

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“…Mathematics provides the natural environment for modelling and analyzing problems from different areas in particular from health sciences, see for instance some applications to the war against cancer like [12,13]. In the next Appendix A we shall present all mathematical machinery used in this work.…”

Section: Discussionmentioning

confidence: 99%

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

et al. 2019

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The objective of the present paper is to describe all the anatomical considerations surrounding the nasopalatine foramen by relating them to the study of bone structure density via an accurate fractal dimension analysis in that area. We consecutively selected a sample of 130 patients, all of them with cone beam computed tomography (CBCT) images performed for treatment needs. We chose a specific window (ROI), which coincides with an axial cut at the level of the anterior nasal spine. Different anthropometric measurements were analyzed and a novel fractal dimension analysis was performed. Our sample consisted of 130 patients and was divided into two groups: group one (consisting of 65 subjects without loss of teeth) and group two (consisting of 65 patients with the absence of some teeth). In the sample, 52.31% were women (68 people). Mann–Whitney tests were applied to obtain the statistical results. The mean age of the patients in that sample was 53 . 67 years with a standard deviation of 8 . 20 years. We conclude that fractal dimension, a mathematical invariant, behaves symmetrically for binary images from the CBCT scanners of each subject of our sample of study. We also conclude that there were no significant differences between all the anthropometric measures used neither in the subjects themselves nor in the different groups. Therefore, some patterns of symmetry were appreciated at a complete range of levels.

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“…11 Regarding chemotherapy (CT), temozolomide (TMZ), an oral alkylating agent, has 12 a favourable toxicity profile [5] and can contribute to reduction in seizure frequency in 13 low-grade glioma (LGG) patients [6]. Phase II trials have demonstrated its effectivity 14 against LGGs [7][8][9]. Also, neoadjuvant CT given to surgically unresectable tumors has 15 allowed subsequent gross total resection in some cases [10], which is of relevance when 16 the tumour is highly infiltrative or located in eloquent areas.…”

Section: Introductionmentioning

confidence: 99%

“…In that context, relevant 21 questions arise such choice of the chemotherapy regimen and the optimal number of 22 cycles to be prescribed. 23 Mathematical models have potential to help in finding optimized treatment 24 schedules/combinations improving survival and/or reducing toxicity [13,14]. Once the 25 base mathematical model is set, patient-specific parameters can be obtained from data.…”

Section: Introductionmentioning

confidence: 99%

Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas

Pérez-Garcı́a

Ayala-Hernández

Belmonte-Beitia

et al. 2019

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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.

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Applied mathematics and nonlinear sciences in the war on cancer

Cited by 38 publications

References 84 publications

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

On the Symmetry of the Bone Structure Density over the Nasopalatine Foramen via Accurate Fractal Dimension Analysis

Computational design of improved standardized chemotherapy protocols for grade II oligodendrogliomas

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