Predicting Outcomes of Prostate Cancer Immunotherapy by Personalized Mathematical Models

Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models.We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cell vaccine. For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient's training set and his validation set. The training set, used for model personalization, contained the patient's initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in 12 of the 15 vaccination-responsive patients (the coefficient of determination between the predicted and observed PSA values was R(2) = 0.972). The model could not account for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. Personalized regimens predicted to enhance the effects of therapy differed among the patients.Using a few initial measurements, we constructed robust patient-specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model-suggested immunotherapy protocols

Blackboard to Bedside: A Mathematical Modeling Bottom-Up Approach Toward Personalized Cancer Treatments

Cancers present with high variability across patients and tumors; thus, cancer care, in terms of disease prevention, detection, and control, can highly benefit from a personalized approach. For a comprehensive personalized oncology practice, this personalization should ideally consider data gathered from various information levels, which range from the macroscale population level down to the microscale tumor level, without omission of the central patient level. Appropriate data mined from each of these levels can significantly contribute in devising personalized treatment plans tailored to the individual patient and tumor. Mathematical models of solid tumors, combined with patient-specific tumor profiles, present a unique opportunity to personalize cancer treatments after detection using a bottom-up approach. Here, we discuss how information harvested from mathematical models and from corresponding in silico experiments can be implemented in preclinical and clinical applications. To conceptually illustrate the power of these models, one such model is presented, and various pertinent tumor and treatment scenarios are demonstrated in silico. The presented model, specifically a multiscale, hybrid cellular automaton, has been fully validated in vitro using multiple cell-line–specific data. We discuss various insights provided by this model and other models like it and their role in designing predictive tools that are both patient, and tumor specific. After refinement and parametrization with appropriate data, such in silico tools have the potential to be used in a clinical setting to aid in treatment protocols and decision making.Publisher PDFPeer reviewe

Statistical optimisation and tuning of GA factors.

This paper presents a practical methodology of improving the efficiency of Genetic Algorithms through tuning the factors significantly affecting GA performance. This methodology is based on the methods of statistical inference and has been successfully applied to both binary- and integer-encoded Genetic Algorithms that search for good chemotherapeutic schedules

An Integrated Disease/Pharmacokinetic/Pharmacodynamic Model Suggests Improved Interleukin-21 Regimens Validated Prospectively for Mouse Solid Cancers

Interleukin (IL)-21 is an attractive antitumor agent with potent immunomodulatory functions. Yet thus far, the cytokine has yielded only partial responses in solid cancer patients, and conditions for beneficial IL-21 immunotherapy remain elusive. The current work aims to identify clinically-relevant IL-21 regimens with enhanced efficacy, based on mathematical modeling of long-term antitumor responses. For this purpose, pharmacokinetic (PK) and pharmacodynamic (PD) data were acquired from a preclinical study applying systemic IL-21 therapy in murine solid cancers. We developed an integrated disease/PK/PD model for the IL-21 anticancer response, and calibrated it using selected “training” data. The accuracy of the model was verified retrospectively under diverse IL-21 treatment settings, by comparing its predictions to independent “validation” data in melanoma and renal cell carcinoma-challenged mice (R2>0.90). Simulations of the verified model surfaced important therapeutic insights: (1) Fractionating the standard daily regimen (50 µg/dose) into a twice daily schedule (25 µg/dose) is advantageous, yielding a significantly lower tumor mass (45% decrease); (2) A low-dose (12 µg/day) regimen exerts a response similar to that obtained under the 50 µg/day treatment, suggestive of an equally efficacious dose with potentially reduced toxicity. Subsequent experiments in melanoma-bearing mice corroborated both of these predictions with high precision (R2>0.89), thus validating the model also prospectively in vivo. Thus, the confirmed PK/PD model rationalizes IL-21 therapy, and pinpoints improved clinically-feasible treatment schedules. Our analysis demonstrates the value of employing mathematical modeling and in silico-guided design of solid tumor immunotherapy in the clinic

Optimization Design of RC Elevated Water Tanks under Seismic Loads

[EN] This paper deals with the seismic column design of 35 elevated RC water storage tanks. Tanks comprise a top conic trunk reservoir, a column with variable hollow square cross-sections, and a shallow foundation on a sand layer. The five-column heights considered are 20, 25, 30, 35, and 40 m. The five tanks are subjected to seven degrees of seismic loading characterized by the reference peak ground acceleration in Eurocode 8. The elevated tanks are designed against the full prescriptions of Eurocode 2, Eurocode 8, and the Spaniard Structural Code of Practice. This includes variable loads for seismicity, wind, snow, etc., together with the action of self-weight and dead loads. The optimization design method considered is a variant of the old bachelor algorithm, an adaptive threshold acceptance method with a neighborhood move based on the mutation operator from genetic algorithms. Column results show the high nonlinearity of the problem since the horizontal seismic forces depend on the rigidity and height of the columns. The main features of the optimized tanks give guidance for the practical design of this kind of elevated RC water tank.Grant PID2020-117056RB-I00 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe".Martínez-Martín, FJ.; Yepes, V.; Gonzalez Vidosa, F.; Hospitaler Pérez, A.; Alcalá-González, J. (2022). Optimization Design of RC Elevated Water Tanks under Seismic Loads. Applied Sciences. 12(11):1-19. https://doi.org/10.3390/app12115635119121

The resonance phenomenon in population persistence: can the same theory guide both national security policies and personalized medicine?

Abstract The theory of resonance in population persistence proposes that the survival of a population that is exposed to externally inflicted loss processes (disturbances) during part of its life cycle is dependent on the relation between the average period of the disturbances and the average generation time of the population. This suggests that the size of a population can be controlled by manipulating the period between external disturbances. This theory, first formalized in a study of intertidal Red Sea mollusks exposed to periodic storms, has been found to apply to such seemingly disparate phenomena as the spread of a pathogen among susceptible individuals and the response of malignant cancer cells to chemotherapy. The current article provides a brief review of the evolution of the resonance theory into a tool that can be applied to designing vaccination policies – specifically, in preparedness for bio-terrorism attacks – and in personalized medicine. A personalized protocol based on the resonance theory was applied to a cancer patient, stabilizing his tumor progression, relieving his hematopoietic toxicity, and extending his surviva

Hybrid Modeling of Cancer Drug Resistance Mechanisms

Cancer is a multi-scale disease and its overwhelming complexity depends upon the multiple interwind events occurring at both molecular and cellular levels, making it very difficult for therapeutic advancements in cancer research. The resistance to cancer drugs is a significant challenge faced by scientists nowadays. The roots of the problem reside not only at the molecular level, due to multiple type of mutations in a single tumor, but also at the cellular level of drug interactions with the tumor. Tumor heterogeneity is the term used by oncologists for the involvement of multiple mutations in the development of a tumor at the sub-cellular level. The mechanisms for tumor heterogeneity are rigorously being explored as a reason for drug resistance in cancer patients. It is important to observe cell interactions not only at intra-tumoral level, but it is also essential to study the drug and tumor cell interactions at cellular level to have a complete picture of the mechanisms underlying drug resistance. The multi-scale nature of cancer drug resistance problem require modeling approaches that can capture all the multiple sub-cellular and cellular interaction factors with respect to dierent scales for time and space. Hybrid modeling offers a way to integrate both discrete and continuous dynamics to overcome this challenge. This research work is focused on the development of hybrid models to understand the drug resistance behaviors in colorectal and lung cancers. The common thing about the two types of cancer is that they both have dierent mutations at epidermal growth factor receptors (EGFRs) and they are normally treated with anti-EGFR drugs, to which they develop resistances with the passage of time. The acquiring of resistance is the sign of relapse in both kind of tumors. The most challenging task in colorectal cancer research nowadays is to understand the development of acquired resistance to anti-EGFR drugs. The key reason for this problem is the KRAS mutations appearance after the treatment with monoclonal antibodies (moAb). A hybrid model is proposed for the analysis of KRAS mutations behavior in colorectal cancer with respect to moAb treatments. The colorectal tumor hybrid model is represented as a single state automata, which shows tumor progression and evolution by means of mathematical equations for tumor sub-populations, immune system components and drugs for the treatment. The drug introduction is managed as a discrete step in this model. To evaluate the drug performance on a tumor, equations for two types of tumors cells are developed, i.e KRAS mutated and KRAS wild-type. Both tumor cell populations were treated with a combination of moAb and chemotherapy drugs. It is observed that even a minimal initial concentration of KRAS mutated cells before the treatment has the ability to make the tumor refractory to the treatment. Moreover, a small population of KRAS mutated cells has a strong influence on a large number of wild-type cells by making them resistant to chemotherapy. Patient's immune responses are specifically taken into considerations and it is found that, in case of KRAS mutations, the immune strength does not affect medication efficacy. Finally, cetuximab (moAb) and irinotecan (chemotherapy) drugs are analyzed as first-line treatment of colorectal cancer with few KRAS mutated cells. Results show that this combined treatment could be only effective for patients with high immune strengths and it should not be recommended as first-line therapy for patients with moderate immune strengths or weak immune systems because of a potential risk of relapse, with KRAS mutant cells acquired resistance involved with them. Lung cancer is more complicated then colorectal cancer because of acquiring of multiple resistances to anti-EGFR drugs. The appearance of EGFR T790M and KRAS mutations makes tumor resistant to a geftinib and AZD9291 drugs, respectively. The hybrid model for lung cancer consists of two non-resistant and resistant states of tumor. The non-resistant state is treated with geftinib drug until resistance to this drug makes tumor regrowth leading towards the resistant state. The resistant state is treated with AZD9291 drug for recovery. In this model the complete resistant state due to KRAS mutations is ignored because of the unavailability of parameter information and patient data. Each tumor state is evaluated by mathematical differential equations for tumor growth and progression. The tumor model consists of four tumor sub-population equations depending upon the type of mutations. The drug administration in this model is also managed as a discrete step for exact scheduling and dosages. The parameter values for the model are obtained by experiments performed in the laboratory. The experimental data is only available for the tumor progression along with the geftinib drug. The model is then fine tuned for obtaining the exact tumor growth patterns as observed in clinic, only for the geftinib drug. The growth rate for EGFR T790M tumor sub-population is changed to obtain the same tumor progression patterns as observed in real patients. The growth rate of mutations largely depends upon the immune system strength and by manipulating the growth rates for different tumor populations, it is possible to capture the factor of immune strength of the patient. The fine tuned model is then used to analyze the effect of AZD9291 drug on geftinib resistant state of the tumor. It is observed that AZD9291 could be the best candidate for the treatment of the EGFR T790M tumor sub-population. Hybrid modeling helps to understand the tumor drug resistance along with tumor progression due to multiple mutations, in a more realistic way and it also provides a way for personalized therapy by managing the drug administration in a strict pattern that avoid the growth of resistant sub-populations as well as target other populations at the same time. The only key to avoid relapse in cancer is the personalized therapy and the proposed hybrid models promises to do that

Directed Intervention Crossover Approaches in Genetic Algorithms with Application to Optimal Control Problems

Genetic Algorithms (GAs) are a search heuristic modeled on the processes of evolution. They have been used to solve optimisation problems in a wide variety of fields. When applied to the optimisation of intervention schedules for optimal control problems, such as cancer chemotherapy treatment scheduling, GAs have been shown to require more fitness function evaluations than other search heuristics to find fit solutions. This thesis presents extensions to the GA crossover process, termed directed intervention crossover techniques, that greatly reduce the number of fitness function evaluations required to find fit solutions, thus increasing the effectiveness of GAs for problems of this type. The directed intervention crossover techniques use intervention scheduling information from parent solutions to direct the offspring produced in the GA crossover process towards more promising areas of a search space. By counting the number of interventions present in parents and adjusting the number of interventions for offspring schedules around it, this allows for highly fit solutions to be found in less fitness function evaluations. The validity of these novel approaches are illustrated through comparison with conventional GA crossover approaches for optimisation of intervention schedules of bio-control application in mushroom farming and cancer chemotherapy treatment. These involve optimally scheduling the application of a bio-control agent to combat pests in mushroom farming and optimising the timing and dosage strength of cancer chemotherapy treatments to maximise their effectiveness. This work demonstrates that significant advantages are gained in terms of both fitness function evaluations required and fitness scores found using the proposed approaches when compared with traditional GA crossover approaches for the production of optimal control schedules