Optimizing the future: how mathematical models inform treatment schedules for cancer

A systematic review on the culture methods and applications of 3D tumoroids for cancer research and personalized medicine

Cancer is a highly heterogeneous disease, and thus treatment responses vary greatly between patients. To improve therapy efficacy and outcome for cancer patients, more representative and patient-specific preclinical models are needed. Organoids and tumoroids are 3D cell culture models that typically retain the genetic and epigenetic characteristics, as well as the morphology, of their tissue of origin. Thus, they can be used to understand the underlying mechanisms of cancer initiation, progression, and metastasis in a more physiological setting. Additionally, co-culture methods of tumoroids and cancer-associated cells can help to understand the interplay between a tumor and its tumor microenvironment. In recent years, tumoroids have already helped to refine treatments and to identify new targets for cancer therapy. Advanced culturing systems such as chip-based fluidic devices and bioprinting methods in combination with tumoroids have been used for high-throughput applications for personalized medicine. Even though organoid and tumoroid models are complex in vitro systems, validation of results in vivo is still the common practice. Here, we describe how both animal- and human-derived tumoroids have helped to identify novel vulnerabilities for cancer treatment in recent years, and how they are currently used for precision medicine.

N-of-1 medicine

ABSTRACT

The fields of precision and personalised medicine have led to promising advances in tailoring treatment to individual patients. Examples include genome/molecular alteration-guided drug selection, single-patient gene therapy design and synergy-based drug combination development, and these approaches can yield substantially diverse recommendations. Therefore, it is important to define each domain and delineate their commonalities and differences in an effort to develop novel clinical trial designs, streamline workflow development, rethink regulatory considerations, create value in healthcare and economics assessments, and other factors. These and other segments are essential to recognise the diversity within these domains to accelerate their respective workflows towards practice-changing healthcare. To emphasise these points, this article elaborates on the concept of digital health and digital medicine-enabled N-of-1 medicine, which individualises combination regimen and dosing using a patient's own data. We will conclude with recommendations for consideration when developing novel workflows based on emerging digital-based platforms.

Predictive, preventive, and personalized medicine in breast cancer: targeting the PI3K pathway

Breast cancer (BC) is a multifaceted disease characterized by distinct molecular subtypes and varying responses to treatment. In BC, the phosphatidylinositol 3-kinase (PI3K) pathway has emerged as a crucial contributor to the development, advancement, and resistance to treatment. This review article explores the implications of the PI3K pathway in predictive, preventive, and personalized medicine for BC. It emphasizes the identification of predictive biomarkers, such as PIK3CA mutations, and the utility of molecular profiling in guiding treatment decisions. The review also discusses the potential of targeting the PI3K pathway for preventive strategies and the customization of therapy based on tumor stage, molecular subtypes, and genetic alterations. Overcoming resistance to PI3K inhibitors and exploring combination therapies are addressed as important considerations. While this field holds promise in improving patient outcomes, further research and clinical trials are needed to validate these approaches and translate them into clinical practice.

Treatment of evolving cancers will require dynamic decision support

Cancer research has traditionally focused on developing new agents, but an underexplored question is that of the dose and frequency of existing drugs. Based on the modus operandi established in the early days of chemotherapies, most drugs are administered according to predetermined schedules that seek to deliver the maximum tolerated dose and are only adjusted for toxicity. However, we believe that the complex, evolving nature of cancer requires a more dynamic and personalized approach. Chronicling the milestones of the field, we show that the impact of schedule choice crucially depends on processes driving treatment response and failure. As such, cancer heterogeneity and evolution dictate that a one-size-fits-all solution is unlikely-instead, each patient should be mapped to the strategy that best matches their current disease characteristics and treatment objectives (i.e. their 'tumorscape'). To achieve this level of personalization, we need mathematical modeling. In this perspective, we propose a five-step 'Adaptive Dosing Adjusted for Personalized Tumorscapes (ADAPT)' paradigm to integrate data and understanding across scales and derive dynamic and personalized schedules. We conclude with promising examples of model-guided schedule personalization and a call to action to address key outstanding challenges surrounding data collection, model development, and integration.

Fractional calculus in mathematical oncology

Even though, nowadays, cancer is one of the leading causes of death, too little is known about the behavior of this disease due to its unpredictability from one patient to another. Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, improvements are still necessary on these models. The primary objective of the present research is to prove the efficiency of fractional order calculus in mathematical oncology, more specifically in tumor growth modeling. For this, a generalization of the four most used differential equation models in tumor volume measurements fitting is realized, using the corresponding fractional order equivalent. Are established the fractional order Exponential, Logistic, Gompertz, General Bertalanffy-Pütter and Classical Bertalanffy-Pütter models for a treated and untreated dataset. The obtained results are compared by Mean Squared Error (MSE) with the integer order correspondent of each model. The results prove the superiority of the fractional order models. The MSE of fractional order models are reduced at least at half in comparison with the MSE of the integer order equivalent. It is demonstrated in this way that fractional order deterministic models can offer a good starting point in finding a proper mathematical model for tumor evolution prediction. Fractional calculus is a suitable method in this case due to its memory property, aspect that particularly characterizes biological processes.

Understanding the Mechanisms and Treatment of Heart Failure: Quantitative Systems Pharmacology Models with a Focus on SGLT2 Inhibitors and Sex-Specific Differences

Heart failure (HF), which is a major clinical and public health challenge, commonly develops when the myocardial muscle is unable to pump an adequate amount of blood at typical cardiac pressures to fulfill the body's metabolic needs, and compensatory mechanisms are compromised or fail to adjust. Treatments consist of targeting the maladaptive response of the neurohormonal system, thereby decreasing symptoms by relieving congestion. Sodium-glucose co-transporter 2 (SGLT2) inhibitors, which are a recent antihyperglycemic drug, have been found to significantly improve HF complications and mortality. They act through many pleiotropic effects, and show better improvements compared to others existing pharmacological therapies. Mathematical modeling is a tool used to describe the pathophysiological processes of the disease, quantify clinically relevant outcomes in response to therapies, and provide a predictive framework to improve therapeutic scheduling and strategies. In this review, we describe the pathophysiology of HF, its treatment, and how an integrated mathematical model of the cardiorenal system was built to capture body fluid and solute homeostasis. We also provide insights into sex-specific differences between males and females, thereby encouraging the development of more effective sex-based therapies in the case of heart failure.

Two-phase model of compressive stress induced on a surrounding hyperelastic medium by an expanding tumour

In vitro experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they are embedded, together with local levels of an externally-supplied, diffusible nutrient (e.g., oxygen), affect the tumour's growth dynamics. In this article, we present a mathematical model that describes these in vitro experiments. We use the model to understand how tumour growth generates mechanical deformations in the hydrogel and how these deformations in turn influence the tumour's growth. The hydrogel is viewed as a nonlinear hyperelastic material and the tumour is modelled as a two-phase mixture, comprising a viscous tumour cell phase and an isotropic, inviscid interstitial fluid phase. Using a combination of numerical and analytical techniques, we show how the tumour's growth dynamics change as the mechanical properties of the hydrogel vary. When the hydrogel is soft, nutrient availability dominates the dynamics: the tumour evolves to a large equilibrium configuration where the proliferation rate of nutrient-rich cells on the tumour boundary balances the death rate of nutrient-starved cells in the central, necrotic core. As the hydrogel stiffness increases, mechanical resistance to growth increases and the tumour's equilibrium size decreases. Indeed, for small tumours embedded in stiff hydrogels, the inhibitory force experienced by the tumour cells may be so large that the tumour is eliminated. Analysis of the model identifies parameter regimes in which the presence of the hydrogel drives tumour elimination.

Model selection for assessing the effects of doxorubicin on triple-negative breast cancer cell lines

Doxorubicin is a chemotherapy widely used to treat several types of cancer, including triple-negative breast cancer. In this work, we use a Bayesian framework to rigorously assess the ability of ten different mathematical models to describe the dynamics of four TNBC cell lines (SUM-149PT, MDA-MB-231, MDA-MB-453, and MDA-MB-468) in response to treatment with doxorubicin at concentrations ranging from 10 to 2500 nM. Each cell line was plated and serially imaged via fluorescence microscopy for 30 days following 6, 12, or 24 h of in vitro drug exposure. We use the resulting data sets to estimate the parameters of the ten pharmacodynamic models using a Bayesian approach, which accounts for uncertainties in the models, parameters, and observational data. The ten candidate models describe the growth patterns and degree of response to doxorubicin for each cell line by incorporating exponential or logistic tumor growth, and distinct forms of cell death. Cell line and treatment specific model parameters are then estimated from the experimental data for each model. We analyze all competing models using the Bayesian Information Criterion (BIC), and the selection of the best model is made according to the model probabilities (BIC weights). We show that the best model among the candidate set of models depends on the TNBC cell line and the treatment scenario, though, in most cases, there is great uncertainty in choosing the best model. However, we show that the probability of being the best model can be increased by combining treatment data with the same total drug exposure. Our analysis points to the importance of considering multiple models, built on different biological assumptions, to capture the observed variations in tumor growth and treatment response.