Neuroblastoma is the most common extra-cranial solid tumour in children. Despite multi-modal therapy, over half of the high-risk patients will succumb. One contributing factor is the one-size-fits-all nature of multi-modal therapy. For example, during the first step (induction chemotherapy), the standard regimen (rapid COJEC) administers fixed doses of chemotherapeutic agents in eight two-week cycles. Perhaps because of differences in resistance, this standard regimen results in highly heterogeneous outcomes in different tumours. In this study, we formulated a mathematical model comprising ordinary differential equations. The equations describe the clonal evolution within a neuroblastoma tumour being treated with vincristine and cyclophosphamide, which are used in the rapid COJEC regimen, including genetically conferred and phenotypic drug resistance. The equations also describe the agents’ pharmacokinetics. We devised an optimisation algorithm to find the best chemotherapy schedules for tumours with different pre-treatment clonal compositions. The optimised chemotherapy schedules exploit the cytotoxic difference between the two drugs and intra-tumoural clonal competition to shrink the tumours as much as possible during induction chemotherapy and before surgical removal. They indicate that induction chemotherapy can be improved by finding and using personalised schedules. More broadly, we propose that the overall multi-modal therapy can be enhanced by employing targeted therapies against the mutations and oncogenic pathways enriched and activated by the chemotherapeutic agents. To translate the proposed personalised multi-modal therapy into clinical use, patient-specific model calibration and treatment optimisation are necessary. This entails a decision support system informed by emerging medical technologies such as multi-region sequencing and liquid biopsies. The results and tools presented in this paper could be the foundation of this decision support system.

Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based model proposed by Orlando et al (2012 Phys. Biol. ), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlando et al ’s assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model—suggesting static protocols under the pro-generalizing and neutral allocation trade-offs—highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.

We take a model-informed approach to the view that a global equitable access (GEA) to Covid-19 vaccines is the key to bring this pandemic to an end. We show that the equitable redistribution (proportional to population size) of the currently available vaccines is not sufficient to stop the pandemic, whereas a 60% increase in vaccine access (the global share of vaccinated people) would have allowed the current distribution to stop the pandemic in about a year of vaccination, saving millions of people in poor countries. We then investigate the interplay between access to vaccines and their distribution among rich and poor countries, showing that the access increase to stop the pandemic gets minimized at + 32% by the equitable distribution (− 36% in rich countries and + 60% in poor ones). To estimate the socio-economic benefits of a vaccination campaign with enhanced global equity and access (eGEA), we compare calibrated simulations of the current scenario with a hypothetical, vaccination-intensive scenario that assumes high rollouts (shown however by many rich and poor countries during the 2021–2022 vaccination campaign) and an improved equity from the current 2.5:1 to a 2:1 rich/poor-ratio of the population fractions vaccinated per day. Assuming that the corresponding + 130% of vaccine production is made possible by an Intellectual Property waiver, we show that the money saved on vaccines globally by the selected eGEA scenario overcomes the 5-year profit of the rights holders in the current situation. This justifies compensation mechanisms in exchange for the necessary licensing agreements. The good news is that the benefits of this eGEA scenario are still relevant, were we ready to implement it now.

Malignant gliomas (MGs) are among the most aggressive primary brain tumors, characterized by a high degree of resistance to therapy and poor prognosis. In this work, we develop a mathematical model to investigate the dynamics of MG under the combined effects of chemotherapy and chimeric antigen receptor cell therapy. The proposed model is a five-dimensional dynamical system incorporating impulsive inputs that correspond to the clinical administration of chemotherapy and immunotherapy. We demonstrate the non-negativity of solutions for non-negative initial conditions, ensuring the biological relevance of the model. We show that if we apply both therapies only once, the trajectories are attracted to an invariant surface corresponding to the tumor carrying capacity. Conversely, under constant administration of both treatments, we identify parameter ranges in which tumor eradication is achievable. Furthermore, we numerically study various treatment combinations to determine optimal protocols at the population level. To this end, we generate a cohort of 104 virtual patients with model parameters sampled uniformly within clinically relevant ranges and carry out in silico trials. Our findings indicate that tumor growth rate, chemotherapy efficacy, and tumor-induced immunosuppression are the key determinants of survival outcomes. We believe that our results provide new theoretical insights into treatment optimization and offer a framework for refining the design of clinical trials for MG therapies.

Summary: The aim of this study was to assess, with numerical simulations, if the complex mechanism of two (or more) interacting spinal/supraspinal structures generating periodic leg movements can be modelled with a single‐generator approach. For this, we have developed the first phenomenological model to generate periodic leg movements in‐silico. We defined the onset of a movement in one leg as the firing of a neuron integrating excitatory and inhibitory inputs from the central nervous system, while the duration of the movement was defined in accordance to statistical evidence. For this study, polysomnographic leg movement data from 32 subjects without periodic leg movements and 65 subjects with periodic leg movements were used. The proportion of single‐leg and double‐leg inputs, as well as their strength and frequency, were calibrated on the without periodic leg movements dataset. For periodic leg movements subjects, we added a periodic excitatory input common to both legs, and the distributions of the generator period and intensity were fitted to their dataset. Besides the many simplifying assumptions – the strongest being the stationarity of the generator processes during sleep – the model‐simulated data did not differ significantly, to a large extent, from the real polysomnographic data. This represents convincing preliminary support for the validity of our single‐generator model for periodic leg movements. Future model extensions will pursue the ambitious project of a supportive diagnostic and therapeutic tool, helping the specialist with realistic forecasting, and with cross‐correlations and clustering with other patient meta‐data.

Human diseases are complex and dynamic. Understanding and controlling diseases require interdisciplinary approaches, aided by advances in digital technology, data analysis, and computational power. Specifically, in his Ph.D. Thesis, Matteo Italia has developed in silico models to study cancers, Restless Legs Syndrome (RLS), and Covid-19. The goals are to answer clinical questions, optimize treatments, and manage healthcare. For cancers, the developed models suggest that dynamic and personalized protocols can overcome drug resistance more effectively than static protocols. For neuroblastoma, the MYCN gene’s role in treatment outcomes is explored. For melanoma, promising drug combinations are identified to overcome vemurafenib resistance. In RLS, the first mathematical model supports the hypothesis that a single neuronal generator triggers periodic leg movements, aiding disease understanding. For Covid-19, a new compartment model, including vaccination policies and protection waning, emphasizes the importance of global equitable vaccine access to mitigate the pandemic. Overall, this ensemble of works highlights the importance of a systematic computational methodology in healthcare, a sort of engineered modus operandi that combines data analysis, systems and control, mathematics, optimization, simulations, and coding, among others.