Mechanistic Mathematical Model Research Articles

GIS-ODE: linking dynamic population models with GIS to predict pathogen vector abundance across a country under climate change scenarios.

Mechanistic mathematical models such as ordinary differential equations (ODEs) have a long history for their use in describing population dynamics and determining estimates of key parameters that summarize the potential growth or decline of a population over time. More recently, geographic information systems (GIS) have become important tools to provide a visual representation of statistically determined parameters and environmental features over space. Here, we combine these tools to form a 'GIS-ODE' approach to generate spatiotemporal maps predicting how projected changes in thermal climate may affect population densities and, uniquely, population dynamics of Ixodes ricinus, an important tick vector of several human pathogens. Assuming habitat and host densities are not greatly affected by climate warming, the GIS-ODE model predicted that, even under the lowest projected temperature increase, I. ricinus nymph densities could increase by 26-99% in Scotland, depending on the habitat and climate of the location. Our GIS-ODE model provides the vector-borne disease research community with a framework option to produce predictive, spatially explicit risk maps based on a mechanistic understanding of vector and vector-borne disease transmission dynamics.

Computational model predicts patient outcomes in Luminal B breast cancer treated with endocrine therapy and CDK4/6 inhibition.

Development of a computational biomarker to predict, prior to treatment, the response to CDK4/6 inhibition (CDK4/6i) in combination with endocrine therapy in patients with breast cancer. A mechanistic mathematical model that accounts for protein signaling and drug mechanisms of action was developed and trained on extensive, publicly available data from breast cancer cell lines. The model was built to provide a patient-specific response score based on the expression of six genes (CCND1, CCNE1, ESR1, RB1, MYC and CDKN1A). The model was validated in five independent cohorts of 148 patients in total with early-stage or advanced breast cancer treated with endocrine therapy and CDK4/6i. Response was measured either by evaluating Ki67 levels and PAM50 risk of relapse (ROR) after neoadjuvant treatment or by evaluating progression-free survival (PFS). The model showed significant association with patient´s outcomes in all five cohorts. The model predicted high Ki67 (area under the curve; AUC (95% confidence interval) of 0.80 (0.64 - 0.92), 0.81 (0.60 - 1.00) and 0.80 (0.65 - 0.93)) and high PAM50 ROR (AUC of 0.78 (0.64 - 0.89)). This observation was not obtained in patients treated with chemotherapy. In the other cohorts, patient stratification based on the model prediction was significantly associated with PFS (hazard ratio=2.92 (95% CI 1.08 - 7.86), p=0.034 and HR=2.16 (1.02 4.55), p=0.043). A mathematical modeling approach accurately predicts patient outcome following CDK4/6i plus endocrine therapy, which marks a step towards more personalized treatments in patients with Luminal B breast cancer.

Normoglycemia and physiological cortisone level maintain glucose homeostasis in a pancreas-liver microphysiological system

Current research on metabolic disorders and diabetes relies on animal models because multi-organ diseases cannot be well studied with standard in vitro assays. Here, we have connected cell models of key metabolic organs, the pancreas and liver, on a microfluidic chip to enable diabetes research in a human-based in vitro system. Aided by mechanistic mathematical modeling, we demonstrate that hyperglycemia and high cortisone concentration induce glucose dysregulation in the pancreas-liver microphysiological system (MPS), mimicking a diabetic phenotype seen in patients with glucocorticoid-induced diabetes. In this diseased condition, the pancreas-liver MPS displays beta-cell dysfunction, steatosis, elevated ketone-body secretion, increased glycogen storage, and upregulated gluconeogenic gene expression. Conversely, a physiological culture condition maintains glucose tolerance and beta-cell function. This method was reproducible in two laboratories and was effective in multiple pancreatic islet donors. The model also provides a platform to identify new therapeutic proteins, as demonstrated with a combined transcriptome and proteome analysis.

Systems modeling of oncogenic G-protein and GPCR signaling reveals unexpected differences in downstream pathway activation

Mathematical models of biochemical reaction networks are an important and emerging tool for the study of cell signaling networks involved in disease processes. One promising potential application of such mathematical models is the study of how disease-causing mutations promote the signaling phenotype that contributes to the disease. It is commonly assumed that one must have a thorough characterization of the network readily available for mathematical modeling to be useful, but we hypothesized that mathematical modeling could be useful when there is incomplete knowledge and that it could be a tool for discovery that opens new areas for further exploration. In the present study, we first develop a mechanistic mathematical model of a G-protein coupled receptor signaling network that is mutated in almost all cases of uveal melanoma and use model-driven explorations to uncover and explore multiple new areas for investigating this disease. Modeling the two major, mutually-exclusive, oncogenic mutations (Gαq/11 and CysLT2R) revealed the potential for previously unknown qualitative differences between seemingly interchangeable disease-promoting mutations, and our experiments confirmed oncogenic CysLT2R was impaired at activating the FAK/YAP/TAZ pathway relative to Gαq/11. This led us to hypothesize that CYSLTR2 mutations in UM must co-occur with other mutations to activate FAK/YAP/TAZ signaling, and our bioinformatic analysis uncovers a role for co-occurring mutations involving the plexin/semaphorin pathway, which has been shown capable of activating this pathway. Overall, this work highlights the power of mechanism-based computational systems biology as a discovery tool that can leverage available information to open new research areas.

Numerical exploration of a fully mechanistic mathematical model of aqueous CO2 corrosion in steel pipelines

A numerical exploration of a comprehensive mechanistic aqueous carbon dioxide (CO2) corrosion model is conducted across a range of temperatures (273–313 K), CO2 partial pressures (0.1–1 bar), and bulk pHs (5–6.5). Contour plots are produced to examine the impact on corrosion rate, surface pH, and surface saturation index of iron carbonate (FeCO3). Two response patterns are identified depending upon the limiting behaviour of the system, with a transition from charge-transfer control to mass-transport control as temperature is increased and partial pressure is reduced. FeCO3 surface saturation shows a strong correlation with the release of Fe2+ and increase in bulk pH.

Advancing cancer drug development with mechanistic mathematical modeling: bridging the gap between theory and practice.

Quantitative predictive modeling of cancer growth, progression, and individual response to therapy is a rapidly growing field. Researchers from mathematical modeling, systems biology, pharmaceutical industry, and regulatory bodies, are collaboratively working on predictive models that could be applied for drug development and, ultimately, the clinical management of cancer patients. A plethora of modeling paradigms and approaches have emerged, making it challenging to compile a comprehensive review across all subdisciplines. It is therefore critical to gauge fundamental design aspects against requirements, and weigh opportunities and limitations of the different model types. In this review,we discuss three fundamental types of cancer models: space-structured models, ecological models, and immune system focused models. For each type, it is our goal to illustrate which mechanisms contribute to variability and heterogeneity in cancer growth and response, so that the appropriate architecture and complexity of a new model becomes clearer. We present the main features addressed by each of the three exemplary modeling types through a subjective collection of literature and illustrative exercises to facilitate inspiration and exchange, with a focus on providing a didactic rather than exhaustive overview. We close by imagining a future multi-scale model design to impact critical decisions in oncology drug development.

Examining the Effects of Temperature on the Evolution of Bacterial tRNA Pools.

The genetic code consists of 61 codons coding for 20 amino acids. These codons are recognized by transfer RNAs (tRNAs) that bind to specific codons during protein synthesis. All organisms utilize less than all 61 possible anticodons due to base pair wobble: the ability to have a mismatch with a codon at its third nucleotide. Previous studies observed a correlation between the tRNA pool of bacteria and the temperature of their respective environments. However, it is unclear if these patterns represent biological adaptations to maintain the efficiency and accuracy of protein synthesis in different environments. A mechanistic mathematical model of mRNA translation is used to quantify the expected elongation rates and error rate for each codon based on an organism's tRNA pool. A comparative analysis across a range of bacteria that accounts for covariance due to shared ancestry is performed to quantify the impact of environmental temperature on the evolution of the tRNA pool. We find that thermophiles generally have more anticodons represented in their tRNA pool than mesophiles or psychrophiles. Based on our model, this increased diversity is expected to lead to increased missense errors. The implications of this for protein evolution in thermophiles are discussed.

Understanding the impact of HIV on mpox transmission in the MSM population: A mathematical modeling study

The recent mpox outbreak (in 2022–2023) has different clinical and epidemiological features compared with previous outbreaks of the disease. During this outbreak, sexual contact was believed to be the primary transmission route of the disease. In addition, the community of men having sex with men (MSM) was disproportionately affected by the outbreak. This population is also disproportionately affected by HIV infection. Given that both diseases can be transmitted sexually, the endemicity of HIV, and the high sexual behavior associated with the MSM community, it is essential to understand the effect of the two diseases spreading simultaneously in an MSM population. Particularly, we aim to understand the potential effects of HIV on an mpox outbreak in the MSM population. We develop a mechanistic mathematical model of HIV and mpox co-infection. Our model incorporates the dynamics of both diseases and considers HIV treatment with anti-retroviral therapy (ART). In addition, we consider a potential scenario where HIV infection increases susceptibility to mpox, and investigate the potential impact of this mechanism on mpox dynamics. Our analysis shows that HIV can facilitate the spread of mpox in an MSM population, and that HIV treatment with ART may not be sufficient to control the spread of mpox in the population. However, we showed that a moderate use of condoms or reduction in sexual contact in the population combined with ART is beneficial in controlling mpox transmission. Based on our analysis, it is evident that effective control of HIV, specifically through substantial ART use, moderate condom compliance, and reduction in sexual contact, is imperative for curtailing the transmission of mpox in an MSM population and mitigating the compounding impact of these intertwined epidemics.

A mechanistic model to predict headspace concentration profile of carvacrol for controlled release packaging

The efficacy of an antimicrobial agent in food packaging depends largely on its concentration profile in the package headspace. In this study, a mechanistic mathematical model was developed to predict the headspace concentration profile of carvacrol, a prominent antimicrobial agent, using the physical principles that govern the movement of carvacrol molecules in a controlled release packaging system. The model and its estimated parameter values were validated using three different sets of gas chromatography measurements—this rigorous process confirms the accuracy and reliability of the model. Advancing beyond existing models, our model enhances the understanding of the dynamics between the concentration profile and its interacting processes including evaporation, adsorption, and gas transmission. It provides packaging developers with a superior alternative to the trial-and-error approach to tailor concentration profiles for optimizing antimicrobial efficacy. It leads to more efficient and better design of controlled release packaging.

Kinetic modelling of glycolytic oscillations.

Glycolytic oscillations have been studied for well over 60 years, but aspects of their function, and mechanisms of regulation and synchronisation remain unclear. Glycolysis is amenable to mechanistic mathematical modelling, as its components have been well characterised, and the system can be studied at many organisational levels: in vitro reconstituted enzymes, cell free extracts, individual cells, and cell populations. In recent years, the emergence of individual cell analysis has opened new ways of studying this intriguing system.

Putting theory to the test: An integrated computational/experimental chemostat model of the tragedy of the commons.

Cooperation via shared public goods is ubiquitous in nature, however, noncontributing social cheaters can exploit the public goods provided by cooperating individuals to gain a fitness advantage. Theory predicts that this dynamic can cause a Tragedy of the Commons, and in particular, a 'Collapsing' Tragedy defined as the extinction of the entire population if the public good is essential. However, there is little empirical evidence of the Collapsing Tragedy in evolutionary biology. Here, we experimentally demonstrate this outcome in a microbial model system, the public good-producing bacterium Pseudomonas aeruginosa grown in a continuous-culture chemostat. In a growth medium that requires extracellular protein digestion, we find that P. aeruginosa populations maintain a high density when entirely composed of cooperating, protease-producing cells but completely collapse when non-producing cheater cells are introduced. We formulate a mechanistic mathematical model that recapitulates experimental observations and suggests key parameters, such as the dilution rate and the cost of public good production, that define the stability of cooperative behavior. We combine model prediction with experimental validation to explain striking differences in the long-term cheater trajectories of replicate cocultures through mutational events that increase cheater fitness. Taken together, our integrated empirical and theoretical approach validates and parametrizes the Collapsing Tragedy in a microbial population, and provides a quantitative, mechanistic framework for generating testable predictions of social behavior.

Quantitative evaluation of trastuzumab deruxtecan pharmacokinetics and pharmacodynamics in mouse models of varying degrees of HER2 expression.

Trastuzumab deruxtecan (T-DXd; DS-8201; ENHERTU®) is a human epithelial growth factor receptor 2 (HER2)-directed antibody drug conjugate (ADC) with demonstrated antitumor activity against a range of tumor types. Aiming to understand the relationship between antigen expression and downstream efficacy outcomes, T-DXd was administered in tumor-bearing mice carrying NCI-N87, Capan-1, JIMT-1, and MDA-MB-468 xenografts, characterized by varying HER2 levels. Plasma pharmacokinetics (PK) of total antibody, T-DXd, and released DXd and tumor concentrations of released DXd were evaluated, in addition to monitoring γΗ2AX and pRAD50 pharmacodynamic (PD) response. A positive relationship was observed between released DXd concentrations in tumor and HER2 expression, with NCI-N87 xenografts characterized by the highest exposures compared to the remaining cell lines. γΗ2AX and pRAD50 demonstrated a sustained increase over several days occurring with a time delay relative to tumoral-released DXd concentrations. Invitro investigations of cell-based DXd disposition facilitated the characterization of DXd kinetics across tumor cells. These outputs were incorporated into a mechanistic mathematical model, utilized to describe PK/PD trends. The model captured plasma PK across dosing arms as well as tumor PK in NCI-N87, Capan-1, and MDA-MB-468 models; tumor concentrations in JIMT-1 xenografts required additional parameter adjustments reflective of complex receptor dynamics. γΗ2AX longitudinal trends were well characterized via a unified PD model implemented across xenografts demonstrating the robustness of measured PD trends. This work supports the application of a mechanistic model as a quantitative tool, reliably projecting tumor payload concentrations upon T-DXd administration, as the first step towards preclinical-to-clinical translation.

Abstract 3872: Multi-ancestral origins of colorectal lesionsMulti-ancestral origins of colorectal lesions

Abstract The widely accepted paradigm that cancer initiation is a monoclonal event has not been definitively resolved. In sporadic cancers this is due to the requirement for longitudinal sampling to study this occult process, which occurs over years to decades. Individuals with familial adenomatous polyposis (FAP) possess a germline APC mutation, leading to hundreds of colonic polyps in adolescence and a 100% lifetime risk of colorectal cancer. Resected colons from FAP patients contain normal mucosa, benign and dysplastic polyps that embed the natural history of colorectal tumorigenesis at different points of malignant progression. Through genome sequencing of 127 independent polyps or mucosa samples from six FAP patients, we characterized the genomic landscape, relative timing of somatic alterations, and clonal dynamics in normal, dysplastic, and invasive colon tissue. Comparison with multi-region sequencing data from FAP patients and sporadic colorectal adenomas and carcinomas indicates similar molecular profiles, with canonical cancer driver genes present across benign and dysplastic premalignant lesions and shared mutational orders. Pairwise sample comparisons and phylogenetic reconstructions revealed extensive heterogeneity and subclonal sharing within a patient’s benign and dysplastic lesions, irrespective of location in the colon. These data imply that polyps were initiated from multiple cells from distinct lineages whose most recent common ancestor arose during development. We corroborate these findings using a mechanistic mathematical model, which infers polyclonality in 100% of benign and 83% of dysplastic samples. Based on these findings, we propose a conceptual model of the multi-ancestral origin of intestinal malignancies. Citation Format: Ryan O. Schenck, Aziz Khan, Aaron Horning, Edward D. Esplin, Debra Van Egeren, HTAN–FAP Consortium, William Greenleaf, James M. Ford, Michael P. Snyder, Christina Curtis. Multi-ancestral origins of colorectal lesionsMulti-ancestral origins of colorectal lesions [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 3872.

A review of mechanistic learning in mathematical oncology.

Mechanistic learning refers to the synergistic combination of mechanistic mathematical modeling and data-driven machine or deep learning. This emerging field finds increasing applications in (mathematical) oncology. This review aims to capture the current state of the field and provides a perspective on how mechanistic learning may progress in the oncology domain. We highlight the synergistic potential of mechanistic learning and point out similarities and differences between purely data-driven and mechanistic approaches concerning model complexity, data requirements, outputs generated, and interpretability of the algorithms and their results. Four categories of mechanistic learning (sequential, parallel, extrinsic, intrinsic) of mechanistic learning are presented with specific examples. We discuss a range of techniques including physics-informed neural networks, surrogate model learning, and digital twins. Example applications address complex problems predominantly from the domain of oncology research such as longitudinal tumor response predictions or time-to-event modeling. As the field of mechanistic learning advances, we aim for this review and proposed categorization framework to foster additional collaboration between the data- and knowledge-driven modeling fields. Further collaboration will help address difficult issues in oncology such as limited data availability, requirements of model transparency, and complex input data which are embraced in a mechanistic learning framework.

A mechanistic mathematical model for the treatment of synthetic oil-field wastewater (produced water) by electrocoagulation process using aluminium electrodes.

Produced water (PW) is the largest by-product that comes out of the oil wells during oil and gas (O&G) field exploration. PW contains high-salt concentration along with other organic and inorganic components; therefore, PW must be treated before disposal. Electrocoagulation (EC) is an effective treatment method to remove pollutants from PW which has been the focus of many experimental studies; however, a mathematical model specifically for PW treatment by EC has not been developed yet. In this work, a comprehensive mathematical model has been developed to elucidate the role of EC operating parameters on the PW treatment performance and determine the mechanism for COD (Chemical Oxygen Demand) removal. The present model considers and identifies the dominant Al-hydroxy complex species and their contribution to the COD removal from synthetic PW samples by estimating their rate constants and comparing their magnitudes and investigates multi-scale modelling of the EC reactor. The influence of working parameters such as current density, initial pH, interelectrode distance, mixing speed and solution volume of PW on Al coagulant production and COD removal was investigated and modelled. The study estimates the rate constants of the reactions taking place for COD removal by EC process and by comparing their magnitudes identifies the dominant reactions and coagulant species involved in the process. The mathematical model prediction of COD removal fits well with the experimental data at 10mAcm-2, 15mAcm-2 and 20mAcm-2 current density with R2 value of 0.96, 0.97 and 0.92, respectively and for dissolved Al concentration R2 value of 0.96, 0.99, and 0.97, respectively. The simulated results reproduced a good fit at initial pH of 6.1, 7.3 and 8.6 with R2 value of 0.92, 0.96 and 0.98, respectively for COD removal. The mathematical model and the experimental results showed the role of dominant Al-hydroxy complex species such as , , , and in controlling the COD removal process. Under different operating conditions considered in the study, the model also predicted the COD removal performance of the EC reactors at different reactor volumes with R2 value of 0.96 for higher solution volume and larger reactor. The model presented and rate constants determined in the study will provide a theoretical basis for designing, scaling up and operating the EC reactor for oil-field PW treatment.

Abstract B008: The polyclonal path towards malignant transformation in familial adenomatous polyposis

Abstract The widely accepted paradigm that cancer initiation is a monoclonal event has not been definitively resolved. This is largely due to the limitations of experimental systems to study cancer initiation, a definitively transient step in tumorigenesis. Individuals with familial adenomatous polyposis (FAP) possess a germline APC mutation, leading to hundreds of colonic polyps in adolescence and an eventual 100% lifetime risk of colorectal cancer. As such, total colectomies are performed once polyp burden becomes unmanageable and provide the resected colons from FAP donors provide a source of histologically normal mucosa, benign and dysplastic polyps, and, on rare occasions, adenocarcinomas, and serve as an exemplary model disease to understand human tumorigenesis. Through whole genome sequencing of 123 independent samples from six patients, we reveal the polyclonal origins of tumorigenesis in FAP. We characterize and contrast the genomic landscape and relative timing of driver mutation acquisition across normal to dysplastic and invasive colon tissue and compare this with multi-region sequencing data from sporadic colorectal cancers (CRC). We find that only early sporadic CRC drivers are common across the more heterogeneous premalignant stages. Selection, as assessed based on the ratio of nonsynonymous to synonymous mutations (dN/dS), is higher in benign than dysplastic FAP lesions and in sporadic adenomas relative to carcinomas. Phylogenetic reconstruction and pairwise sample comparisons reveal extensive heterogeneity and subclonal sharing within a patient’s benign and dysplastic lesions. Using a mechanistic mathematical model, we infer polyclonality for 90-100% of benign and 53-83% of dysplastic samples. Based on these findings, we propose a conceptual framework for the polyclonal origin of intestinal malignancies where inconsequential mutations, arising during colon formation in utero, are present across the colon and are valuable markers to uncover polyclonal ancestry. Citation Format: Ryan O. Schenck, Aziz Khan, Aaron M. Horning, Edward D. Esplin, HTAN Consortia, William J. Greenleaf, James M. Ford, Michael P. Snyder, Christina Curtis. The polyclonal path towards malignant transformation in familial adenomatous polyposis [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Translating Cancer Evolution and Data Science: The Next Frontier; 2023 Dec 3-6; Boston, Massachusetts. Philadelphia (PA): AACR; Cancer Res 2024;84(3 Suppl_2):Abstract nr B008.

Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences.

Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

Dynamic heterogeneity in COVID-19: Insights from a mathematical model.

Critical illness, such as severe COVID-19, is heterogenous in presentation and treatment response. However, it remains possible that clinical course may be influenced by dynamic and/or random events such that similar patients subject to similar injuries may yet follow different trajectories. We deployed a mechanistic mathematical model of COVID-19 to determine the range of possible clinical courses after SARS-CoV-2 infection, which may follow from specific changes in viral properties, immune properties, treatment modality and random external factors such as initial viral load. We find that treatment efficacy and baseline patient or viral features are not the sole determinant of outcome. We found patients with enhanced innate or adaptive immune responses can experience poor viral control, resolution of infection or non-infectious inflammatory injury depending on treatment efficacy and initial viral load. Hypoxemia may result from poor viral control or ongoing inflammation despite effective viral control. Adaptive immune responses may be inhibited by very early effective therapy, resulting in viral load rebound after cessation of therapy. Our model suggests individual disease course may be influenced by the interaction between external and patient-intrinsic factors. These data have implications for the reproducibility of clinical trial cohorts and timing of optimal treatment.

Assessment of calcium alginate gels as wall materials for encapsulation systems.

Calcium alginate gels are widely used to encapsulate active compounds. Some characteristic parameters of these gels are necessary to describe the release of active compounds through mechanistic mathematical models. In this work, transport and kinetics properties of calcium alginate gels were determined through simple experimental techniques. The weight-average molecular weight ( = 192 × 103 Da) and the fraction of residues of α-l-guluronic acid ( = 0.356) of sodium alginate were determined by capillary viscometry and 1 H-nuclear magnetic resonance at 25 °C, respectively. Considering the half egg-box model, both values were used to estimate the molecular weight of calcium alginate as = 2.02 × 105 Da. An effective diffusion coefficient of water ( = 2.256 × 10-9 m2 s-1 ) in calcium alginate was determined using a diffusion cell at 37 °C. Finally, a kinetics constant of depolymerization ( = 9.72 × 10-9 m3 mol-1 s-1 ) of calcium alginate was obtained considering dissolution of calcium to a medium under intestinal conditions. The experimental techniques used are simple and easily reproducible. The obtained values may be useful in the design, production, and optimization of the alginate-based delivery systems that require specific release kinetics of the encapsulated active compounds. © 2023 Society of Chemical Industry.

Computational markers for personalized prediction of outcomes in non-small cell lung cancer patients with brain metastases.

Intracranial progression after curative treatment of early-stage non-small cell lung cancer (NSCLC) occurs from 10 to 50% and is difficult to manage, given the heterogeneity of clinical presentations and the variability of treatments available. The objective of this study was to develop a mechanistic model of intracranial progression to predict survival following a first brain metastasis (BM) event occurring at a time [Formula: see text]. Data included early-stage NSCLC patients treated with a curative intent who had a BM as the first and single relapse site (N = 31). We propose a mechanistic mathematical model able to derive computational markers from primary tumor and BM data at [Formula: see text] and estimate the amount and sizes of (visible and invisible) BMs, as well as their future behavior. These two key computational markers are [Formula: see text], the proliferation rate of a single tumor cell; and [Formula: see text], the per day, per cell, probability to metastasize. The predictive value of these individual computational biomarkers was evaluated. The model was able to correctly describe the number and size of metastases at [Formula: see text] for 20 patients. Parameters [Formula: see text] and [Formula: see text] were significantly associated with overall survival (OS) (HR 1.65 (1.07-2.53) p = 0.0029 and HR 1.95 (1.31-2.91) p = 0.0109, respectively). Adding the computational markers to the clinical ones significantly improved the predictive value of OS (c-index increased from 0.585 (95% CI 0.569-0.602) to 0.713 (95% CI 0.700-0.726), p < 0.0001). We demonstrated that our model was applicable to brain oligoprogressive patients in NSCLC and that the resulting computational markers had predictive potential. This may help lung cancer physicians to guide and personalize the management of NSCLC patients with intracranial oligoprogression.