Comparison of classical tumour growth models for patient derived and cell-line derived xenografts using the nonlinear mixed-effects framework

Predicting Tumor Volume Doubling Time and Progression-Free Survival in Untreated Patients from Patient-Derived-Xenograft (PDX) Models: A Translational Model-Based Approach

Tumor volume doubling time (TVDT) has been shown to be a potential surrogate marker of biological tumor activity. However, its availability in clinics is strongly limited due to ethical and practical reasons, as its assessment requires at least two subsequent tumor volume measurements in untreated patients. Here, a translational modeling framework to predict TVDT distributions in untreated cancer patient populations from tumor growth data in patient-derived xenograft (PDX) mice is proposed. Eleven solid cancer types were considered. For each of them, a set of tumor growth studies in PDX mice was selected and analyzed through a mathematical model to characterize the distribution of the exponential tumor growth rate in mice. Then, assuming an exponential growth of the tumor mass in humans, the growth rates were scaled from PDX mice to humans through an allometric scaling approach and used to predict TVDTs in untreated patients. A very good agreement was found between model predicted and clinically observed TVDTs, with 91% of the predicted TVDT medians fell within 1.5-fold of observations. Further, exploiting the intrinsic relationship between tumor growth dynamics and progression free survival (PFS), the exponential growth rates in humans were used to generate the expected PFS curves in absence of anticancer treatment. Predicted curves were extremely close to published PFS data from studies involving patient cohorts treated with supportive care or low effective therapies. The proposed approach shows promise as a potential tool to increase knowledge about TVDT in humans without the need of directly measuring tumor dimensions in untreated patients, and to predict PFS curves in untreated patients, that could fill the absence of placebo-controlled arms against which to compare treaded arms during clinical trials. However, further validation and refinement are needed to fully assess its effectiveness in this regard.

Explaining in-vitro to in-vivo efficacy correlations in oncology pre-clinical development via a semi-mechanistic mathematical model

In-vitro to in-vivo correlations (IVIVC), relating in-vitro parameters like IC50 to in-vivo drug exposure in plasma and tumour growth, are widely used in oncology for experimental design and dose decisions. However, they lack a deeper understanding of the underlying mechanisms. Our paper therefore focuses on linking empirical IVIVC relations for small-molecule kinase inhibitors with a semi-mechanistic tumour-growth model. We develop an approach incorporating parameters like the compound's peak-trough ratio (PTR), Hill coefficient of in-vitro dose-response curves, and xenograft-specific properties. This leads to formulas for determining efficacious doses for tumor stasis under linear pharmacokinetics equivalent to traditional empirical IVIVC relations, but enabling more systematic analysis. Our findings reveal that in-vivo xenograft-specific parameters, specifically the growth rate (g) and decay rate (d), along with the average exposure, are generally more significant determinants of tumor stasis and effective dose than the compound's peak-trough ratio. However, as the Hill coefficient increases, the dependency of tumor stasis on the PTR becomes more pronounced, indicating that the compound is more influenced by its maximum or trough values rather than the average exposure. Furthermore, we discuss the translation of our method to predict population dose ranges in clinical studies and propose a resistance mechanism that solely relies on specific in-vivo xenograft parameters instead of IC50 exposure coverage. In summary, our study aims to provide a more mechanistic understanding of IVIVC relations, emphasizing the importance of xenograft-specific parameters and PTR on tumor stasis.

Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment

Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.

Mathematical Modeling of Clonal Interference by Density-Dependent Selection in Heterogeneous Cancer Cell Lines

Many cancer cell lines are aneuploid and heterogeneous, with multiple karyotypes co-existing within the same cell line. Karyotype heterogeneity has been shown to manifest phenotypically, thus affecting how cells respond to drugs or to minor differences in culture media. Knowing how to interpret karyotype heterogeneity phenotypically would give insights into cellular phenotypes before they unfold temporally. Here, we re-analyzed single cell RNA (scRNA) and scDNA sequencing data from eight stomach cancer cell lines by placing gene expression programs into a phenotypic context. Using live cell imaging, we quantified differences in the growth rate and contact inhibition between the eight cell lines and used these differences to prioritize the transcriptomic biomarkers of the growth rate and carrying capacity. Using these biomarkers, we found significant differences in the predicted growth rate or carrying capacity between multiple karyotypes detected within the same cell line. We used these predictions to simulate how the clonal composition of a cell line would change depending on density conditions during in-vitro experiments. Once validated, these models can aid in the design of experiments that steer evolution with density-dependent selection.

A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions

Mathematical models used in preclinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumor volume; however, they typically have little connection with the underlying physiologic processes. This lack of a mechanistic underpinning restricts their flexibility and potentially inhibits their translation across studies including from animal to human. Here we present a mathematical model describing tumor growth for the evaluation of single-agent cytotoxic compounds that is based on mechanistic principles. The model can predict spatial distributions of cell subpopulations and account for spatial drug distribution effects within tumors. Importantly, we demonstrate that the model can be reduced to a growth law similar in form to the ones currently implemented in pharmaceutical drug development for preclinical trials so that it can integrated into the current workflow. We validate this approach for both cell-derived xenograft and patient-derived xenograft (PDX) data. This shows that our theoretical model fits as well as the best performing and most widely used models. However, in addition, the model is also able to accurately predict the observed growing fraction of tumours. Our work opens up current preclinical modeling studies to also incorporating spatially resolved and multimodal data without significant added complexity and creates the opportunity to improve translation and tumor response predictions.

Significance

This theoretical model has the same mathematical structure as that currently used for drug development. However, its mechanistic basis enables prediction of growing fraction and spatial variations in drug distribution.