Practical Understanding of Cancer Model Identifiability in Clinical Applications

Practical parameter identifiability and handling of censored data with Bayesian inference in mathematical tumour models

Mechanistic mathematical models (MMs) are a powerful tool to help us understand and predict the dynamics of tumour growth under various conditions. In this work, we use 5 MMs with an increasing number of parameters to explore how certain (often overlooked) decisions in estimating parameters from data of experimental tumour growth affect the outcome of the analysis. In particular, we propose a framework for including tumour volume measurements that fall outside the upper and lower limits of detection, which are normally discarded. We demonstrate how excluding censored data results in an overestimation of the initial tumour volume and the MM-predicted tumour volumes prior to the first measurements, and an underestimation of the carrying capacity and the MM-predicted tumour volumes beyond the latest measurable time points. We show in which way the choice of prior for the MM parameters can impact the posterior distributions, and illustrate that reporting the most likely parameters and their 95% credible interval can lead to confusing or misleading interpretations. We hope this work will encourage others to carefully consider choices made in parameter estimation and to adopt the approaches we put forward herein.

Convergence, sampling and total order estimator effects on parameter orthogonality in global sensitivity analysis

Dynamical system models typically involve numerous input parameters whose "effects" and orthogonality need to be quantified through sensitivity analysis, to identify inputs contributing the greatest uncertainty. Whilst prior art has compared total-order estimators' role in recovering "true" effects, assessing their ability to recover robust parameter orthogonality for use in identifiability metrics has not been investigated. In this paper, we perform: (i) an assessment using a different class of numerical models representing the cardiovascular system, (ii) a wider evaluation of sampling methodologies and their interactions with estimators, (iii) an investigation of the consequences of permuting estimators and sampling methodologies on input parameter orthogonality, (iv) a study of sample convergence through resampling, and (v) an assessment of whether positive outcomes are sustained when model input dimensionality increases. Our results indicate that Jansen or Janon estimators display efficient convergence with minimum uncertainty when coupled with Sobol and the lattice rule sampling methods, making them prime choices for calculating parameter orthogonality and influence. This study reveals that global sensitivity analysis is convergence driven. Unconverged indices are subject to error and therefore the true influence or orthogonality of the input parameters are not recovered. This investigation importantly clarifies the interactions of the estimator and the sampling methodology by reducing the associated ambiguities, defining novel practices for modelling in the life sciences.

Structural and practical identifiability of contrast transport models for DCE-MRI

Contrast transport models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

Structural and practical identifiability of contrast transport models for DCE-MRI

Compartment models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

A comparative analysis of 2D and 3D experimental data for the identification of the parameters of computational models

Computational models are becoming an increasingly valuable tool in biomedical research. Their accuracy and effectiveness, however, rely on the identification of suitable parameters and on appropriate validation of the in-silico framework. Both these steps are highly dependent on the experimental model used as a reference to acquire the data. Selecting the most appropriate experimental framework thus becomes key, together with the analysis of the effect of combining results from different experimental models, a common practice often necessary due to limited data availability. In this work, the same in-silico model of ovarian cancer cell growth and metastasis, was calibrated with datasets acquired from traditional 2D monolayers, 3D cell culture models or a combination of the two. The comparison between the parameters sets obtained in the different conditions, together with the corresponding simulated behaviours, is presented. It provides a framework for the study of the effect of the different experimental models on the development of computational systems. This work also provides a set of general guidelines for the comparative testing and selection of experimental models and protocols to be used for parameter optimization in computational models.