Mechanism-Based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

Abstract

Multiparametric imaging is a critical tool in the noninvasive study and assessment of cancer. Imaging methods have evolved over the past several decades to provide quantitative measures of tumor and healthy tissue characteristics related to, for example, cell number, blood volume fraction, blood flow, hypoxia, and metabolism. Mechanistic models of tumor growth also have matured to a point where the incorporation of patient-specific measures could provide clinically relevant predictions of tumor growth and response. In this review, we identify and discuss approaches that use multiparametric imaging data, including diffusion-weighted magnetic resonance imaging, dynamic contrast-enhanced magnetic resonance imaging, diffusion tensor imaging, contrast-enhanced computed tomography, [¹⁸F]fluorodeoxyglucose positron emission tomography, and [¹⁸F]fluoromisonidazole positron emission tomography to initialize and calibrate mechanistic models of tumor growth and response. We focus the discussion on brain and breast cancers; however, we also identify three emerging areas of application in kidney, pancreatic, and lung cancers. We conclude with a discussion of the future directions for incorporating multiparametric imaging data and mechanistic modeling into clinical decision making for patients with cancer.

FIG 1.

Example multiparametric data acquired in a patient with breast cancer before and after one cycle of neoadjuvant chemotherapy. Diffusion-weighted magnetic resonance imaging (DW-MRI) returns estimates of the apparent diffusion coefficient (ADC), which can be used to provide estimates of cellularity. Dynamic contrast-enhanced MRI (DCE-MRI) provides estimates of tissue blood flow and permeability (K^trans), extracellular-extravascular volume fraction (v_e), and plasma volume fraction (v_p). [¹⁸F]Fluorodeoxyglucose positron emission tomography (¹⁸FDG-PET) provides estimates of the glucose standardized uptake value (SUV). These imaging measurements can be acquired noninvasively before, during, and after the start of therapy to characterize functional changes in tumor properties.

FIG 2.

Schematic of model calibration, selection, and validation framework. (A) A deterministic or statistical approach to model calibration is used to minimize the error between the model and the measurement of a specific quantity of interest (eg, tumor volume, cell density distribution). In this example, the model is initialized at time point 1 (t₁), and the error is calculated at time point 2 (t₂). (B) Model selection criteria are used to select the most appropriate model that accurately describes the data. (C) The selected model is then evaluated in a validation stage by simulating tumor growth at time point 3 (t₃) and comparing it with the measured tumor growth. If the model error is within a prescribed error threshold for a quantity of interest, it is considered valid.

FIG 3.

Modeling framework that describes how a mathematical model can be developed and implemented. (A) In vitro experiments provide data to calibrate a particular tumor model. (B) Triphase computed tomography data are acquired (before and after treatment), segmented, and registered. (C) The domain is discretized so that the model can be calibrated and validated to patient data. If the model meets validation criteria, it can be used to predict tumor evolution.