The goal of this study is to calibrate a multiscale model of tumor angiogenesis with time-resolved data to allow for systematic testing of mathematical predictions of vascular sprouting. The multi-scale model consists of an agent-based description of tumor and endothelial cell dynamics coupled to a continuum model of vascular endothelial growth factor concentration. First, we calibrate ordinary differential equation models to time-resolved protein concentration data to estimate the rates of secretion and consumption of vascular endothelial growth factor by endothelial and tumor cells, respectively. These parameters are then input into the multiscale tumor angiogenesis model, and the remaining model parameters are then calibrated to time resolved confocal microscopy images obtained within a 3D vascularized microfluidic platform. The microfluidic platform mimics a functional blood vessel with a surrounding collagen matrix seeded with inflammatory breast cancer cells, which induce tumor angiogenesis. Once the multi-scale model is fully parameterized, we forecast the spatiotemporal distribution of vascular sprouts at future time points and directly compare the predictions to experimentally measured data. We assess the ability of our model to globally recapitulate angiogenic vasculature density, resulting in an average relative calibration error of 17.7% ± 6.3% and an average prediction error of 20.2% ± 4% and 21.7% ± 3.6% using one and four calibrated parameters, respectively. We then assess the model's ability to predict local vessel morphology (individualized vessel structure as opposed to global vascular density), initialized with the first time point and calibrated with two intermediate time points. In this study, we have rigorously calibrated a mechanism-based, multiscale, mathematical model of angiogenic sprouting to multimodal experimental data to make specific, testable predictions.

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

While acquired chemoresistance is recognized as a key challenge to treating many types of cancer, the dynamics with which drug sensitivity changes after exposure are poorly characterized. Most chemotherapeutic regimens call for repeated dosing at regular intervals, and if drug sensitivity changes on a similar time scale then the treatment interval could be optimized to improve treatment performance. Theoretical work suggests that such optimal schedules exist, but experimental confirmation has been obstructed by the difficulty of deconvolving the simultaneous processes of death, adaptation, and regrowth taking place in cancer cell populations. Here we present a method of optimizing drug schedules in vitro through iterative application of experimentally calibrated models, and demonstrate its ability to characterize dynamic changes in sensitivity to the chemotherapeutic doxorubicin in three breast cancer cell lines subjected to treatment schedules varying in concentration, interval between pulse treatments, and number of sequential pulse treatments. Cell populations are monitored longitudinally through automated imaging for 600-800 hours, and this data is used to calibrate a family of cancer growth models, each consisting of a system of ordinary differential equations, derived from the bi-exponential model which characterizes resistant and sensitive subpopulations. We identify a model incorporating both a period of growth arrest in surviving cells and a delay in the death of chemosensitive cells which outperforms the original bi-exponential growth model in Akaike Information Criterion based model selection, and use the calibrated model to quantify the performance of each drug schedule. We find that the inter-treatment interval is a key variable in determining the performance of sequential dosing schedules and identify an optimal retreatment time for each cell line which extends regrowth time by 40%-239%, demonstrating that the time scale of changes in chemosensitivity following doxorubicin exposure allows optimization of drug scheduling by varying this inter-treatment interval.

MOTIVATION: Motions of transmembrane receptors on cancer cell surfaces can reveal biophysical features of the cancer cells, thus providing a method for characterizing cancer cell phenotypes. While conventional analysis of receptor motions in the cell membrane mostly relies on the mean-squared displacement plots, much information is lost when producing these plots from the trajectories. Here we employ deep learning to classify breast cancer cell types based on the trajectories of epidermal growth factor receptor (EGFR). Our model is an artificial neural network trained on the EGFR motions acquired from six breast cancer cell lines of varying invasiveness and receptor status: MCF7 (hormone receptor positive), BT474 (HER2-positive), SKBR3 (HER2-positive), MDA-MB-468 (triple negative, TN), MDA-MB-231 (TN) and BT549 (TN). RESULTS: The model successfully classified the trajectories within individual cell lines with 83% accuracy and predicted receptor status with 85% accuracy. To further validate the method, epithelial-mesenchymal transition (EMT) was induced in benign MCF10A cells, noninvasive MCF7 cancer cells and highly invasive MDA-MB-231 cancer cells, and EGFR trajectories from these cells were tested. As expected, after EMT induction, both MCF10A and MCF7 cells showed higher rates of classification as TN cells, but not the MDA-MB-231 cells. Whereas deep learning-based cancer cell classifications are primarily based on the optical transmission images of cell morphology and the fluorescence images of cell organelles or cytoskeletal structures, here we demonstrated an alternative way to classify cancer cells using a dynamic, biophysical feature that is readily accessible. AVAILABILITY AND IMPLEMENTATION: A python implementation of deep learning-based classification can be found at https://github.com/soonwoohong/Deep-learning-for-EGFR-trajectory-classification. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.

The overall goal of this study is to employ quantitative magnetic resonance imaging (MRI) data to constrain a patient-specific, computational fluid dynamics (CFD) model of blood flow and interstitial transport in breast cancer. We develop image processing methodologies to generate tumor-related vasculature-interstitium geometry and realistic material properties, using dynamic contrast enhanced MRI (DCE-MRI) and diffusion weighted MRI (DW-MRI) data. These data are used to constrain CFD simulations for determining the tumor-associated blood supply and interstitial transport characteristics unique to each patient. We then perform a proof-of-principle statistical comparison between these hemodynamic characteristics in 11 malignant and 5 benign lesions from 12 patients. Significant differences between groups (i.e., malignant versus benign) were observed for the median of tumor-associated interstitial flow velocity ( P = 0.028 ), and the ranges of tumor-associated blood pressure (P = 0.016) and vascular extraction rate (P = 0.040). The implication is that malignant lesions tend to have larger magnitude of interstitial flow velocity, and higher heterogeneity in blood pressure and vascular extraction rate. Multivariable logistic models based on combinations of these hemodynamic data achieved excellent differentiation between malignant and benign lesions with an area under the receiver operator characteristic curve of 1.0, sensitivity of 1.0, and specificity of 1.0. This image-based model system is a fundamentally new way to map flow and pressure fields related to breast tumors using only non-invasive, clinically available imaging data and established laws of fluid mechanics. Furthermore, the results provide preliminary evidence for this methodology's utility for the quantitative characterization of breast cancer.

OBJECTIVE: To employ machine learning methods to predict the eventual therapeutic response of breast cancer patients after a single cycle of neoadjuvant chemotherapy (NAC). MATERIALS AND METHODS: Quantitative dynamic contrast-enhanced MRI and diffusion-weighted MRI data were acquired on 28 patients before and after one cycle of NAC. A total of 118 semiquantitative and quantitative parameters were derived from these data and combined with 11 clinical variables. We used Bayesian logistic regression in combination with feature selection using a machine learning framework for predictive model building. RESULTS: The best predictive models using feature selection obtained an area under the curve of 0.86 and an accuracy of 0.86, with a sensitivity of 0.88 and a specificity of 0.82. DISCUSSION: With the numerous options for NAC available, development of a method to predict response early in the course of therapy is needed. Unfortunately, by the time most patients are found not to be responding, their disease may no longer be surgically resectable, and this situation could be avoided by the development of techniques to assess response earlier in the treatment regimen. The method outlined here is one possible solution to this important clinical problem. CONCLUSIONS: Predictive modeling approaches based on machine learning using readily available clinical and quantitative MRI data show promise in distinguishing breast cancer responders from non-responders after the first cycle of NAC.

Compressive sensing (CS) in Cartesian magnetic resonance imaging (MRI) involves random partial Fourier acquisitions. The random nature of these acquisitions can lead to variance in reconstruction errors. In quantitative MRI, variance in the reconstructed images translates to an uncertainty in the derived quantitative maps. We show that for a spatially regularized 2 ×-accelerated human breast CS DCE-MRI acquisition with a 192 (2) matrix size, the coefficients of variation (CoVs) in voxel-level parameters due to the random acquisition are 1.1%, 0.96%, and 1.5% for the tissue parameters K(trans), v(e), and v(p), with an average error in the mean of -2.5%, -2.0%, and -3.7%, respectively. Only 5% of the acquisition schemes had a systematic underestimation larger than than 4.2%, 3.7%, and 6.1%, respectively. For a 2 × -accelerated rat brain CS DSC-MRI study with a 64(2) matrix size, the CoVs due to the random acquisition were 19%, 9.5%, and 15% for the cerebral blood flow and blood volume and mean transit time, respectively, and the average errors in the tumor mean were 9.2%, 0.49%, and -7.0%, respectively. Across 11 000 different CS reconstructions, we saw no outliers in the distribution of parameters, suggesting that, despite the random undersampling schemes, CS accelerated quantitative MRI may have a predictable level of performance.