Patient-Specific, Mechanistic Models of Tumor Growth Incorporating Artificial Intelligence and Big Data.

Despite the remarkable advances in cancer diagnosis, treatment, and management over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by personalizing the delivery of therapies according to the predicted response for each individual patient. The design of personalized therapies requires the integration of patient-specific information with an appropriate mathematical model of tumor response. A fundamental barrier to realizing this paradigm is the current lack of a rigorous yet practical mathematical theory of tumor initiation, development, invasion, and response to therapy. We begin this review with an overview of different approaches to modeling tumor growth and treatment, including mechanistic as well as data-driven models based on big data and artificial intelligence. We then present illustrative examples of mathematical models manifesting their utility and discuss the limitations of stand-alone mechanistic and data-driven models. We then discuss the potential of mechanistic models for not only predicting but also optimizing response to therapy on a patient-specific basis. We describe current efforts and future possibilities to integrate mechanistic and data-driven models. We conclude by proposing five fundamental challenges that must be addressed to fully realize personalized care for cancer patients driven by computational models.

The ISMRM Open Science Initiative for Perfusion Imaging (OSIPI): Results from the OSIPI-Dynamic Contrast-Enhanced challenge.

PURPOSE: K trans $$ {K}^{\mathrm{trans}} $$ has often been proposed as a quantitative imaging biomarker for diagnosis, prognosis, and treatment response assessment for various tumors. None of the many software tools for K trans $$ {K}^{\mathrm{trans}} $$ quantification are standardized. The ISMRM Open Science Initiative for Perfusion Imaging-Dynamic Contrast-Enhanced (OSIPI-DCE) challenge was designed to benchmark methods to better help the efforts to standardize K trans $$ {K}^{\mathrm{trans}} $$ measurement. METHODS: A framework was created to evaluate K trans $$ {K}^{\mathrm{trans}} $$ values produced by DCE-MRI analysis pipelines to enable benchmarking. The perfusion MRI community was invited to apply their pipelines for K trans $$ {K}^{\mathrm{trans}} $$ quantification in glioblastoma from clinical and synthetic patients. Submissions were required to include the entrants' K trans $$ {K}^{\mathrm{trans}} $$ values, the applied software, and a standard operating procedure. These were evaluated using the proposed OSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score defined with accuracy, repeatability, and reproducibility components. RESULTS: Across the 10 received submissions, the OSIP I gold $$ \mathrm{OSIP}{\mathrm{I}}_{\mathrm{gold}} $$ score ranged from 28% to 78% with a 59% median. The accuracy, repeatability, and reproducibility scores ranged from 0.54 to 0.92, 0.64 to 0.86, and 0.65 to 1.00, respectively (0-1 = lowest-highest). Manual arterial input function selection markedly affected the reproducibility and showed greater variability in K trans $$ {K}^{\mathrm{trans}} $$ analysis than automated methods. Furthermore, provision of a detailed standard operating procedure was critical for higher reproducibility. CONCLUSIONS: This study reports results from the OSIPI-DCE challenge and highlights the high inter-software variability within K trans $$ {K}^{\mathrm{trans}} $$ estimation, providing a framework for ongoing benchmarking against the scores presented. Through this challenge, the participating teams were ranked based on the performance of their software tools in the particular setting of this challenge. In a real-world clinical setting, many of these tools may perform differently with different benchmarking methodology.

Towards integration of time-resolved confocal microscopy of a 3D in vitro microfluidic platform with a hybrid multiscale model of tumor angiogenesis.

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.

An untrained deep learning method for reconstructing dynamic MR images from accelerated model-based data.

PURPOSE: To implement physics-based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. METHODS: The ConvDecoder (CD) neural network was trained with a physics-based regularization term incorporating the spoiled gradient echo equation that describes variable-flip angle data. Fully-sampled variable-flip angle k-space data were retrospectively accelerated by factors of R = {8, 12, 18, 36} and reconstructed with CD, CD with the proposed regularization (CD + r), locally low-rank (LR) reconstruction, and compressed sensing with L1-wavelet regularization (L1). Final images from CD + r training were evaluated at the "argmin" of the regularization loss; whereas the CD, LR, and L1 reconstructions were chosen optimally based on ground truth data. The performance measures used were the normalized RMS error, the concordance correlation coefficient, and the structural similarity index. RESULTS: The CD + r reconstructions, chosen using the stopping condition, yielded structural similarity indexs that were similar to the CD (p = 0.47) and LR structural similarity indexs (p = 0.95) across R and that were significantly higher than the L1 structural similarity indexs (p = 0.04). The concordance correlation coefficient values for the CD + r T1 maps across all R and subjects were greater than those corresponding to the L1 (p = 0.15) and LR (p = 0.13) T1 maps, respectively. For R ≥ 12 (≤4.2 min scan time), L1 and LR T1 maps exhibit a loss of spatially refined details compared to CD + r. CONCLUSION: The use of an untrained neural network together with a physics-based regularization loss shows promise as a measure for determining the optimal stopping point in training without relying on fully-sampled ground truth data.

Analysis of simplicial complexes to determine when to sample for quantitative DCE MRI of the breast.

PURPOSE: A method is presented to select the optimal time points at which to measure DCE-MRI signal intensities, leaving time in the MR exam for high-spatial resolution image acquisition. THEORY: Simplicial complexes are generated from the Kety-Tofts model pharmacokinetic parameters Ktrans and ve . A geometric search selects optimal time points for accurate estimation of perfusion parameters. METHODS: The DCE-MRI data acquired in women with invasive breast cancer (N = 27) were used to retrospectively compare parameter maps fit to full and subsampled time courses. Simplicial complexes were generated for a fixed range of Kety-Tofts model parameters and for the parameter ranges weighted by estimates from the fully sampled data. The largest-area manifolds determined the optimal three time points for each case. Simulations were performed along with retrospectively subsampled data fits. The agreement was computed between the model parameters fit to three points and those fit to all points. RESULTS: The optimal three-point sample times were from the data-informed simplicial complex analysis and determined to be 65, 204, and 393 s after arrival of the contrast agent to breast tissue. In the patient data, tumor-median parameter values fit using all points and the three selected time points agreed with concordance correlation coefficients of 0.97 for Ktrans and 0.67 for ve . CONCLUSION: It is possible to accurately estimate pharmacokinetic parameters from three properly selected time points inserted into a clinical DCE-MRI breast exam. This technique can provide guidance on when to capture images for quantitative data between high-spatial-resolution DCE-MRI images.

Quantification of long-term doxorubicin response dynamics in breast cancer cell lines to direct treatment schedules.

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.

Deep learning-based classification of breast cancer cells using transmembrane receptor dynamics.

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.

Multi-Site Concordance of Diffusion-Weighted Imaging Quantification for Assessing Prostate Cancer Aggressiveness.

BACKGROUND: Diffusion-weighted imaging (DWI) is commonly used to detect prostate cancer, and a major clinical challenge is differentiating aggressive from indolent disease. PURPOSE: To compare 14 site-specific parametric fitting implementations applied to the same dataset of whole-mount pathologically validated DWI to test the hypothesis that cancer differentiation varies with different fitting algorithms. STUDY TYPE: Prospective. POPULATION: Thirty-three patients prospectively imaged prior to prostatectomy. FIELD STRENGTH/SEQUENCE: 3 T, field-of-view optimized and constrained undistorted single-shot DWI sequence. ASSESSMENT: Datasets, including a noise-free digital reference object (DRO), were distributed to the 14 teams, where locally implemented DWI parameter maps were calculated, including mono-exponential apparent diffusion coefficient (MEADC), kurtosis (K), diffusion kurtosis (DK), bi-exponential diffusion (BID), pseudo-diffusion (BID*), and perfusion fraction (F). The resulting parametric maps were centrally analyzed, where differentiation of benign from cancerous tissue was compared between DWI parameters and the fitting algorithms with a receiver operating characteristic area under the curve (ROC AUC). STATISTICAL TEST: Levene's test, P < 0.05 corrected for multiple comparisons was considered statistically significant. RESULTS: The DRO results indicated minimal discordance between sites. Comparison across sites indicated that K, DK, and MEADC had significantly higher prostate cancer detection capability (AUC range = 0.72-0.76, 0.76-0.81, and 0.76-0.80 respectively) as compared to bi-exponential parameters (BID, BID*, F) which had lower AUC and greater between site variation (AUC range = 0.53-0.80, 0.51-0.81, and 0.52-0.80 respectively). Post-processing parameters also affected the resulting AUC, moving from, for example, 0.75 to 0.87 for MEADC varying cluster size. DATA CONCLUSION: We found that conventional diffusion models had consistent performance at differentiating prostate cancer from benign tissue. Our results also indicated that post-processing decisions on DWI data can affect sensitivity and specificity when applied to radiological-pathological studies in prostate cancer. LEVEL OF EVIDENCE: 1 TECHNICAL EFFICACY: Stage 3.

Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth.

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.

Model selection for assessing the effects of doxorubicin on triple-negative breast cancer cell lines.

Doxorubicin is a chemotherapy widely used to treat several types of cancer, including triple-negative breast cancer. In this work, we use a Bayesian framework to rigorously assess the ability of ten different mathematical models to describe the dynamics of four TNBC cell lines (SUM-149PT, MDA-MB-231, MDA-MB-453, and MDA-MB-468) in response to treatment with doxorubicin at concentrations ranging from 10 to 2500 nM. Each cell line was plated and serially imaged via fluorescence microscopy for 30 days following 6, 12, or 24 h of in vitro drug exposure. We use the resulting data sets to estimate the parameters of the ten pharmacodynamic models using a Bayesian approach, which accounts for uncertainties in the models, parameters, and observational data. The ten candidate models describe the growth patterns and degree of response to doxorubicin for each cell line by incorporating exponential or logistic tumor growth, and distinct forms of cell death. Cell line and treatment specific model parameters are then estimated from the experimental data for each model. We analyze all competing models using the Bayesian Information Criterion (BIC), and the selection of the best model is made according to the model probabilities (BIC weights). We show that the best model among the candidate set of models depends on the TNBC cell line and the treatment scenario, though, in most cases, there is great uncertainty in choosing the best model. However, we show that the probability of being the best model can be increased by combining treatment data with the same total drug exposure. Our analysis points to the importance of considering multiple models, built on different biological assumptions, to capture the observed variations in tumor growth and treatment response.

Optimizing combination therapy in a murine model of HER2+ breast cancer.

Human epidermal growth factor receptor 2 positive (HER2+) breast cancer is frequently treated with drugs that target the HER2 receptor, such as trastuzumab, in combination with chemotherapy, such as doxorubicin. However, an open problem in treatment design is to determine the therapeutic regimen that optimally combines these two treatments to yield optimal tumor control. Working with data quantifying temporal changes in tumor volume due to different trastuzumab and doxorubicin treatment protocols in a murine model of human HER2+ breast cancer, we propose a complete framework for model development, calibration, selection, and treatment optimization to find the optimal treatment protocol. Through different assumptions for the drug-tumor interactions, we propose ten different models to characterize the dynamic relationship between tumor volume and drug availability, as well as the drug-drug interaction. Using a Bayesian framework, each of these models are calibrated to the dataset and the model with the highest Bayesian information criterion weight is selected to represent the biological system. The selected model captures the inhibition of trastuzumab due to pre-treatment with doxorubicin, as well as the increase in doxorubicin efficacy due to pre-treatment with trastuzumab. We then apply optimal control theory (OCT) to this model to identify two optimal treatment protocols. In the first optimized protocol, we fix the maximum dosage for doxorubicin and trastuzumab to be the same as the maximum dose delivered experimentally, while trying to minimize tumor burden. Within this constraint, optimal control theory indicates the optimal regimen is to first deliver two doses of trastuzumab on days 35 and 36, followed by two doses of doxorubicin on days 37 and 38. This protocol predicts an additional 45% reduction in tumor burden compared to that achieved with the experimentally delivered regimen. In the second optimized protocol we fix the tumor control to be the same as that obtained experimentally, and attempt to reduce the doxorubicin dose. Within this constraint, the optimal regimen is the same as the first optimized protocol but uses only 43% of the doxorubicin dose used experimentally. This protocol predicts tumor control equivalent to that achieved experimentally. These results strongly suggest the utility of mathematical modeling and optimal control theory for identifying therapeutic regimens maximizing efficacy and minimizing toxicity.

A Case Series Exploration of Multi-Regional Expression Heterogeneity in Triple-Negative Breast Cancer Patients.

Extensive intratumoral heterogeneity (ITH) is believed to contribute to therapeutic failure and tumor recurrence, as treatment-resistant cell clones can survive and expand. However, little is known about ITH in triple-negative breast cancer (TNBC) because of the limited number of single-cell sequencing studies on TNBC. In this study, we explored ITH in TNBC by evaluating gene expression-derived and imaging-derived multi-region differences within the same tumor. We obtained tissue specimens from 10 TNBC patients and conducted RNA sequencing analysis of 2-4 regions per tumor. We developed a novel analysis framework to dissect and characterize different types of variability: between-patients (inter-tumoral heterogeneity), between-patients across regions (inter-tumoral and region heterogeneity), and within-patient, between-regions (regional intratumoral heterogeneity). We performed a Bayesian changepoint analysis to assess and classify regional variability as low (convergent) versus high (divergent) within each patient feature (TNBC and PAM50 subtypes, immune, stroma, tumor counts and tumor infiltrating lymphocytes). Gene expression signatures were categorized into three types of variability: between-patients (108 genes), between-patients across regions (183 genes), and within-patients, between-regions (778 genes). Based on the between-patient gene signature, we identified two distinct patient clusters that differed in menopausal status. Significant intratumoral divergence was observed for PAM50 classification, tumor cell counts, and tumor-infiltrating T cell abundance. Other features examined showed a representation of both divergent and convergent results. Lymph node stage was significantly associated with divergent tumors. Our results show extensive intertumoral heterogeneity and regional ITH in gene expression and image-derived features in TNBC. Our findings also raise concerns regarding gene expression based TNBC subtyping. Future studies are warranted to elucidate the role of regional heterogeneity in TNBC as a driver of treatment resistance.

Quantitative multiparametric MRI predicts response to neoadjuvant therapy in the community setting.

BACKGROUND: The purpose of this study was to determine whether advanced quantitative magnetic resonance imaging (MRI) can be deployed outside of large, research-oriented academic hospitals and into community care settings to predict eventual pathological complete response (pCR) to neoadjuvant therapy (NAT) in patients with locally advanced breast cancer. METHODS: Patients with stage II/III breast cancer (N = 28) were enrolled in a multicenter study performed in community radiology settings. Dynamic contrast-enhanced (DCE) and diffusion-weighted (DW)-MRI data were acquired at four time points during the course of NAT. Estimates of the vascular perfusion and permeability, as assessed by the volume transfer rate (Ktrans) using the Patlak model, were generated from the DCE-MRI data while estimates of cell density, as assessed by the apparent diffusion coefficient (ADC), were calculated from DW-MRI data. Tumor volume was calculated using semi-automatic segmentation and combined with Ktrans and ADC to yield bulk tumor blood flow and cellularity, respectively. The percent change in quantitative parameters at each MRI scan was calculated and compared to pathological response at the time of surgery. The predictive accuracy of each MRI parameter at different time points was quantified using receiver operating characteristic curves. RESULTS: Tumor size and quantitative MRI parameters were similar at baseline between groups that achieved pCR (n = 8) and those that did not (n = 20). Patients achieving a pCR had a larger decline in volume and cellularity than those who did not achieve pCR after one cycle of NAT (p < 0.05). At the third and fourth MRI, changes in tumor volume, Ktrans, ADC, cellularity, and bulk tumor flow from baseline (pre-treatment) were all significantly greater (p < 0.05) in the cohort who achieved pCR compared to those patients with non-pCR. CONCLUSIONS: Quantitative analysis of DCE-MRI and DW-MRI can be implemented in the community care setting to accurately predict the response of breast cancer to NAT. Dissemination of quantitative MRI into the community setting allows for the incorporation of these parameters into the standard of care and increases the number of clinical community sites able to participate in novel drug trials that require quantitative MRI.

Mean Apparent Diffusion Coefficient Is a Sufficient Conventional Diffusion-weighted MRI Metric to Improve Breast MRI Diagnostic Performance: Results from the ECOG-ACRIN Cancer Research Group A6702 Diffusion Imaging Trial.

Background The Eastern Cooperative Oncology Group and American College of Radiology Imaging Network Cancer Research Group A6702 multicenter trial helped confirm the potential of diffusion-weighted MRI for improving differential diagnosis of suspicious breast abnormalities and reducing unnecessary biopsies. A prespecified secondary objective was to explore the relative value of different approaches for quantitative assessment of lesions at diffusion-weighted MRI. Purpose To determine whether alternate calculations of apparent diffusion coefficient (ADC) can help further improve diagnostic performance versus mean ADC values alone for analysis of suspicious breast lesions at MRI. Materials and Methods This prospective trial (ClinicalTrials.gov identifier: NCT02022579) enrolled consecutive women (from March 2014 to April 2015) with a Breast Imaging Reporting and Data System category of 3, 4, or 5 at breast MRI. All study participants underwent standardized diffusion-weighted MRI (b = 0, 100, 600, and 800 sec/mm2). Centralized ADC measures were performed, including manually drawn whole-lesion and hotspot regions of interest, histogram metrics, normalized ADC, and variable b-value combinations. Diagnostic performance was estimated by using the area under the receiver operating characteristic curve (AUC). Reduction in biopsy rate (maintaining 100% sensitivity) was estimated according to thresholds for each ADC metric. Results Among 107 enrolled women, 81 lesions with outcomes (28 malignant and 53 benign) in 67 women (median age, 49 years; interquartile range, 41-60 years) were analyzed. Among ADC metrics tested, none improved diagnostic performance versus standard mean ADC (AUC, 0.59-0.79 vs AUC, 0.75; P = .02-.84), and maximum ADC had worse performance (AUC, 0.52; P < .001). The 25th-percentile ADC metric provided the best performance (AUC, 0.79; 95% CI: 0.70, 0.88), and a threshold using median ADC provided the greatest reduction in biopsy rate of 23.9% (95% CI: 14.8, 32.9; 16 of 67 BI-RADS category 4 and 5 lesions). Nonzero minimum b value (100, 600, and 800 sec/mm2) did not improve the AUC (0.74; P = .28), and several combinations of two b values (0 and 600, 100 and 600, 0 and 800, and 100 and 800 sec/mm2; AUC, 0.73-0.76) provided results similar to those seen with calculations of four b values (AUC, 0.75; P = .17-.87). Conclusion Mean apparent diffusion coefficient calculated with a two-b-value acquisition is a simple and sufficient diffusion-weighted MRI metric to augment diagnostic performance of breast MRI compared with more complex approaches to apparent diffusion coefficient measurement. © RSNA, 2020 Online supplemental material is available for this article.

Simulating the spread of COVID-19 via a spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion.

We present an early version of a Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model based on partial differential equations coupled with a heterogeneous diffusion model. The model describes the spatio-temporal spread of the COVID-19 pandemic, and aims to capture dynamics also based on human habits and geographical features. To test the model, we compare the outputs generated by a finite-element solver with measured data over the Italian region of Lombardy, which has been heavily impacted by this crisis between February and April 2020. Our results show a strong qualitative agreement between the simulated forecast of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data collected at the municipality level. Additional simulations exploring alternative scenarios for the relaxation of lockdown restrictions suggest that reopening strategies should account for local population densities and the specific dynamics of the contagion. Thus, we argue that data-driven simulations of our model could ultimately inform health authorities to design effective pandemic-arresting measures and anticipate the geographical allocation of crucial medical resources.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response. We apply this framework to breast cancer cells to integrate single cell transcriptomic data with longitudinal bulk cell population (bulk time course) data. We demonstrate that the explicit inclusion of the phenotypic composition estimate, derived from single cell RNA-sequencing data (scRNA-seq), improves accuracy in the prediction of new treatments with a concordance correlation coefficient (CCC) of 0.92 compared to a prediction accuracy of CCC = 0.64 when fitting on longitudinal bulk cell population data alone. To our knowledge, this is the first work that explicitly integrates single cell clonally-resolved transcriptome datasets with bulk time-course data to jointly calibrate a mathematical model of drug resistance dynamics. We anticipate this approach to be a first step that demonstrates the feasibility of incorporating multiple data types into mathematical models to develop optimized treatment regimens from data.

CD4 T-cell immune stimulation of HER2 + breast cancer cells alters response to trastuzumab in vitro.

INTRODUCTION: The HER2 + tumor immune microenvironment is composed of macrophages, natural killer cells, and tumor infiltrating lymphocytes, which produce pro-inflammatory cytokines. Determining the effect of T-cells on HER2 + cancer cells during therapy could guide immunogenic therapies that trigger antibody-dependent cellular cytotoxicity. This study utilized longitudinal in vitro time-resolved microscopy to measure T-cell influence on trastuzumab in HER2 + breast cancer. METHODS: Fluorescently-labeled breast cancer cells (BT474, SKBR3, MDA-MB-453, and MDA-MB-231) were co-cultured with CD4 + T-cells (Jurkat cell line) and longitudinally imaged to quantify cancer cell viability when treated with or without trastuzumab (10, 25, 50 and 100 µg/mL). The presence and timing of T-cell co-culturing was manipulated to determine immune stimulation of trastuzumab-treated HER2 + breast cancer. HER2 and TNF-α expression were evaluated with western blot and ELISA, respectively. Significance was calculated using a two-tailed parametric t-test. RESULTS: The viability of HER2 + cancer cells significantly decreased when exposed to 25 µg/mL trastuzumab and T-cells, compared to cancer cells exposed to trastuzumab without T-cells (p = 0.01). The presence of T-cells significantly increased TNF-α expression in trastuzumab-treated cancer cells (p = 0.02). Conversely, cancer cells treated with TNF-α and trastuzumab had a similar decrease in viability as trastuzumab-treated cancer cells co-cultured with T-cells (p = 0.32). CONCLUSIONS: The presence of T-cells significantly increases the efficacy of targeted therapies and suggests trastuzumab may trigger immune mediated cytotoxicity. Increased TNF-α receptor expression suggest cytokines may interact with trastuzumab to create a state of enhanced response to therapy in HER2 + breast cancer, which has potential to reducing tumor burden.

Anti-HER2 induced myeloid cell alterations correspond with increasing vascular maturation in a murine model of HER2+ breast cancer.

BACKGROUND: Therapy targeted to the human epidermal growth factor receptor type 2 (HER2) is used in combination with cytotoxic therapy in treatment of HER2+ breast cancer. Trastuzumab, a monoclonal antibody that targets HER2, has been shown pre-clinically to induce vascular changes that can increase delivery of chemotherapy. To quantify the role of immune modulation in treatment-induced vascular changes, this study identifies temporal changes in myeloid cell infiltration with corresponding vascular alterations in a preclinical model of HER2+ breast cancer following trastuzumab treatment. METHODS: HER2+ tumor-bearing mice (N = 46) were treated with trastuzumab or saline. After extraction, half of each tumor was analyzed by immunophenotyping using flow cytometry. The other half was quantified by immunohistochemistry to characterize macrophage infiltration (F4/80), vascularity (CD31 and α-SMA), proliferation (Ki67) and cellularity (H&E). Additional mice (N = 10) were used to quantify differences in tumor cytokines between control and treated groups. RESULTS: Immunophenotyping showed an increase in macrophage infiltration 24 h after trastuzumab treatment (P ≤ 0.05). With continued trastuzumab treatment, the M1 macrophage population increased (P = 0.02). Increases in vessel maturation index (i.e., the ratio of α-SMA to CD31) positively correlated with increases in tumor infiltrating M1 macrophages (R = 0.33, P = 0.04). Decreases in VEGF-A and increases in inflammatory cytokines (TNF-α, IL-1ß, CCL21, CCL7, and CXCL10) were observed with continued trastuzumab treatment (P ≤ 0.05). CONCLUSIONS: Preliminary results from this study in a murine model of HER2+ breast cancer show correlations between immune modulation and vascular changes, and reveals the potential for anti-HER2 therapy to reprogram immunosuppressive components of the tumor microenvironment. The quantification of immune modulation in HER2+ breast cancer, as well as the mechanistic insight of vascular alterations after anti-HER2 treatment, represent novel contributions and warrant further assessment for potential clinical translation.

In vitro vascularized tumor platform for modeling tumor-vasculature interactions of inflammatory breast cancer.

Inflammatory breast cancer (IBC), a rare form of breast cancer associated with increased angiogenesis and metastasis, is largely driven by tumor-stromal interactions with the vasculature and the extracellular matrix (ECM). However, there is currently a lack of understanding of the role these interactions play in initiation and progression of the disease. In this study, we developed the first three-dimensional, in vitro, vascularized, microfluidic IBC platform to quantify the spatial and temporal dynamics of tumor-vasculature and tumor-ECM interactions specific to IBC. Platforms consisting of collagen type 1 ECM with an endothelialized blood vessel were cultured with IBC cells, MDA-IBC3 (HER2+) or SUM149 (triple negative), and for comparison to non-IBC cells, MDA-MB-231 (triple negative). Acellular collagen platforms with endothelialized blood vessels served as controls. SUM149 and MDA-MB-231 platforms exhibited a significantly (p < .05) higher vessel permeability and decreased endothelial coverage of the vessel lumen compared to the control. Both IBC platforms, MDA-IBC3 and SUM149, expressed higher levels of vascular endothelial growth factor (p < .05) and increased collagen ECM porosity compared to non-IBCMDA-MB-231 (p < .05) and control (p < .01) platforms. Additionally, unique to the MDA-IBC3 platform, we observed progressive sprouting of the endothelium over time resulting in viable vessels with lumen. The newly sprouted vessels encircled clusters of MDA-IBC3 cells replicating a key feature of in vivo IBC. The IBC in vitro vascularized platforms introduced in this study model well-described in vivo and clinical IBC phenotypes and provide an adaptable, high throughput tool for systematically and quantitatively investigating tumor-stromal mechanisms and dynamics of tumor progression.

A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.

We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.