Simulation Of Tumor Growth Research Articles

Linking radiomic PET features with metabolic tissue parameters using a hybrid mathematical model of tumor growth

114 Objectives: The genetic diversity in tumor cells and the varying microenvironments lead to phenotypic heterogeneity within and between tumors (Marusyk et al., 2010), which can be assessed using PET imaging. More heterogeneous tumors may be more resilient to treatment and result in complications that are harder to treat (Hirata et al., 2017). Thus, understanding how tissue and tumor microparameters are linked to observable PET imaging features is of great interest, motivating the development of novel radiomics-based biomarkers. The objective of this work is to develop a multiscale mathematical model of tumor growth in vascularized tissue that can generate synthetic PET images of glucose metabolism. Using the model, we aim to establish a link between radiomic features and tissue microparameters. Methods: We simulate tumor growth using a hybrid mathematical model, which combines 1) grids of agents, namely autonomous decision-making entities representing blood vessels and different cell types (normal cells, tumor cells, hypoxic cells, necrotic cells), and 2) partial differential equation grids to simulate the tumor microenvironment (Robertson-Tessi, 2015). Blood is the source of oxygen and glucose (drugs or radionuclides can also be incorporated), which diffuse through tissue and are consumed by cells. In each simulation step, the state of each agent and the next action is determined based on the local microenvironment. The model uses realistic biological parameters, such as oxygen diffusion coefficient in tissue (1.62x10-5 cm2/s), consumption rates (2.5x10-18 to 2.0x10-15 mol/min/cell), and average cell size (20um). The oxygen consumption rate follows the Michaelis-Menten kinetics and is simplified to a constant for each cell type (Grimes et al, 2014). The simulated grid size was 1000x1000 cells (2x2 cm). The time-sequences of agent maps were converted to pseudo-standardized uptake value (pSUV) maps, assuming the relative glucose consumption rates 1, 8, 12, and 0 for normal, cancer, cancer hypoxic, and necrotic cells, respectively. pSUV maps were downsampled to a resolution of 3 mm (mid-point between pre-clinical and clinical PET resolution). The assumed PET tracer is a glucose analog, applicable to 18F-fluorodeoxyglucose (FDG). Results: To demonstrate the utility of our method, we used different combinations of microparameters to simulate 3 distinct tumor types (Fig. 1). Altered parameters included blood vessel density (types A,C: 20/mm2, B: 100/mm2), spatial arrangement (types A,C: random placement, B: uniform-density placement), and vascular network alteration by tumor cells such as vessel removal probability (types A,B: 1, C: 0.05). The resulting tumors of different types had very distinct phenotypes, which were visually distinguishable in the corresponding pSUV PET images (Fig. 2). The model produced diverse and realistic tumor growth rates, ranging from ~80 to ~310 days to reach a 1-cm tumor diameter (Fig. 3). Likewise, 4 radiomic features computed from the synthetic PET images of tumors (pSUV mean uptake, shape compactness, Haralick texture contrast and homogeneity), were significantly different between the tumor types. Specifically, the values for 1-cm tumors were: mean pSUV - 4.58 ± 0.03 (type A), 7.63 ± 0.72 (type B), 4.71 ± 0.04 (type C); Compactness - 0.91 ± 0.01 (A), 0.95 ± 0.01 (B), 0.94 ± 0.005 (C); Contrast - 1.67 ± 0.08 (A), 1.58 ± 0.04 (B), 1.36 ± 0.1 (C); Homogeneity - 0.71 ± 0.01 (A), 0.80 ± 0.006 (B), 0.79 ± 0.01 (C). From a combination of all 4 features, each tumor phenotype and set of tissue parameters can be uniquely identified. Conclusions: Realistic tumor growth can be achieved through modeling tissue and tumor microparameters. By changing the parameter values, distinctly different tumor phenotypes were obtained measurable through PET image radiomics. Hence, the model can help establish a link between tissue metabolic parameters and PET radiomics, and identify optimal radiomic features for tumor assessment.

Abstract PS3-22: A new computational model for visualization and prediction of breast cancer growth based on reinforcement learning

Abstract Introduction: Breast cancer is a complex disease with no simple solution, which is why researchers are tackling it from every angle. A relatively new effort of predictive oncology is to develop a systematic method for predicting the future status of an individual breast tumor given representation of the initial conditions and an appropriate mathematical model. Using a medical imaging-based approach, the goal of this preclinical research project was to obtain high resolution images of the tumor angiogenic network and predict cancer growth using a novel mathematical model that we recently develop. Methodology: In the proposed model, we consider each cell and vessel as an agent and decisions are made based on the state-action-reward-state-action (SARSA) concept, which is an incremental reinforcement learning algorithm. Two types of cells (i.e. cancer and normal) and vessels (i.e. tip and stalk) are used in the environment. This spatial collection of cells and vessels then have six (i.e. apoptosis, hypoxia, necrosis, migration, proliferation and quiescence) and three (i.e. branch, expansion and sprout) allowable actions. The model agent has a high degree of autonomy and performs actions based on the knowledge it receives from the surrounding environment. One of the more important parts of our model is the release and diffusion of select nutrients into the tumor environment, e.g. oxygen, vascular endothelial growth factor (VEGF), etc. Using a breast cancer xenograft mouse model, animals were administrated an intravascular contrast agent (200 microliters, ExiTron Nano 12000, Miltenyi Biotec) and tumors were scanned using an ultrahigh resolution computed tomography (CT) system (OI/CT, MILabs). The tumor microvascular network was segmented and used as an input and initial state of our model that then simulated cancer growth. Subsequent CT scans (on the order of weeks) were performed to validate model accuracy. Results: Initial results demonstrate that the SARSA model can simulate tumor growth. As the concentration of available nutrients around the tumor decreases, normal cells began to decline sharply and were eliminated by selecting the apoptotic phenotype. Cancer cells were more resistant to nutrient deficiencies during simulation. Consequently, these cancer cells proliferated, and tumor volume increased. Our findings also revealed that decreased oxygen availability (i.e. hypoxia) stimulated VEGF production and growth of the microvascular network, which agreed with repeat in vivo CT imaging results. Conclusion: A predictive model of breast cancer growth was developed and preliminary preclinical results using in vivo medical images of breast cancer-bearing animals highlighted the utility of this new oncological tool. Citation Format: M. Hossein Zangooei, Ryan Margolis, Kenneeth Hoyt. A new computational model for visualization and prediction of breast cancer growth based on reinforcement learning [abstract]. In: Proceedings of the 2020 San Antonio Breast Cancer Virtual Symposium; 2020 Dec 8-11; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2021;81(4 Suppl):Abstract nr PS3-22.

Accounting for intraoperative brain shift ascribable to cavity collapse during intracranial tumor resection

Purpose: For many patients with intracranial tumors, accurate surgical resection is a mainstay of their treatment paradigm. During surgical resection, image guidance is used to aid in localization and resection. Intraoperative brain shift can invalidate these guidance systems. One cause of intraoperative brain shift is cavity collapse due to tumor resection, which will be referred to as "debulking." We developed an imaging-driven finite element model of debulking to create a comprehensive simulation data set to reflect possible intraoperative changes. The objective was to create a method to account for brain shift due to debulking for applications in image-guided neurosurgery. We hypothesized that accounting for tumor debulking in a deformation atlas data framework would improve brain shift predictions, which would enhance image-based surgical guidance. Approach: This was evaluated in a six-patient intracranial tumor resection intraoperative data set. The brain shift deformation atlas data framework consisted of simulated deformations to account for effects due to gravity-induced and hyperosmotic drug-induced brain shift, which reflects previous developments. An additional complement of deformations involving simulated tumor growth followed by debulking was created to capture observed intraoperative effects not previously included. Results: In five of six patient cases evaluated, inclusion of debulking mechanics improved brain shift correction by capturing global mass effects resulting from the resected tumor. Conclusions: These findings suggest imaging-driven brain shift models used to create a deformation simulation data framework of observed intraoperative events can be used to assist in more accurate image-guided surgical navigation in the brain.

Understanding the effect of measurement time on drug characterization.

In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: εmax is the maximum possible effect of a drug, and IC50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the εmax and IC50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC50 and εmax. Using traditional methods, we then calculate the IC50 and εmax values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC50 value decreases and the measured εmax increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC50 and εmax rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC50 estimates become more accurate at later measurement times while εmax is more accurate at early measurement times.

Computational modelling and simulation of cancer growth and migration within a 3D heterogeneous tissue: The effects of fibre and vascular structure

The term cancer covers a multitude of bodily diseases, broadly categorised by having cells which do not behave normally. Since cancer cells can arise from any type of cell in the body, cancers can grow in or around any tissue or organ making the disease highly complex. Our research is focused on understanding the specific mechanisms that occur in the tumour microenvironment via mathematical and computational modeling. We present a 3D individual-based model which allows one to simulate the behaviour of, and spatio-temporal interactions between, cells, extracellular matrix fibres and blood vessels. Each agent (a single cell, for example) is fully realised within the model and interactions are primarily governed by mechanical forces between elements. However, as well as the mechanical interactions we also consider chemical interactions, for example, by coupling the code to a finite element solver to model the diffusion of oxygen from blood vessels to cells. The current state of the art of the model allows us to simulate tumour growth around an arbitrary blood-vessel network or along the striations of fibrous tissue.

Abstract 1942: Volume and vascular evolution assessed with ultrasound in tumor growth: First steps for a future tool of predictive responses of treatment

Abstract Background: Mathematical models have been developed to simulate tumor growth, as a goal to predict therapy response. We implemented three models and we investigated their agreement with tumor size assessed by ultrasound. We also investigated the link between microvascular flow parameters and future tumor size evolution. Methods: Three ordinary differential equation tumor growth models were implemented in Matlab. The exponential-linear model (EL) assumes growth rate tends to linear after initial exponential growth as nutrient support becomes limited. The Gompertz model (G) describes demographic growth with a fixed carrying capacity because growth cannot exceed the capacity of the environment. The dynamic carrying capacity model (DCC) assumes this carrying capacity can change with time, for example, due to angiogenesis or necrosis formation. Experimental data were acquired in 11 control and 10 antiangiogenic (AA) treated mice with ectopic murine colorectal carcinoma (CT26) on Days 7, 9, 13, 15 and 21 after implantation (therapy started at day 7). Ellipsoidal volume (V) was estimated from B-mode measurements of the major transverse and longitudinal axes and used to estimate Relative Growth Rate (RGR): (t{n}) = [V(t_{n}-V(t_{n-1})]/[(t_{n}-t_{n-1}).V(t_{n-1})]. Contrast-Enhanced Ultrasound (CEUS) data were acquired along the longitudinal axis with Sequoia 512, 7-14 MHz probe. Regions with no contrast-enhancement were identified. Average contrast intensity vs. time curves in the perfused zone were fit to a lognormal model to estimate Area Under the Curve (AUC), Peak Enhancement (PE), Time to Peak (TTP), Mean Transit Time (MTT), Wash In Rate (WIR) and Wash Out Rate (WOR). The Akaike Information Criterion (AIC) was used to evaluate the relative quality of the models to describe the tumor size evolution. AIC penalizes models with more parameters to deal with the trade-off between goodness of fit and the model’s simplicity. Results: Initial implementation of the models using a fixed (1 mm3) and free initial tumor size were compared. In this data set where earliest measured tumor size (day 4) varied from 15 to 39 mm3, the additional free parameter resulted in improved mean AIC (EL: 37 vs. 40 ; G: 37 vs. 41 ; DCC: 43 vs. 45 - free and fixed initial volume respectively). AIC was lowest on average for the G model in control mice. The TTP, WIR and WOR at t_n were linked with future RGR between t_n and t_{n+1} (RS = -0.51, 0.44 and -0.46 respectively for C (TTP and WIR) or AA (WOR) group, p<0.01, non-parametric Spearman correlation coefficient). Conclusions: The microvascular function includes additional information related to tumor growth. The integration of size and vascularization parameters into the mathematical models is the next step for predictive tumor growth. Such a model based on predictive quantitative ultrasound images has potential application in treatment follow-up. Citation Format: Jerome Griffon, Zixin Yang, Delphine Le Guillou-Buffello, Alexandre Dizeux, Michele Lamuraglia, Lori Bridal. Volume and vascular evolution assessed with ultrasound in tumor growth: First steps for a future tool of predictive responses of treatment [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 1942.

TMOD-15. RELIABILITY OF IMAGING-BASED MEASURES OF TUMOR ‘MASS-EFFECT’– EVIDENCE FROM A COMPUTATIONAL STUDY

Elevated tumor mass-effect is associated to poor prognosis in GBM [1,2]. However, tumor mass-effect is poorly quantified in clinical practice. Recently, Steed et al. [2] proposed ‘Lateral ventricle displacement’ (LVd), defined as the change in center-of-mass position of the lateral ventricles between an undeformed reference and the tumor-bearing anatomy, as quantitative imaging measure of mass-effect. They found that the magnitude of LVd in GBM patients can be associated with overall survival. These results show the clinical importance of tumor mass-effect in GBM, warranting robust clinical measures. This study characterizes image-derived estimates of tumor mass-effect by their ability to measure mass-effect accurately and reliably. We use a mathematical model to simulate tumor growth, which allows us to control and objectively quantify ‘mass-effect’ [3]. For given simulation parameters and growth location, we compute estimates of mass-effect from anatomical deformation during the growth process. We use multiple regression analysis to evaluate the ability of different estimates to explain the tumor’s objective mass-effect, measured by the tumor-induced pressure on the skull.

Study of tumor growth indicates the existence of an "immunological threshold" separating states of pro- and antitumoral peritumoral inflammation.

BackgroundPeritumoral inflammation—a response mainly involving polimorphonuclear neutrophils—has traditionally been thought protumoral in its effects. In recent years, however, a number of studies have indicated that it may play an important antitumoral role. This discrepancy has been difficult to explain.Methods and findingsThis work describes a tool for simulating tumor growth that obeys the universal model of tumor growth dynamics, and shows through its use that low intensity peritumoral inflammation exerts a protumoral effect, while high intensity inflammation exerts a potent antitumoral effect. Indeed, the simulation results obtained indicate that a sufficiently strong antitumoral effect can reverse tumor growth, as has been suggested several times in the clinical literature.ConclusionsThe present result indicate that an ‘immunological threshold’ must exist, marking the boundary between states in which peritumoral inflammation is either harmful or beneficial. These findings lend support to the idea that stimulating intense peritumoral inflammation could be used as a treatment against solid tumors.

Abstract 4530: A biophysical model for necrosis development in glioblastoma informed by subject-specific MRI measurements

Abstract Introduction We have previously developed the means to use quantitative magnetic resonance imaging (MRI) data to initialize a biophysical model (Model 1) of tumor growth which accurately predicts future tumor volume but fails to capture the development of low-cellularity (or necrotic) regions in a murine model of glioblastoma. In this work, we expand upon this biophysical model (Model 2) to characterize necrosis by relating tissue perfusion to cell death. We evaluate the accuracy of both models to in vivo measurements of tumor growth. Methods To evaluate this model, rats (n = 4) with C6 gliomas were imaged with dynamic contrast enhanced MRI (DCE-MRI) and diffusion-weighted MRI (DW-MRI) seven times over 10 days. DCE-MRI was used to identify tumor regions and estimate tissue perfusion (as estimated by the parameter Ktrans), while DW-MRI was used to estimate cell number. For both Models 1 and 2, parameters describing tumor proliferation, diffusion, and carrying capacity were optimized from the first three imaging time points. For Model 1, these parameters were then used in a forward evaluation of the model to predict future tumor growth at the later days. For Model 2, additional parameters describing cell death and sensitivity to Ktrans were estimated from the all timepoints and used to simulate tumor growth over the final four time points. Error was assessed between the model and observed tumor growth by calculating the percent error in tumor volume, percent error in voxel cell number, and the concordance correlation coefficient (CCC) over the final four days. Results No statistically significant differences for percent error in tumor volume were observed between Model 1 (6.49 ± 4.70%, mean and 95% confidence interval) and Model 2 (6.77 ± 4.77%). Model 1 had 12.0 ± 0.3% error in voxel cell number in low cellularity regions (where cellularity was between 60-80% of carrying capacity). Model 2, however, exhibited a statistically significant decrease (P < 0.05) in error at the voxel level (8.3 ± 0.2%) in the same low cellularity regions. No significant differences for percent error in voxel cell number were observed between the models at high cellularity regions (greater than 80% of carrying capacity). Model 2 had stronger agreement (CCC = 0.69) between the measured and model described cell number in low cellularity regions compared to model 1 (CCC = 0.57). Both model 1 and 2 had CCC > 0.90 in high cellularity regions. Conclusion Incorporating a model of cell death informed by tissue perfusion improves the overall tumor growth characterization by decreasing the error in predicted cell number at the voxel level in the low cellularity (or hypoxic) regions. The lack of a model for Ktrans in the current implementation, however, requires a posteriori measurements to update tissue perfusion. Further work is needed to develop a predictive model for the spatial-temporal evolution of Ktrans. Citation Format: David A. Hormuth, Thomas E. Yankeelov. A biophysical model for necrosis development in glioblastoma informed by subject-specific MRI measurements [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr 4530. doi:10.1158/1538-7445.AM2017-4530

Low grade glioma growth modeling considering chemotherapy and radiotherapy effects from magnetic resonance images.

Studying tumor growth using mathematical models from magnetic resonance (MR) images is an important application that is believed to play a major role in cancer treatment by predicting tumor evolution, quantifying the response to therapy, and treatment planning. Reaction diffusion is the most popular model because of its simplicity and consistency with the biological growth process. However, most of the current growth models focus on presurgical images and likely without treatment. In this paper, we propose a new reaction diffusion model to consider the chemotherapy and radiotherapy effects on the tumor growth modelling for patients with low grade glioma. The proposed model does not consider the tensor information from diffusion tensor imaging. Instead it uses a weighted parameter to promote higher diffusivity in white matter. The radiotherapy and chemotherapy effects are considered as a loss terms in the proposed model. The preliminary results of the proposed model on synthetic and 2 real MR images show that, our model can effectively simulate tumor growth with high accuracies when treatments are administrated to low grade glioma patients.

Modeling the efficacy of the extent of surgical resection in the setting of radiation therapy for glioblastoma.

Standard therapy for glioblastoma (GBM) includes maximal surgical resection and radiation therapy. While it is established that radiation therapy provides the greatest survival benefit of standard treatment modalities, the impact of the extent of surgical resection (EOR) on patient outcome remains highly controversial. While some studies describe no correlation between EOR and patient survival even up to total resection, others propose either qualitative (partial versus subtotal versus complete resection) or quantitative EOR thresholds, below which there is no correlation with survival. This work uses a mathematical model in the form of a reaction–diffusion partial differential equation to simulate tumor growth and treatment with radiation therapy and surgical resection based on tumor‐specific rates of diffusion and proliferation. Simulation of 36 tumors across a wide spectrum of diffusion and proliferation rates suggests that while partial or subtotal resections generally do not provide a survival advantage, complete resection significantly improves patient outcomes. Furthermore, our model predicts a tumor‐specific quantitative threshold below which EOR has no effect on patient survival and demonstrates that this threshold increases with tumor aggressiveness, particularly with the rate of proliferation. Thus, this model may serve as an aid for determining both when surgical resection is indicated as well as the surgical margins necessary to provide clinically significant improvements in patient survival. In addition, by assigning relative benefits to radiation and surgical resection based on tumor invasiveness and proliferation, this model confirms that (with the exception of the least aggressive tumors) the survival benefit of radiation therapy exceeds that of surgical resection.

In silico study of the impact of cancer stem cell dynamics and radiobiological hypoxia on tumour response to hyperfractionated radiotherapy.

Advanced head and neck carcinomas (HNCs) are aggressive tumours, mainly due to hypoxia and a cancer stem cell (CSC) subpopulation. The aim of this study was to simulate tumour growth and behaviour during radiotherapy of three HNC groups (governed by different growth kinetics, hypoxia levels and CSC division pattern) to determine correlation between resistance factors and responses to hyperfractionated radiotherapy. An in silico HNC model was developed based on biologically realistic input parameters. During radiotherapy simulation, three parameters were studied: growth kinetics, hypoxia and probability of CSC symmetrical division. Both independent and combined effects on tumour response to hyperfractionated radiotherapy were assessed. Oxic and very mildly hypoxic HNCs were revealed to be controlled by hyperfractionated radiotherapy, irrespective of growth kinetics and CSC division pattern. Moderately hypoxic tumours had different responses to radiotherapy: while slowly proliferating HNCs were still controllable, tumours with higher cell turnover were more resistant. In rapidly proliferating tumours, the number of fractions needed for tumour control increased exponentially with the probability of CSC symmetrical division, whereas in moderately growing HNC, this behaviour was linear. Severely hypoxic tumours could not be controlled by radiotherapy alone. Tumours with CSCs in a severely hypoxic niche required adjuvant therapies to be eradicated. Growth kinetics strongly influence tumour responses to treatment. Slowly growing tumours showed linear dependence between dose and hypoxia/CSC, whereas rapidly growing tumours followed exponential behaviour.

Simulation of Tumor Response to Immunotherapy Using a Hybrid Cellular Automata Model

A cellular automata model is presented to describe the interaction between a growing tumor next to the presence of nutrient elements, and the immune response as well as the immunotherapy intervention and its stimulator effect on immune cell activity. A comparison between tumor growth before and after immunotherapy effect is discussed, and many characteristics of simulated tumor growth patterns are extracted such as the fractal dimension, the fractality of tumor boundary and the number of cancerous cells on tumor periphery. The simulation results shed light on the factor that may play a central role in immunotherapy effectiveness and which is related to tumor morphology.

Abstract A43: Context-dependent growth effects of progestins in estrogen receptor-positive breast cancer patient-derived xenografts (PDX)

Abstract Introduction: Progesterone (P4) and progesterone receptors (PR) play elusive roles in breast cancer. Synthetic progestins in hormone replacement therapy increase breast tumorigenesis, yet these same progestins at high doses can be an effective therapy for some advanced breast tumors. The literature supports that progestins can either stimulate or inhibit breast cancer cell growth, and an increasing body of evidence supports P4 promotes expansion of breast cancer stem cells. Interplay between PR and estrogen receptors (ER) is emerging as important in dictating growth and response to treatment. There is historical precedence for PR interference of ER dependent gene transcription; recent reports identify that PR modulate ER DNA binding events. Given the importance of PR as a biomarker and potential therapeutic target, and the uncertainty surrounding its context-dependent actions, we aimed resolve this using breast cancer PDX models. The purpose of this study was to evaluate the effects of natural and synthetic progestins on growth and estrogen-dependent gene expression in luminal breast tumors, and to define contexts that dictate their divergent effects. Experimental procedures: Six luminal breast cancer PDX developed at UCD-AMC were used for these studies. Most profiled as Luminal B subtype. Tumors generally fell into two types: a pure luminal phenotype and a mixed luminal/basal phenotype based on cytokeratin expression. Tumors varied in expression of ER, PR, and androgen receptors (AR) from low (<10% positive cells), moderate (30-50%), to high (>90%). Tumors were grown in vivo under conditions of continuous placebo, 17β-estradiol (estrogen), estrogen plus progesterone (P4), or estrogen plus the synthetic progestin medroxyprogesterone acetate (MPA) for several months and growth parameters monitored. Receptor content was measure by immunohistochemistry and western blots. Gene expression profiles of select tumors were determined using Affymetrix® GeneChip human gene microarrays and/or RNAseq and results analyzed using Partek Genomics Suite™ software, and Metacore™ pathway analysis. Summary: In two pure luminal PDX with high receptor levels (ER, PR, AR) both P4 and MPA significantly inhibited estrogen-dependent growth (growth-inhibited, GI). Two PDX (one pure luminal, one mixed) with moderate ER and low PR and AR showed no significant effect of P4 or MPA on estrogen-dependent growth (growth neutral, GN). One mixed luminal/basal PDX with low ER and PR and moderate AR showed no effect with P4, whereas MPA simulated tumor growth above that with estrogen alone (growth stimulated, GS). Study of one PDX is ongoing. In the GI tumors both P4 and MPA reversed expression of ~30% of estrogen regulated genes. In particular these tumors had high estrogen-dependent expression of the Notch pathway, which was blocked by both P4 and MPA. Progestins did not alter estrogen-dependent genes in the GN or GS tumors, which did not include the Notch pathway. MPA stimulated a unique set of genes in the GS tumor, and was able to mobilize AR to the nucleus whereas P4 did not. Conclusion: Progestins have mixed effects on breast cancer PDX tumor growth. Tumors that have high ER and PR and are highly estrogen-dependent are more likely to exhibit strong growth inhibition by progestins (both P4 and MPA). Tumors with mixed luminal/basal phenotype that have less ER and PR and are moderately estrogen-dependent are less likely to be progestin-inhibited. In tumors with low ER and PR but high AR content MPA can act as an AR agonist to stimulate growth. Tumor-specific downstream estrogen-dependent pathways such as Notch may indicate whether progestins are therapeutic. Additional tumors are needed to confirm these results with the long term goal of developing a molecular assay to define those tumors that may benefit from progestin treatment. Citation Format: Jessica Finlay-Schultz, Heather M. Brechbuhl, Rachel B. Rosen, Austin E. Gillen, Britta M. Jacobsen, Peter Kabos, Carol A. Sartorius. Context-dependent growth effects of progestins in estrogen receptor-positive breast cancer patient-derived xenografts (PDX). [abstract]. In: Proceedings of the AACR Special Conference on Advances in Breast Cancer Research; Oct 17-20, 2015; Bellevue, WA. Philadelphia (PA): AACR; Mol Cancer Res 2016;14(2_Suppl):Abstract nr A43.

Abstract 3759: Xenograft rebound kinetics are consistent with the founder effect

Abstract Introduction Tumors are often composed of a heterogeneous cell population growing over time subject to the forces of evolutionary dynamics. These principles offer insights not only for bulk tumor growth, but also for small cell populations such as in metastases or de-bulked tumors following treatment. In this work, we investigate whether the evolutionary effects of small population sizes are evident in in vivo pre-clinically through a meta-analysis of xenograft rebound growth kinetics following treatment. Methods We first used a HCT116 cell fitness distribution we have previously measured in soft agar to demonstrate the expected population fitness trajectory as a function of starting population size. We sampled subclone fitnesses from this distribution to initialize either large or small theoretical tumors, and simulated tumor growth as a Moran process to find the probability distribution of expected outcomes in final tumor population fitness. Since initial tumor volumes in xenografts experiments have a narrow range of volume (equivalently, population size), we next identified tumor volume measurements following suspension of treatment with anticancer agents from in-house historical xenograft growth datasets. Each of 1359 tumor volume trajectories after treatment was fit using non-linear regression to determine the exponential growth rate (population fitness), and compared to both the volume at treatment end as well as the average control group growth rate from the corresponding experiment. Results The simulated tumors demonstrate the “founder effect” in heterogeneous populations: large populations become dominated by the fastest growing, most fit subclones while small populations are sensitive to initial clonal sampling as well as random births and deaths. Rebound growth in xenografts post-treatment displayed large variability compared to the growth of the corresponding experimental control group. Post-treatment and untreated growth rates are poorly correlated (R2 = 0.1) consistent with a significant change in the tumor cell population following a period of selective pressure. Two additional observations are coherent with a founder effect following a bottleneck event (i.e., treatment). The relationship between post-treatment starting volume and growth rate has a positive slope (p = 0.01, F-test) while growth rate variance decreases with starting volume (p < 0.01 F-test). Both results concur with the Moran simulations showing smaller populations have more stochastic outcomes while larger populations deterministically drift to greater fitness. Conclusions We find that xenograft growth kinetics following cessation of treatment with anticancer agents are consistent with a selection process and the founder effect. Application of evolutionary theory to small cell populations in preclinical models may yield new strategies to combat metastases and resistance emergence. Citation Format: Andrew Chen, Christopher J. Zopf, Jing-Tao Wu, Wen Chyi Shyu, Arijit Chakravarty. Xenograft rebound kinetics are consistent with the founder effect. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 3759. doi:10.1158/1538-7445.AM2015-3759

Abstract 372: Choosing the right schedule for progression free survival: A systems pharmacology approach

Abstract Drug resistance is a common feature of many cancer therapies and often limits their long-term effectiveness. Most anticancer agents are developed with an initial focus on Objective Response (short-term response), despite clinical evidence that, for most cancers, this does not correlate with long term therapeutic benefit (Progression-Free Survival), due to the emergence of resistance. Viewing cancer as a disease of somatic Darwinian evolution reframes resistance as a consequence of competing populations of tumor cells within a polyclonal tumor, each responding differentially to selection pressure. In this context, the amplification of pre-existing resistance to therapy has been implicated as a common cause of treatment failure. Here we ask how drug scheduling can impact long-term response to therapy, using an evolutionary model of tumor kinetics. First, we apply a dynamic model of tumor kinetics with competing subclones of tumor cells to a published dataset of prostate cancer progression (Treatment thalidomide+docetaxel or ketoconazole+ hydrocortisone+alendronate), and show that it is capable of closely predicting Progression Free Survival. Tumor cells are modeled as being either sensitive or resistant, cell growth is modeled using a simple exponential growth model, and drug effect is incorporated in the model as overall inhibition on the growth-rate. Competition between tumor sub-populations is modeled as frequency-dependent fitness, using a logistic tumor growth model. Next, we use this dynamic model derived from the prostate cancer dataset to understand the effect of schedule on resistance, simulating tumor growth upon drug treatment for different doses and schedules. Beyond a literal simulation of resistance for a given drug schedule, we assess the contributions of resistance made by dose amplitude and dose frequency. Our model predicts that for a graded dose-response curve (Hill slope of 1), more frequent dosing schedules minimize the emergence of resistance. On the other hand, for a steep dose-response curve (Hill slope of 5), for constant dose density, we find that a high infrequent schedule is better than a low frequent dosing schedule for low doses. As the dose density increases, the low frequency schedule again emerges as optimal for minimizing resistance. As a final test, a competition term between the subpopulations is also included in our model, with essentially identical results. We then apply our model to published datasets of clinical response to treatment, and find close agreement with published results. Our generalized approach to this problem provides a framework for dissecting the underlying drivers of the emergence of resistance, and provides a recommendation for the minimization of resistance in a practical setting. Citation Format: Mayankbhai Patel, Jerome Mettetal, Matthew Cohen, Santhosh Palani, Keisuke Kuida, Mark Hixon, Joseph Bolen, Wen Chyi Shyu, Dennis Noe, Arijit Chakravarty. Choosing the right schedule for progression free survival: A systems pharmacology approach. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 372. doi:10.1158/1538-7445.AM2014-372

Abstract 698: Variability in xenograft growth rates can be explained by intra-tumor evolutionary dynamics

Abstract Growing evidence frames cancer as a disease of somatic Darwinian evolution. Recent reports establish both inter- and intra-tumor genetic heterogeneity within patients, and evolution in response to treatment. Cell lines and xenografts also display genetic heterogeneity arising from chromosomal instability, and evolve in response to experimental conditions. Although selection pressures in culture or in a mouse differ from those in a patient, studying the evolutionary process pre-clinically may yield insights useful in the design of experimental systems of cancer. Using the soft agar colony growth assay, we previously showed that individual colonies in soft agar have widely divergent growth rates that are mostly inherited over experimental timescales. In this work we ask what the impact of that divergence is on xenograft growth kinetics, and examine the implications for the development of resistance. First, we applied a stochastic, dynamic model of tumor kinetics to simulate clonal heterogeneity in xenograft growth rates. Each simulated “virtual tumor” consisted of a set of independently growing subclone cells, whose growth rates were bootstrapped from a distribution derived from 104 individual HCT-116 colonies in the soft agar colony growth assay. Both the sampling distribution variance and the number of subclones sampled to found each xenograft were varied to test the effect of intercell heterogeneity and starting population size on overall xenograft growth rate. We simulated tumor growth profiles over both a two-week implant and a three-week observation period to reflect experimental conditions. Three stochastic simulation scenarios were considered for possible cellular events: birth only; birth and death; and birth, death, and mutation. We compared the simulation results to an experimentally determined distribution derived from 308 individual HCT-116 xenograft tumors. Our findings suggest the variability of whole tumors is related to the clonal growth rate diversity within the HCT-116 cell line. In particular, the observed xenograft growth rate heterogeneity can be explained entirely by a scenario where many orders of magnitude fewer cells survive to initiate each tumor than the millions of cells implanted experimentally. This finding is consistent with previously published experimental results that have been interpreted to suggest the existence of cancer stem cells. We demonstrate the small number of founder cells in each xenograft leads to evolutionary drift under treatment conditions, when a resistant mutant may come to dominate stochastically due to the small population size.We then extend this work to ask questions about experimental design - how to develop a xenograft model system that is either more reproducible (less heterogeneity) or more heterogeneous (less reproducible). The latter system may be particularly valuable in studying the emergence of resistance. Citation Format: Christopher J. Zopf, Andrew Chen, Mayank Patel, Santhosh Palani, Syamala Bandi, Derek Blair, Wen Chyi Shyu, Arijit Chakravarty. Variability in xenograft growth rates can be explained by intra-tumor evolutionary dynamics. [abstract]. In: Proceedings of the 105th Annual Meeting of the American Association for Cancer Research; 2014 Apr 5-9; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2014;74(19 Suppl):Abstract nr 698. doi:10.1158/1538-7445.AM2014-698

B16/F10 tumors in aged 3D collagen in vitro simulate tumor growth and gene expression in aged mice in vivo

Although the incidence of cancer rises with age, tumor growth is often slowed in older hosts. The B16/F10 melanoma cell line is commonly used in murine models of age-related tumor growth suppression. We wished to determine if the growth pattern and gene expression of B16/10 tumors grown in aged mice could be simulated in 3D collagen matrices derived from aged mice. Outcome measures were tumor size in vitro and gene expression of the key growth regulatory molecules: growth hormone receptor (GHR), IL-10Rβ, IL-4Rα, and IL-6. B16/F10 tumors were grown in 20-25-mo-old C57/BL6 male mice. Tumor sizes ranged from 30 to 4,910 mg in vivo. Tumors from a subset of mice were removed after euthanasia, and equivalent amounts of each tumor were placed in aged 3D collagen and grown for 5 d. Tumor sizes in aged 3D collagen correlated highly with their original tumor size in vivo. Gene expression changes noted in vivo were also maintained during tumor growth in aged 3D collagen in vitro. The relative expression of GHR was increased, IL-10Rβ was unchanged, and IL-4Rα and IL-6 were decreased in the larger tumors relative to the smaller tumors in vitro, in a pattern similar to that noted in vivo. We propose that 3D matrices from aged mice provide an in vitro model of tumor growth that correlates highly with tumor size and expression of key regulatory molecules in vivo.

TU-C-BRB-09: In Silico Model of Glioblastoma Tumor Microenvironment to Predict Radiotherapy Outcome

Purpose: We developed a tumor model for glioblastomas with the aim to study tumor growth, transition from avascular to vascular, oxygenation effects, cell repair, and to predict glioma control or recurrence when the malignancy is treated with ionizing radiation. Methods: Anatomical structures imaged using MRI were contoured and compartmentalized to simulate white matter, grey matter, and vasculature structures proximal to a simulated glioblastoma tumor. The gliomas were modeled using micro compartments to represent groups of tumor cells of the same structure and functionality. The model incorporates the interactions between healthy and tumor tissue using a mechanistic approach based on forces and link strengths between cells and the extra cellular matrix. The evolution and response of the cells to biomolecules, nutrients, and oxygen distribution were modeled through discrete transport and diffusion equations. Cell biology was simulated using parameters that represent nutrient consumption, cell cycle, cell history, and cell oxygenation. The delivered dose was modeled using a probabilistic approach to compute the likelihood of DNA damage and repair. Results: We successfully simulated tumor growth, invasion, and disruption of the local anatomy and tumor control or recurrence under ionizing radiation stress. We modeled tumor radiotherapy under hypoxic and oxic conditions. Results of these numerical experiments show qualitative agreement with observed tumor evolution and response to ionizing radiation treatment. Transition from an avascular to a vascular tumor and recruitment of blood vessels was also successfully modeled. Spatial resolution of compartments is higher than current imaging devices, making our model a valuable tool to link simulations with anatomical and functional imaging. Conclusions: We developed a micro compartmental model of glioblastoma tumors to evaluate the role of the local anatomy and the microenvironment oxygenation when the malignancy is treated with ionizing radiation. The model can be used to predict glioblastoma growth and response to radiotherapy.

Optimization of vascular-targeting drugs in a computational model of tumor growth

A biophysical tool is introduced that seeks to provide a theoretical basis for helping drug design teams assess the most promising drug targets and design optimal treatment strategies. The tool is grounded in a previously validated computational model of the feedback that occurs between a growing tumor and the evolving vasculature. In this paper, the model is particularly used to explore the therapeutic effectiveness of two drugs that target the tumor vasculature: angiogenesis inhibitors (AIs) and vascular disrupting agents (VDAs). Using sensitivity analyses, the impact of VDA dosing parameters is explored, as is the effects of administering a VDA with an AI. Further, a stochastic optimization scheme is utilized to identify an optimal dosing schedule for treatment with an AI and a chemotherapeutic. The treatment regimen identified can successfully halt simulated tumor growth, even after the cessation of therapy.