Biology subjects

Enderling, H.

Publications and source records attributed to Enderling, H..

14 recordsLinked to original sources

bioRxiv2023

Logistic tumor-population growth and ghost-points symmetry

The observed time evolution of a population is well approximated by a logistic function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential at a constant rate and capped at a limit size, i.e., the carrying capacity. In mathematical oncology, the carrying capacity has been postulated to be co-evolving and thus patient-specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic functions rotation symmetry can help estimate the populations growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against a classic oncology database of logistic tumor growth, achieving a 30% to 40% reduction in the time necessary to correctly estimate the logistic growth rate and carrying capacity. Our results will improve tumor dynamics forecasting and augment the clinical decision-making process.

cancer biology↗

bioRxiv2022

Breast Cancer Reaction-Diffusion from Spectral-Spatial Analysis in Immunohistochemistry

Cancer is a prevalent disease, and while many significant advances have been made, the ability to accurately predict how an individual tumor will grow - and ultimately respond to therapy - remains limited. We use spatial-spectral analysis of 20 patients accrued to a phase II study of preoperative SABR with 9.5 x 3 Gy for early-stage breast cancer whose tissues were stained with multiplex immunofluorescence. We employ the reaction-diffusion framework to compare the data-deduced two-point correlation function and the corresponding spatial power spectral distribution with the theoretically predicted ones. A single histopathological slice suffices to characterize the reaction-diffusion equation dynamics through its power spectral density giving us an interpretative key in terms of infiltration and diffusion of cancer on a per-patient basis. This novel approach tackles model-parameter-inference problems for tumor infiltration and can immediately inform clinical treatments.

cancer biology↗

bioRxiv2021

Classical Mathematical Models for Prediction of Response to Chemotherapy and Immunotherapy

Classical mathematical models of tumor growth have shaped our understanding of cancer and have broad practical implications for treatment scheduling and dosage. However, even the simplest textbook models have been barely validated in real world-data of human patients. In this study, we fitted a range of differential equation models to tumor volume measurements of patients undergoing chemotherapy or cancer immunotherapy for solid tumors. We used a large dataset of 1472 patients with three or more measurements per target lesion, of which 652 patients had six or more data points. We show that the early treatment response shows only moderate correlation with the final treatment response, demonstrating the need for nuanced models. We then perform a head-to-head comparison of six classical models which are widely used in the field: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. Several models provide a good fit to tumor volume measurements, with the Gompertz model providing the best balance between goodness of fit and number of parameters. Similarly, when fitting to early treatment data, the general Bertalanffy and Gompertz models yield the lowest mean absolute error to forecasted data, indicating that these models could potentially be effective at predicting treatment outcome. In summary, we provide a quantitative benchmark for classical textbook models and state-of-the art models of human tumor growth. We publicly release an anonymized version of our original data, providing the first benchmark set of human tumor growth data for evaluation of mathematical models. Author SummaryMathematical oncology uses quantitative models for prediction of tumor growth and treatment response. The theoretical foundation of mathematical oncology is provided by six classical mathematical models: the Exponential, Logistic, Classic Bertalanffy, General Bertalanffy, Classic Gompertz and General Gompertz model. These models have been introduced decades ago, have been used in thousands of scientific articles and are part of textbooks and curricula in mathematical oncology. However, these models have not been systematically tested in clinical data from actual patients. In this study, we have collected quantitative tumor volume measurements from thousands of patients in five large clinical trials of cancer immunotherapy. We use this dataset to systematically investigate how accurately mathematical models can describe tumor growth, showing that there are pronounced differences between models. In addition, we show that two of these models can predict tumor response to immunotherapy and chemotherapy at later time points when trained on early tumor growth dynamics. Thus, our article closes a conceptual gap in the literature and at the same time provides a simple tool to predict response to chemotherapy and immunotherapy on the level of individual patients.

cancer biology↗

bioRxiv2020

T2 heterogeneity provides a sensitive measure of early tumor response to radiotherapy

PurposeExternal beam radiotherapy (XRT) is a widely used cancer treatment, yet responses vary dramatically between patients. These differences are not accounted for in clinical practice, in part due to a lack of sensitive biomarkers of early response. In this work, we test the hypothesis that quantification of intratumor heterogeneity is a sensitive and robust biomarker of early response to XRT. A novel Magnetic Resonance Imaging (MRI) approach is proposed, utilizing histogram analysis of clinically-used T2 relaxation measurements to assess early changes in the tumor heterogeneity following irradiation in murine models of pancreatic cancer, indicative of radiotherapy response. Methods and MaterialsDynamic Magnetic Resonance T2 relaxation imaging was performed every 72h following 10 Gy dose XRT in two murine models of pancreatic cancer. Proposed biomarker of radiotherapy response was compared with tumor growth kinetics, and biological validation was performed through quantitative histology analysis. ResultsQuantification of tumor T2 interquartile range (IQR) as a measure of histogram width showed excellent sensitivity for detection of XRT-induced tumor changes as early as 72h after treatment, outperforming whole tumor T2 and Diffusion weighted MRI metrics. This response was observed both in quantitative T2 maps and in T2-weighted images that are routine in clinical practice. Histological comparison revealed the T2 IQR provides a measure of spatial heterogeneity in tumor cell density, related to radiation-induced necrosis. The early IQR changes were found to presage subsequent tumor volume changes in two distinct pancreatic models, suggesting promise for treatment response prediction. The metric showed excellent test-retest robustness. ConclusionsOur preclinical findings indicate that spatial heterogeneity analysis of T2 MRI can provide a sensitive and readily translatable method for early radiotherapy response assessment in pancreatic cancer. We propose that this will be useful in adaptive radiotherapy, specifically in MRI-guided treatment paradigms.

biophysics↗

bioRxiv2020

High school Internship Program in Integrated Mathematical Oncology (HIP IMO) - five-year experience at Moffitt Cancer Center

Modern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well-versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education is traditionally provided in disciplinary silos, which creates a steep learning curve at the graduate and postdoctoral levels that increasingly bridge multiple disciplines. Numerous colleges have begun to embrace interdisciplinary curricula, but students who double-major in mathematics (or other quantitative sciences) and biology (or medicine) remain scarce. We identified the need to educate junior and senior high school students about integrating mathematical and biological skills, through the lens of mathematical oncology, to better prepare students for future careers at the interdisciplinary interface. The High school Internship Program in Integrated Mathematical Oncology (HIP IMO) at Moffitt Cancer Center has so far trained 59 students between 2015 and 2019. We report here on the program structure, training deliverables, curriculum, and outcomes. We hope to promote such interdisciplinary educational activities early in a students career.

scientific communication and education↗

bioRxiv2020

Harnessing tumor immune ecosystem dynamics to personalize radiotherapy

Radiotherapy is a pillar of cancer care and augments the response to immunotherapies. However, little is known regarding the relationships between the tumor immune ecosystem (TIES) and intrinsic radiosensitivity, and a pressing question in oncology is how to optimize radiotherapy to improve patient responses to immune therapies. To address this challenge, we profiled over 10,000 primary tumors for their metrics of radiosensitivity and immune cell infiltrate (ICI), and applied a new integrated in silico model that mimics the dynamic relationships between tumor growth, ICI flux and the response to radiation. We then validated this model with a separate cohort of 59 lung cancer patients treated with radiotherapy. These analyses explain radiation response based on its effect on the TIES and quantifies the likelihood that radiation can promote a shift to anti-tumor immunity. Dynamic modeling of the relationship between tumor radiosensitivity and the TIES may provide opportunity to personalize combined radiation and immunotherapy approaches.

cancer biology↗

bioRxiv2019

Predicting patient-specific radiotherapy responses in head and neck cancer to personalize radiation dose fractionation

Human papillomavirus (HPV) related oropharyngeal cancer (OPC) is one of the few types of cancers increasing in incidence. HPV+ OPC treatment with radiotherapy (RT) provides 75-95% five-year locoregional control (LRC). Why some but not all patients with similar clinical stage and molecular profile are controlled remains unknown. We propose the proliferation saturation index, PSI, as a mathematical modeling biomarker of tumor growth and RT response. The model predicts that patients with PSI<0.75 are likely to be cured by radiation, and that hyperfractionated radiation could improve response rates for patients with higher PSI that are predicted to fail standard of care RT. Prospective evaluation is currently ongoing.

cancer biology↗

bioRxiv2019

Prostate-Specific Antigen Dynamics Predict Individual Responses to Intermittent Androgen Deprivation

BackgroundIntermittent androgen deprivation therapy (IADT) is an attractive treatment approach for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off can reduce cumulative dose, limit toxicities, and delay development of treatment resistance. To optimize treatment within the context of ongoing intratumoral evolution, underlying mechanisms of resistance and actionable biomarkers need to be identified.\n\nMethodsWe have developed a quantitative framework to simulate enrichment of prostate cancer stem cell (PCaSC) dynamics during treatment as a plausible mechanism of resistance evolution.\n\nResultsSimulated dynamics of PCaSC and non-stem cancer cells demonstrate that stem cell proliferation patterns correlate with longitudinal serum prostate-specific antigen (PSA) measurements in 70 PCa patients undergoing multiple cycles of IADT. By learning the dynamics from each treatment cycle, individual model simulations predict evolution of resistance in the subsequent IADT cycle with a sensitivity and specificity of 57% and 94%, respectively and an overall accuracy of 90%. Additionally, we evaluated the potential benefit of docetaxel for IADT in biochemically recurrent PCa. Model simulations based on response dynamics from the first IADT cycle identify patients who would or would not benefit from concurrent docetaxel in subsequent cycles.\n\nConclusionOur results demonstrate the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics continuously updated with each treatment cycle.\n\nTranslational RelevanceCompared to continuous androgen deprivation therapy, intermittent androgen deprivation (IADT) has been shown to reduce toxicity and delay time to progression in prostate cancer. While numerous mathematical models have been developed to study the response to both continuous and intermittent androgen deprivation, very few have identified actionable biomarkers of resistance and exploited them to predict how patients will or will not respond to subsequent treatment. Here, we identify prostate-specific antigen (PSA) dynamics as the first such biomarker. Mechanistic mathematical modeling of prostate cancer stem cell dynamics that dictate prostate-specific antigen serum levels predicts individual responses to IADT with 90% overall accuracy and can be used to develop patient-specific adaptive treatment protocols, and potentially identify patients that may benefit from concurrent chemotherapy. Model results demonstrate the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics continuously updated with each treatment cycle.

cancer biology↗

bioRxiv2019

Harnessing patient-specific response dynamics to optimize evolutionary therapies for metastatic clear cell renal cell carcinoma - Learning to adapt

Renal cell carcinoma (RCC) is one of the ten most common and lethal cancers in the United States. Tumor heterogeneity and development of resistance to treatment suggest that patient-specific evolutionary therapies may hold the key to better patients prognosis. Mathematical models are a powerful tool to help develop such strategies; however, they depend on reliable biomarker information. In this paper, we present a dynamic model of tumor-immune interactions, as well as the treatment effect on tumor cells and the tumor-immune environment. We hypothesize that the neutrophil-to-lymphocyte ratio (NLR) is a powerful biomarker that can be used to predict an individual patients response to treatment. Using randomly sampled virtual patients, we show that the model recapitulates patient outcomes from clinical trials in RCC. Finally, we use in silico patient data to recreate realistic tumor behaviors and simulate various treatment strategies to find optimal treatments for each virtual patient.

cancer biology↗

bioRxiv2018

Proliferation Saturation Index in an adaptive Bayesian approach to predict patient-specific radiotherapy responses

PurposeRadiotherapy prescription dose and dose fractionation protocols vary little between individual patients having the same tumor grade and stage. To personalize radiotherapy a predictive model is needed to simulate radiation response. Previous modeling attempts with multiple variables and parameters have been shown to yield excellent data fits at the cost of nonidentifiability and clinically unrealistic results.\n\nMaterials and MethodsWe develop a mathematical model based on a proliferation saturation index (PSI) that is a measurement of pre-treatment tumor volume-to-carrying capacity ratio that modulates intrinsic tumor growth and radiation response rates. In an adaptive Bayesian approach, we utilize an increasing number of data points for individual patients for predicting response to subsequent radiation doses.\n\nResultsModel analysis shows that using PSI as the only patient-specific parameter, model simulations can fit longitudinal clinical data with high accuracy (R2=0.84). By analyzing tumor response to radiation using daily CT scans early in the treatment, response to the remaining treatment fractions can be predicted after two weeks with high accuracy (c-index=0.89).\n\nConclusionThe PSI model may be suited to forecast treatment response for individual patients and offer actionable decision points for mid-treatment protocol adaptation. The presented work provides an actionable image-derived biomarker prior to and during therapy to personalize and adapt radiotherapy.

cancer biology↗

bioRxiv2018

Overcoming non-small cell lung cancer radiation resistance by modulating the tumor-immune ecosystem

Non-small-cell lung cancer is the leading cause of cancer death worldwide. Although radiotherapy is an effective treatment choice for early-stage cases, the 5-year survival rate of patients diagnosed in late-stages remains poor. Increasing evidence suggests that the local and systemic effects of radiotherapy dependent on the induced anti-tumor immune responses. We believe that an educated adaptation of radiotherapy plans based not only on the induced immune responses, but also on the tumor-immune ecosystem composition at the beginning of treatment might increase local tumor control. We propose two different mathematical models to evaluate the potential of the tumor-immune context to inform adaptation of treatment plans with the aim of improving outcomes.

immunology↗

bioRxiv2018

A new paradigm for personalized cancer screening

A series of distinct histologic lesions precedes the onset of malignancy in many common cancers, yet early detection remains a major challenge. Many patients still experience late (stage IV) diagnoses and thus poor prognosis and limited options for therapeutic intervention. For cancers with known biomarkers of premalignant progression, optimized patient-specific screening protocols would minimize the risk of undetected progression to advanced stage disease. Here, we propose simple, cost-effective mathematical and statistical approaches to forecasting disease progression that could guide the personalization of optimal screening times for high-risk patients.

epidemiology↗

bioRxiv2017

Temporally-Feathered Intensity Modulated Radiation Therapy: A technique to reduce normal tissue toxicity

PurposeIntensity modulated radiation therapy (IMRT) has allowed optimization of three-dimensional spatial radiation dose distributions permitting target coverage while reducing normal tissue toxicity. However, radiation-induced normal tissue toxicity is a major contributor to patients quality of life and often a dose-limiting factor in the definitive treatment of cancer with radiation therapy. We propose the next logical step in the evolution of IMRT using canonical radiobiological principles, optimizing the temporal dimension through which radiation therapy is delivered to further reduce radiation-induced toxicity by increased time for normal tissue recovery. We term this novel treatment planning strategy \"temporally feathered radiotherapy\" (TFRT).\n\nMethodsTFRT plans were generated as a composite of five simulated treatment plans each with altered constraints on particular hypothetical organs at risk (OARs) to be delivered sequentially. For each of these TFRT plans, OARs chosen for feathering receive higher doses while the remaining OARs receive lower doses than the standard fractional dose delivered in a conventional fractionated IMRT plan. Each TFRT plan is delivered a specific weekday, which in effect leads to a higher dose once weekly followed by four lower fractional doses to each temporally feathered OAR. We compared normal tissue toxicity between TFRT and conventional fractionated IMRT plans by using a dynamical mathematical model to describe radiation-induced tissue damage and repair over time.\n\nResultsModel-based simulations of TFRT demonstrated potential for reduced normal tissue toxicity compared to conventionally planned IMRT. The sequencing of high and low fractional doses delivered to OARs by TFRT plans suggested increased normal tissue recovery, and hence less overall radiation-induced toxicity, despite higher total doses delivered to OARs compared to conventional fractionated IMRT plans. The magnitude of toxicity reduction by TFRT planning was found to depend on the corresponding standard fractional dose of IMRT and organ-specific recovery rate of sublethal radiation-induced damage.\n\nConclusionsTFRT is a novel technique for treatment planning and optimization of therapeutic radiotherapy that considers the non-linear aspects of tissue repair to optimize toxicity profiles. Model-based simulations of TFRT to carefully conceptualized clinical cases have demonstrated potential for normal tissue toxicity reduction in a previously described dynamical model of normal tissue complication probability (NTCP).

biophysics↗

bioRxiv2017

The evolution of tumour composition during fractionated radiotherapy: implications for outcome

Current protocols for delivering radiotherapy are based primarily on tumour stage and nodal and metastases status, even though it is well known that tumours and their microenvironments are highly heterogeneous. It is well established that the local oxygen tension plays an important role in radiation-induced cell death, with hypoxic tumour regions responding poorly to irradiation. Therefore, to improve radiation response, it is important to understand more fully the spatiotemporal distribution of oxygen within a growing tumour before and during fractionated radiation. To this end, we have extended a spatially-resolved mathematical model of tumour growth first proposed by Greenspan (Stud. Appl. Math., 1972) to investigate the effects of oxygen heterogeneity on radiation-induced cell death. In more detail, cell death due to radiation at each location in the tumour, as determined by the well-known linear-quadratic model, is assumed also to depend on the local oxygen concentration. The oxygen concentration is governed by a reaction-diffusion equation that is coupled to an integro-differential equation that determines the size of the assumed spherically-symmetric tumour. We combine numerical and analytical techniques to investigate radiation response of tumours with different intra-tumoral oxygen distribution profiles. Model simulations reveal a rapid transient increase in hypoxia upon re-growth of the tumour spheroid post-irradiation. We investigate the response to different radiation fractionation schedules and identify a tumour-specific relationship between inter-fraction time and dose per fraction to achieve cure. The rich dynamics exhibited by the model suggest that spatial heterogeneity may be important for predicting tumour response to radiotherapy for clinical applications.

cancer biology↗