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Immune checkpoint inhibitor (ICI)-based immunotherapies have profoundly changed the cancer treatment landscape and improved therapeutic outcomes by leveraging a patient¡¯s own immune system to fight their disease. Despite the success of ICIs in many solid tumor types (such as lung, melanoma and colorectal cancers), most patients fail to respond to ICI therapy, and reliable methods of identifying patients who will respond early in the course of treatment remain elusive. Our ongoing work in mathematical modeling of ICI therapy is yielding valuable insights into dose-response relationships and associated immunotherapy response outcomes, which may help overcome this limitation.

The model shown here describes the total tumor burden over time under ICI therapy based on the key, mechanistic biological factors or processes and physical factors that underlie ICI immunotherapy intervention. By mathematically linking the relationships between these processes and their effects on the tumor, our model quantifies their combined effects (and the feedback processes between them) on the time-dependent change in tumor burden (¦Ñ) after ICI therapy. This model can be solved using only non-invasive imaging-based measurements of solid tumors, making it usable without changing current clinical protocols. In a series of publications, we have shown how our model is able to predict patient response and survival due to ICI intervention. Importantly, the model has also been shown to work on seven cancer types to date and to be robustly unaffected by prior therapies patients may have received, increasing its potential for widespread clinical application. We are now building on these successes to include other therapies in the model to better describe the realities of clinical practice, where patients may receive combinations of multiple drugs or other periodic salvage therapies.

Deep learning and artificial intelligence methods are emerging as powerful prediction tools, and it is likely that they can be leveraged to predict cancer therapy outcomes. However, the black-box nature of such models is at odds with the level of detailed understanding sought by scientific research, and lack of mechanistic understanding behind predictions from these models limits how they can be used to optimize treatment protocols. Mechanistic mathematical models are robust to these limitations, but they are often dependent on non-standard-of-care data that may be difficult or resource-intensive to obtain, and they often cannot take as input some standard clinical measures that likely are indicative of response. This limits their potential for rapid integration into clinical workflows and possibly reduces predictive accuracy. Deep learning approaches are well-suited to use data that mechanistic models may struggle to integrate, but they are intrinsically data-hungry, and they may fail in applications where data is limited, such as clinical trials or rare diseases.

Mechanistic modeling and deep learning robustly balance the strengths and weaknesses of each approach, making leveraging them together for predicting treatment outcomes and optimizing clinical strategies an attractive option. It is likely that modeling predictions may be optimized by ensembling both methods into composite models. We are exploring a variety of methods to ensemble these approaches with encouraging results. Studies to date have demonstrated that predictions of patient survival and tumor response to treatment using deep learning model predictions are more accurate when using values calculated from mechanistic models as covariates compared to models built only on measured clinical data. We are now exploring how mechanistic models may be best solved using neural networks, enabling us to solve differential equations directly from standard of care measures such as CT or MRI images.

Although it is likely that these approaches will provide some moderate improvements in model performance over pure mechanistic methods, we hypothesize that these methods will also enable us to overcome many of the current barriers to clinical adaptation of mechanistic models. These include unavailability of methods to measure model parameters and the need to collect potentially expensive data that may only be used for models. We are developing robust physics-based deep learning models that have increased accuracy, require reduced manual data processing and are more easily deployable to the community at large.

Commonly, equation-based mathematical models describe only one type of treatment, but in the clinic, patients often receive multiple therapies to better address their individual needs. These therapies may interact in complex ways, and if we can quantify these interactions and how they affect the patient, the efficacy of each treatment and the disease, then we can use known optimization methods to engineer personalized combination treatment plans to better achieve long-term disease control. This will require robust mathematical descriptions of how each treatment affects the disease and how they interact. Currently, we are building combination models of immunotherapy used together with radiation.

Immunotherapy and radiation therapy are often used together and are known to have both synergistic and inhibitory interactions, but guidelines for optimal usage remain elusive, making this problem particularly relevant to current clinical practice. Numerous trials have reported conflicting outcomes when delivering radiotherapy (XRT) alongside immune checkpoint inhibitors (ICI). Some have reported improved progression-free or overall survival, while others have reported failure to reach their endpoint of objective response rate (ORR) improvement or even demonstrated reduced ORR when radiation is added to ICI. Evidence is emerging that which lesions receive XRT and the sequence of therapeutic delivery are critical to therapeutic success, but robust methods to identify which lesions and when to deliver XRT at what dose remain an unmet clinical need. This is a complex ¡ª and still unsolved ¡ª optimization problem. Mechanistic mathematical modeling offers a powerful way gain a more complete, quantified understanding of the complex synergistic and inhibitory interactions between both therapies to study, understand and solve this problem on an individual patient basis.

We have expanded our previous immune checkpoint inhibitor immunotherapy to include the key mechanisms of radiation therapy and its mechanisms of interaction with ICI. We are now performing extensive model testing, refinement and validation in a large patient cohort with melanoma brain metastases. We hope to identify reliable methods to determine which brain lesions may benefit from XRT and which will not. Avoiding radiation in brain tumors that will not benefit can avoid potentially devastating side effects and give oncologists an opportunity to deliver a potentially more effective intervention in the narrow time window before the disease progresses. We are also exploring how treatment may be optimized across all tumors in the patient by considering the whole tumor landscape as a single multicompartment domain.

We have developed a series of custom made, highly detailed multiscale agent-based models of the pubertal mammary terminal end bud and early-stage ductal carcinoma in situ (DCIS). These are providing new insights on how cell hierarchies and endocrine and paracrine pathways are involved in healthy gland development, as well as the roles that breaking these pathways play in disease initiation and development. Simulating the full organ lifecycle from development through disease initiation and progression has allowed us to extensively calibrate model design and assumptions by verifying that the model correctly reproduces literature-reported behaviors across many key phases of the complete organ lifecycle.

Mammary gland development is a well-studied process that occurs during mammalian puberty. We have extensively this process in silico study using both a two-dimensional, lattice-based hybrid agent-based model description of the mammary terminal end bud (TEB) and a three-dimensional lattice-free TEB model. Both models implement a discrete, agent-based description of each cell at the cellular scale and a continuum finite element method description of tissue-scale spatiotemporal molecular profiles, which are mathematically linked into a hybrid multiscale model.

This lattice-free pubertal development TEB model was then transitioned into a post-menopausal early-stage DCIS model, used for study of the phenotypic dynamics and molecular signaling disruptions involved in development of the DCIS tumor mass. Both TEB and DCIS models implemented simplified, literature-based cellular phenotypic developmental hierarchies and endocrine and paracrine signaling pathways. All models provided valuable insights into the effects of these aspects on the development of both the healthy gland and the pre-invasive DCIS cancer state, and results from model outputs were found to be within literature supported ranges. Cells of both healthy and cancerous phenotypes were found to be sensitive to changes in molecular signaling intensities and phenotypic hierarchies, which played an important part in organ and disease development, with all cases demonstrating a greater effect of upstream estrogen paracrine signaling relative to the downstream AREG-FGF epithelial to stromal pathway also tested. This study also shed additional light on the need for stem cell hierarchal plasticity, which forms the foundation for long-term maintenance of stem-like and progenitor cell populations.