Predicting intratumoral fluid pressure and liposome accumulation using physics informed deep learning.

Liposome-based anticancer agents take advantage of the increased vascular permeability and transvascular pressure gradients for selective accumulation in tumors, a phenomenon known as the enhanced permeability and retention(EPR) effect. The EPR effect has motivated the clinical use of nano-therapeutics, with mixed results on treatment outcome. High interstitial fluid pressure (IFP) has been shown to limit liposome drug delivery to central tumour regions. Furthermore, high IFP is an independent prognostic biomarker for treatment efficacy in radiation therapy and chemotherapy for some solid cancers. Therefore, accurately measuring spatial liposome accumulation and IFP distribution within a solid tumour is crucial for optimal treatment planning. In this paper, we develop a model capable of predicting voxel-by-voxel intratumoral liposome accumulation and IFP using pre and post administration imaging. Our approach is based on physics informed machine learning, a novel technique combining machine learning and partial differential equations. through application to a set of mouse data and a set of synthetically-generated tumours, we show that our approach accurately predicts the spatial liposome accumulation and IFP for an individual tumour while relying on minimal information. This is an important result with applications for forecasting tumour progression and designing treatment.

Deep learning characterization of brain tumours with diffusion weighted imaging.

Glioblastoma multiforme (GBM) is one of the most deadly forms of cancer. Methods of characterizing these tumours are valuable for improving predictions of their progression and response to treatment. A mathematical model called the proliferation-invasion (PI) model has been used extensively in the literature to model the growth of these tumours, though it relies on known values of two key parameters: the tumour cell diffusivity and proliferation rate. Unfortunately, these parameters are difficult to estimate in a patient-specific manner, making personalized tumour forecasting challenging. In this paper, we develop and apply a deep learning model capable of making accurate estimates of these key GBM-characterizing parameters while simultaneously producing a full prediction of the tumour progression curve. Our method uses two sets of multi sequence MRI in order to produce estimations and relies on a preprocessing pipeline which includes brain tumour segmentation and conversion to tumour cellularity. We first apply our deep learning model to synthetic tumours to showcase the model's capabilities and identify situations where prediction errors are likely to occur. We then apply our model to a clinical dataset consisting of five patients diagnosed with GBM. For all patients, we derive evidence-based estimates for each of the PI model parameters and predictions for the future progression of the tumour, along with estimates of the parameter uncertainties. Our work provides a new, easily generalizable method for the estimation of patient-specific tumour parameters, which can be built upon to aid physicians in designing personalized treatments.

Temporal optimization of radiation therapy to heterogeneous tumour populations and cancer stem cells.

External beam radiation therapy is a key part of modern cancer treatments which uses high doses of radiation to destroy tumour cells. Despite its widespread usage and extensive study in theoretical, experimental, and clinical works, many questions still remain about how best to administer it. Many mathematical studies have examined optimal scheduling of radiotherapy, and most come to similar conclusions. Importantly though, these studies generally assume intratumoral homogeneity. But in recent years, it has become clear that tumours are not homogeneous masses of cancerous cells, but wildly heterogeneous masses with various subpopulations which grow and respond to treatment differently. One subpopulation of particular importance is cancer stem cells (CSCs) which are known to exhibit higher radioresistence compared with non-CSCs. Knowledge of these differences between cell types could theoretically lead to changes in optimal treatment scheduling. Only a few studies have examined this question, and interestingly, they arrive at apparent conflicting results. However, an understanding of their assumptions reveals a key difference which leads to their differing conclusions. In this paper, we generalize the problem of temporal optimization of dose distribution of radiation therapy to a two cell type model. We do so by creating a mathematical model and a numerical optimization algorithm to find the distribution of dose which leads to optimal cell kill. We then create a data set of optimization solutions and use data analysis tools to learn the relationships between model parameters and the qualitative behaviour of optimization results. Analysis of the model and discussion of biological importance are provided throughout. We find that the key factor in predicting the behaviour of the optimal distribution of radiation is the ratio between the radiosensitivities of the present cell types. These results can provide guidance for treatment in cases where clinicians have knowledge of tumour heterogeneity and of the abundance of CSCs.

The role of calcium oscillations in the phenotype selection in endothelial cells.

Angiogenesis is an important process in the formation and maintenance of tissues which is driven by a complex system of intracellular and intercellular signaling mechanisms. Endothelial cells taking part in early angiogenesis must select their phenotype as either a tip cells (leading, migratory) or a stalk cells (following). Recent experiments have demonstrated that rapid calcium oscillations within active cells characterize this phenotype selection process and that these oscillations play a necessary role in governing phenotype selection and eventual vessel architecture. In this work, we develop a mathematical model capable of describing these oscillations and their role in phenotype selection then use it to improve our understanding of the biological mechanisms at play. We developed a model based on two previously published and experimentally validated mathematical models of calcium and angiogenesis then use our resulting model to simulate various multi-cell scenarios. We are able to capture essential calcium oscillation dynamics and intercellular communication between neighboring cells. The results of our model show that although the late DLL4 (a transmembrane protein that activates Notch pathway) levels of a cell are connected with its initial IP3 (Inositol 1,4,5-trisphosphate) level, cell-to-cell communication determines its eventual phenotype.

Modeling the impact of public response on the COVID-19 pandemic in Ontario.

The outbreak of SARS-CoV-2 is thought to have originated in Wuhan, China in late 2019 and has since spread quickly around the world. To date, the virus has infected tens of millions of people worldwide, compelling governments to implement strict policies to counteract community spread. Federal, provincial, and municipal governments have employed various public health policies, including social distancing, mandatory mask wearing, and the closure of schools and businesses. However, the implementation of these policies can be difficult and costly, making it imperative that both policy makers and the citizenry understand their potential benefits and the risks of non-compliance. In this work, a mathematical model is developed to study the impact of social behaviour on the course of the pandemic in the province of Ontario. The approach is based upon a standard SEIRD model with a variable transmission rate that depends on the behaviour of the population. The model parameters, which characterize the disease dynamics, are estimated from Ontario COVID-19 epidemiological data using machine learning techniques. A key result of the model, following from the variable transmission rate, is the prediction of the occurrence of a second wave using the most current infection data and disease-specific traits. The qualitative behaviour of different future transmission-reduction strategies is examined, and the time-varying reproduction number is analyzed using existing epidemiological data and future projections. Importantly, the effective reproduction number, and thus the course of the pandemic, is found to be sensitive to the adherence to public health policies, illustrating the need for vigilance as the economy continues to reopen.

In silico analysis of hypoxia activated prodrugs in combination with anti angiogenic therapy through nanocell delivery.

Tumour hypoxia is a well-studied phenomenon with implications in cancer progression, treatment resistance, and patient survival. While a clear adverse prognosticator, hypoxia is also a theoretically ideal target for guided drug delivery. This idea has lead to the development of hypoxia-activated prodrugs (HAPs): a class of chemotherapeutics which remain inactive in the body until metabolized within hypoxic regions. In theory, these drugs have the potential for increased tumour selectivity and have therefore been the focus of numerous preclinical studies. Unfortunately, HAPs have had mixed results in clinical trials, necessitating further study in order to harness their therapeutic potential. One possible avenue for the improvement of HAPs is through the selective application of anti angiogenic agents (AAs) to improve drug delivery. Such techniques have been used in combination with other conventional chemotherapeutics to great effect in many studies. A further benefit is theoretically achieved through nanocell administration of the combination, though this idea has not been the subject of any experimental or mathematical studies to date. In the following, a mathematical model is outlined and used to compare the predicted efficacies of separate vs. nanocell administration for AAs and HAPs in tumours. The model is experimentally motivated, both in mathematical form and parameter values. Preliminary results of the model are highlighted throughout which qualitatively agree with existing experimental evidence. The novel prediction of our model is an improvement in the efficacy of AA/HAP combination therapies when administered through nanocells as opposed to separately. While this study specifically models treatment on glioblastoma, similar analyses could be performed for other vascularized tumours, making the results potentially applicable to a range of tumour types.

Role of hypoxia-activated prodrugs in combination with radiation therapy: An in silico approach.

Tumour hypoxia has been associated with increased resistance to various cancer treatments, particularly radiation therapy. Conversely, tumour hypoxia is a validated and ideal target for guided cancer drug delivery. For this reason, hypoxia-activated prodrugs (HAPs) have been developed, which remain inactive in the body until in the presence of tissue hypoxia, allowing for an activation tendency in hypoxic regions. We present here an experimentally motivated mathematical model predicting the effectiveness of HAPs in a variety of clinical settings. We first examined HAP effectiveness as a function of the amount of tumour hypoxia and showed that the drugs have a larger impact on tumours with high levels of hypoxia. We then combined HAP treatment with radiation to examine the effects of combination therapies. Our results showed radiation-HAP combination therapies to be more effective against highly hypoxic tumours. The analysis of combination therapies was extended to consider schedule sequencing of the combination treatments. These results suggested that administering HAPs before radiation was most effective in reducing total cell number. Finally, a sensitivity analysis of the drug-related parameters was done to examine the effect of drug diffusivity and enzyme abundance on the overall effectiveness of the drug. Altogether, the results highlight the importance of the knowledge of tumour hypoxia levels before administration of HAPs in order to ensure positive results.

Spatial optimization for radiation therapy of brain tumours.

Glioblastomas are the most common primary brain tumours. They are known for their highly aggressive growth and invasion, leading to short survival times. Treatments for glioblastomas commonly involve a combination of surgical intervention, chemotherapy, and external beam radiation therapy (XRT). Previous works have not only successfully modelled the natural growth of glioblastomas in vivo, but also show potential for the prediction of response to radiation prior to treatment. This suggests that the efficacy of XRT can be optimized before treatment in order to yield longer survival times. However, while current efforts focus on optimal scheduling of radiotherapy treatment, they do not include a similarly sophisticated spatial optimization. In an effort to improve XRT, we present a method for the spatial optimization of radiation profiles. We expand upon previous results in the general problem and examine the more physically reasonable cases of 1-step and 2-step radiation profiles during the first and second XRT fractions. The results show that by including spatial optimization in XRT, while retaining a constant prescribed total dose amount, we are able to increase the total cell kill from the clinically-applied uniform case.