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.

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia.

The over-expression of the Bcl-2 protein is a common feature of many solid cancers and hematological malignancies, and it is typically associated with poor prognosis and resistance to chemotherapy. Bcl-2-specific inhibitors, such as venetoclax, have recently been approved for the treatment of chronic lymphocytic leukemia and small lymphocytic lymphoma, and they are showing promise in clinical trials as a targeted therapy for patients with relapsed or refractory acute myeloid leukemia (AML). However, successful treatment of AML with Bcl-2-specific inhibitors is often followed by the rapid development of drug resistance. An emerging paradigm for overcoming drug resistance in cancer treatment is through the targeting of mitochondrial energetics and metabolism. In AML in particular, it was recently observed that inhibition of mitochondrial translation via administration of the antibiotic tedizolid significantly affects mitochondrial bioenergetics, activating the integrated stress response (ISR) and subsequently sensitizing drug-resistant AML cells to venetoclax. Here we develop an integrative systems biology approach to acquire a deeper understanding of the molecular mechanisms behind this process, and in particular, of the specific role of the ISR in the commitment of cells to apoptosis. Our multi-scale mathematical model couples the ISR to the intrinsic apoptosis pathway in venetoclax-resistant AML cells, includes the metabolic effects of treatment, and integrates RNA, protein level, and cellular viability data. Using the mathematical model, we identify the dominant mechanisms by which ISR activation helps to overcome venetoclax resistance, and we study the temporal sequencing of combination treatment to determine the most efficient and robust combination treatment protocol.

SARS-CoV-2 Quantum Sensor Based on Nitrogen-Vacancy Centers in Diamond.

The development of highly sensitive and rapid biosensing tools targeted to the highly contagious virus SARS-CoV-2 is critical to tackling the COVID-19 pandemic. Quantum sensors can play an important role because of their superior sensitivity and fast improvements in recent years. Here we propose a molecular transducer designed for nitrogen-vacancy (NV) centers in nanodiamonds, translating the presence of SARS-CoV-2 RNA into an unambiguous magnetic noise signal that can be optically read out. We evaluate the performance of the hybrid sensor, including its sensitivity and false negative rate, and compare it to widespread diagnostic methods. The proposed method is fast and promises to reach a sensitivity down to a few hundreds of RNA copies with false negative rate less than 1%. The proposed hybrid sensor can be further implemented with different solid-state defects and substrates, generalized to diagnose other RNA viruses, and integrated with CRISPR technology.

The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population.

The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network.

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 impact of random microenvironmental fluctuations on tumor control probability.

The tumor control probability (TCP) is a metric used to calculate the probability of controlling or eradicating tumors through radiotherapy. Cancer cells vary in their response to radiation, and although many factors are involved, the tumor microenvironment is a crucial one that determines radiation efficacy. The tumor microenvironment plays a significant role in cancer initiation and propagation, as well as in treatment outcome. We have developed stochastic formulations to study the impact of arbitrary microenvironmental fluctuations on TCP and extinction probability (EP), which is defined as the probability of cancer cells removal in the absence of treatment. Since the derivation of analytical solutions are not possible for complicated cases, we employ a modified Gillespie algorithm to analyze TCP and EP, considering the random variations in cellular proliferation and death rates. Our results show that increasing the standard deviation in kinetic rates initially enhances the probability of tumor eradication. However, if the EP does not reach a probability of 1, the increase in the standard deviation subsequently has a negative impact on probability of cancer cells removal, decreasing the EP over time. The greatest effect on EP has been observed when both birth and death rates are being randomly modified and are anticorrelated. In addition, similar results are observed for TCP, where radiotherapy is included, indicating that increasing the standard deviation in kinetic rates at first enhances the probability of tumor eradication. But, it has a negative impact on treatment effectiveness if the TCP does not reach a probability of 1.

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.

Combining hypoxia-activated prodrugs and radiotherapy in silico: Impact of treatment scheduling and the intra-tumoural oxygen landscape.

Hypoxia-activated prodrugs (HAPs) present a conceptually elegant approach to not only overcome, but better yet, exploit intra-tumoural hypoxia. Despite being successful in vitro and in vivo, HAPs are yet to achieve successful results in clinical settings. It has been hypothesised that this lack of clinical success can, in part, be explained by the insufficiently stringent clinical screening selection of determining which tumours are suitable for HAP treatments. Taking a mathematical modelling approach, we investigate how tumour properties and HAP-radiation scheduling influence treatment outcomes in simulated tumours. The following key results are demonstrated in silico: (i) HAP and ionising radiation (IR) monotherapies may attack tumours in dissimilar, and complementary, ways. (ii) HAP-IR scheduling may impact treatment efficacy. (iii) HAPs may function as IR treatment intensifiers. (iv) The spatio-temporal intra-tumoural oxygen landscape may impact HAP efficacy. Our in silico framework is based on an on-lattice, hybrid, multiscale cellular automaton spanning three spatial dimensions. The mathematical model for tumour spheroid growth is parameterised by multicellular tumour spheroid (MCTS) data.

The effects of phenotypic plasticity on the fixation probability of mutant cancer stem cells.

The cancer stem cell hypothesis claims that tumor growth and progression are driven by a (typically) small niche of the total cancer cell population called cancer stem cells (CSCs). These CSCs can go through symmetric or asymmetric divisions to differentiate into specialised, progenitor cells or reproduce new CSCs. While it was once held that this differentiation pathway was unidirectional, recent research has demonstrated that differentiated cells are more plastic than initially considered. In particular, differentiated cells can de-differentiate and recover their stem-like capacity. Two recent papers have considered how this rate of plasticity affects the evolutionary dynamic of an invasive, malignant population of stem cells and differentiated cells into existing tissue (Mahdipour-Shirayeh et al., 2017; Wodarz, 2018). These papers arrive at seemingly opposing conclusions, one claiming that increased plasticity results in increased invasive potential, and the other that increased plasticity decreases invasive potential. Here, we show that what is most important, when determining the effect on invasive potential, is how one distributes this increased plasticity between the compartments of resident and mutant-type cells. We also demonstrate how these results vary, producing non-monotone fixation probability curves, as inter-compartmental plasticity changes when differentiated cell compartments are allowed to continue proliferating, highlighting a fundamental difference between the two models. We conclude by demonstrating the stability of these qualitative results over various parameter ranges. Keywords: cancer stem cells, plasticity, de-differentiation, fixation probability.

Quantifying the effects of antiangiogenic and chemotherapy drug combinations on drug delivery and treatment efficacy.

Tumor-induced angiogenesis leads to the development of leaky tumor vessels devoid of structural and morphological integrity. Due to angiogenesis, elevated interstitial fluid pressure (IFP) and low blood perfusion emerge as common properties of the tumor microenvironment that act as barriers for drug delivery. In order to overcome these barriers, normalization of vasculature is considered to be a viable option. However, insight is needed into the phenomenon of normalization and in which conditions it can realize its promise. In order to explore the effect of microenvironmental conditions and drug scheduling on normalization benefit, we build a mathematical model that incorporates tumor growth, angiogenesis and IFP. We administer various theoretical combinations of antiangiogenic agents and cytotoxic nanoparticles through heterogeneous vasculature that displays a similar morphology to tumor vasculature. We observe differences in drug extravasation that depend on the scheduling of combined therapy; for concurrent therapy, total drug extravasation is increased but in adjuvant therapy, drugs can penetrate into deeper regions of tumor.

The effect of spatial randomness on the average fixation time of mutants.

The mean conditional fixation time of a mutant is an important measure of stochastic population dynamics, widely studied in ecology and evolution. Here, we investigate the effect of spatial randomness on the mean conditional fixation time of mutants in a constant population of cells, N. Specifically, we assume that fitness values of wild type cells and mutants at different locations come from given probability distributions and do not change in time. We study spatial arrangements of cells on regular graphs with different degrees, from the circle to the complete graph, and vary assumptions on the fitness probability distributions. Some examples include: identical probability distributions for wild types and mutants; cases when only one of the cell types has random fitness values while the other has deterministic fitness; and cases where the mutants are advantaged or disadvantaged. Using analytical calculations and stochastic numerical simulations, we find that randomness has a strong impact on fixation time. In the case of complete graphs, randomness accelerates mutant fixation for all population sizes, and in the case of circular graphs, randomness delays mutant fixation for N larger than a threshold value (for small values of N, different behaviors are observed depending on the fitness distribution functions). These results emphasize fundamental differences in population dynamics under different assumptions on cell connectedness. They are explained by the existence of randomly occurring "dead zones" that can significantly delay fixation on networks with low connectivity; and by the existence of randomly occurring "lucky zones" that can facilitate fixation on networks of high connectivity. Results for death-birth and birth-death formulations of the Moran process, as well as for the (haploid) Wright Fisher model are presented.

Mathematical Modeling of the Effects of Tumor Heterogeneity on the Efficiency of Radiation Treatment Schedule.

Radiotherapy uses high doses of energy to eradicate cancer cells and control tumors. Various treatment schedules have been developed and tried in clinical trials, yet significant obstacles remain to improving the radiotherapy fractionation. Genetic and non-genetic cellular diversity within tumors can lead to different radiosensitivity among cancer cells that can affect radiation treatment outcome. We propose a minimal mathematical model to study the effect of tumor heterogeneity and repair in different radiation treatment schedules. We perform stochastic and deterministic simulations to estimate model parameters using available experimental data. Our results suggest that gross tumor volume reduction is insufficient to control the disease if a fraction of radioresistant cells survives therapy. If cure cannot be achieved, protocols should balance volume reduction with minimal selection for radioresistant cells. We show that the most efficient treatment schedule is dependent on biology and model parameter values and, therefore, emphasize the need for careful tumor-specific model calibration before clinically actionable conclusions can be drawn.

Tumor deconstruction as a tool for advanced drug screening and repositioning.

A major focus of contemporary drug screening strategies is the identification of novel anticancer compounds, which often results in underutilization of resources. Current drug evaluation involves in vivo tumor (xenograft) regression as proof-of-principle for cytotoxicity (POC). However, this end-point lacks any assessment of drug resistance of the residual tumor and its capability to establish refractory and/or recurrent disease, which would represent more appropriate indicators of therapeutic failure. We have recently developed a flow cytometry-based approach for the analyses of intra-tumor cellular heterogeneity across stem cell hierarchies, genetic instability and differential cell cycling fractions, which can potentially be predictive of refractory disease and tumor relapse. Iterating this approach after initial POC screening in the drug discovery pipeline would have a great impact in terms of precision of drug evaluation, design of optimal drug combinations and/or drug repositioning. In this perspective, we highlight how through embracing of a comprehensive, informative and analytical assessment of the cellular content of residual tumors, the fidelity and statistical robustness of preclinical drug discovery can be greatly improved.

A microscale mathematical model for metabolic symbiosis: Investigating the effects of metabolic inhibition on ATP turnover in tumors.

Cancer cells are notorious for their metabolic adaptations to hypoxic and acidic conditions, and especially for highly elevated glycolytic rates in tumor tissues. An end product of glycolysis is lactate, a molecule that cells can utilize instead of glucose to fuel respiration in the presence of oxygen. This could be beneficial to those cells that do not have sufficient oxygen as it conserves glucose for glycolysis. To better quantify this phenomenon we develop a diffusion-reaction mathematical model for nutrient concentrations in cancerous tissue surrounding a single cylindrical microvessel. We use our model to analyze the interdependence between cell populations' metabolic behaviors on a microscopic scale, specifically the emerging paradigm of metabolic symbiosis that exists between aerobic and glycolytic cells. The ATP turnover rates are calculated as a function of distance from the blood vessel, which exhibit a lactate-consuming population at intermediate distances from the vessel. We also consider the ramifications of the Warburg effect where cells utilize aerobic glycolysis along with this lactate-consuming respiration. We also investigate the effect of inhibiting metabolic pathways on cancer cells since insufficient ATP can trigger cell apoptosis. Effects that could be induced by metabolic inhibitors are analyzed by calculating the total ATP turnover in a unit tissue annulus in various parameter regimes that correspond to treatment conditions where specific metabolic pathways are knocked out. We conclude that therapies that target glycolysis, e.g. lactate dehydrogenase inhibitors or glycolytic enzyme inhibition, are the keys to successful metabolic repression.

Modeling age-dependent radiation-induced second cancer risks and estimation of mutation rate: an evolutionary approach.

Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of radiation-induced secondary malignancies. In this work, a novel evolutionary stochastic model is introduced that couples short-term formalism (during radiotherapy) and long-term formalism (post-treatment). This framework is used to estimate the risks of second cancer as a function of spontaneous background and radiation-induced mutation rates of normal and pre-malignant cells. By fitting the model to available clinical data for spontaneous background risk together with data of Hodgkin's lymphoma survivors (for various organs), the second cancer mutation rate is estimated. The model predicts a significant increase in mutation rate for some cancer types, which may be a sign of genomic instability. Finally, it is shown that the model results are in agreement with the measured results for excess relative risk (ERR) as a function of exposure age and that the model predicts a negative correlation of ERR with increase in attained age. This novel approach can be used to analyze several radiotherapy protocols in current clinical practice and to forecast the second cancer risks over time for individual patients.

Stochastic model for tumor control probability: effects of cell cycle and (a)symmetric proliferation.

BACKGROUND: Estimating the required dose in radiotherapy is of crucial importance since the administrated dose should be sufficient to eradicate the tumor and at the same time should inflict minimal damage on normal cells. The probability that a given dose and schedule of ionizing radiation eradicates all the tumor cells in a given tissue is called the tumor control probability (TCP), and is often used to compare various treatment strategies used in radiation therapy. METHOD: In this paper, we aim to investigate the effects of including cell-cycle phase on the TCP by analyzing a stochastic model of a tumor comprised of actively dividing cells and quiescent cells with different radiation sensitivities. Moreover, we use a novel numerical approach based on the method of characteristics for partial differential equations, validated by the Gillespie algorithm, to compute the TCP as a function of time. RESULTS: We derive an exact phase-diagram for the steady-state TCP of the model and show that at high, clinically-relevant doses of radiation, the distinction between active and quiescent tumor cells (i.e. accounting for cell-cycle effects) becomes of negligible importance in terms of its effect on the TCP curve. However, for very low doses of radiation, these proportions become significant determinants of the TCP. We also present the results of TCP as a function of time for different values of asymmetric division factor. CONCLUSION: We observe that our results differ from the results in the literature using similar existing models, even though similar parameters values are used, and the reasons for this are discussed.

Cell viability prediction and optimization in extrusion-based bioprinting via neural network-based Bayesian optimization models.

The fields of regenerative medicine and cancer modeling have witnessed tremendous growth in the application of 3D bioprinting. Maintaining high cell viability throughout the bioprinting process is crucial for the success of this technology, as it directly affects the accuracy of the 3D bioprinted models, the validity of experimental results, and the discovery of new therapeutic approaches. Therefore, optimizing bioprinting conditions, which include numerous variables influencing cell viability during and after the procedure, is of utmost importance to achieve desirable results. So far, these optimizations have been accomplished primarily through trial and error and repeating multiple time-consuming and costly experiments. To address this challenge, we initiated the process by creating a dataset of these parameters for gelatin and alginate-based bioinks and the corresponding cell viability by integrating data obtained in our laboratory and those derived from the literature. Then, we developed machine learning models to predict cell viability based on different bioprinting variables. The trained neural network yielded regressionR2value of 0.71 and classification accuracy of 0.86. Compared to models that have been developed so far, the performance of our models is superior and shows great prediction results. The study further introduces a novel optimization strategy that employs the Bayesian optimization model in combination with the developed regression neural network to determine the optimal combination of the selected bioprinting parameters to maximize cell viability and eliminate trial-and-error experiments. Finally, we experimentally validated the optimization model's performance.

Development of bioactive short fiber-reinforced printable hydrogels with tunable mechanical and osteogenic properties for bone repair.

Personalized bone-regenerative materials have attracted substantial interest in recent years. Modern clinical settings demand the use of engineered materials incorporating patient-derived cells, cytokines, antibodies, and biomarkers to enhance the process of regeneration. In this work, we formulated short microfiber-reinforced hydrogels with platelet-rich fibrin (PRF) to engineer implantable multi-material core-shell bone grafts. By employing 3D bioprinting technology, we fabricated a core-shell bone graft from a hybrid composite hydroxyapatite-coated poly(lactic acid) (PLA) fiber-reinforced methacryolyl gelatin (GelMA)/alginate hydrogel. The overall concept involves 3D bioprinting of long bone mimic microstructures that resemble a core-shell cancellous-cortical structure, with a stiffer shell and a softer core with our engineered biomaterial. We observed a significantly enhanced stiffness in the hydrogel scaffold incorporated with hydroxyapatite (HA)-coated PLA microfibers compared to the pristine hydrogel construct. Furthermore, HA non-coated PLA microfibers were mixed with PRF and GelMA/alginate hydrogel to introduce a slow release of growth factors which can further enhance cell maturation and differentiation. These patient-specific bone grafts deliver cytokines and growth factors with distinct spatiotemporal release profiles to enhance tissue regeneration. The biocompatible and bio-responsive bone mimetic core-shell multi-material structures enhance osteogenesis and can be customized to have materials at a specific location, geometry, and material combination.

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.

Investigation of the evolution of tumor-induced microvascular network under the inhibitory effect of anti-angiogenic factor, angiostatin: A mathematical study.

Anti-angiogenesis as a treatment strategy for normalizing the microvascular network of tumors is of great interest among researchers, especially in combination with chemotherapy or radiotherapy. According to the vital role that angiogenesis plays in tumor growth and in exposing the tumor to therapeutic agents, this work develops a mathematical framework to study the influence of angiostatin, a plasminogen fragment that shows the anti-angiogenic function, in the evolutionary behavior of tumor-induced angiogenesis. Angiostatin-induced microvascular network reformation is investigated in a two-dimensional space by considering two parent vessels around a circular tumor by a modified discrete angiogenesis model in different tumor sizes. The effects of imposing modifications on the existing model, i.e., the matrix-degrading enzyme effect, proliferation and death of endothelial cells, matrix density function, and a more realistic chemotactic function, are investigated in this study. Results show a decrease in microvascular density in response to the angiostatin. A functional relationship exists between angiostatin's ability to normalize the capillary network and tumor size or progression stage, such that capillary density decreases by 55%, 41%, 24%, and 13% in tumors with a non-dimensional radius of 0.4, 0.3, 0.2, and 0.1, respectively, after angiostatin administration.