On Probabilistic Certification of Combined Cancer Therapies Using Strongly Uncertain Models

This paper proposes a general framework for probabilistic certification of cancer therapies. The certification is defined in terms of two key issues which are the tumor contraction and the lower admissible bound on the circulating lymphocytes which is viewed as indicator of the patient health. The certification is viewed as the ability to guarantee with a predefined high probability the success of the therapy over a finite horizon despite of the unavoidable high uncertainties affecting the dynamic model that is used to compute the optimal scheduling of drugs injection. The certification paradigm can be viewed as a tool for tuning the treatment parameters and protocols as well as for getting a rational use of limited or expensive drugs. The proposed framework is illustrated using the specific problem of combined immunotherapy/chemotherapy of cancer.Comment: Submitted to Journal of theoretical Biolog

The influence of toxicity constraints in models of chemotherapeutic protocol escalation

The prospect of exploiting mathematical and computational models to gain insight into the influence of scheduling on cancer chemotherapeutic effectiveness is increasingly being considered. However, the question of whether such models are robust to the inclusion of additional tumour biology is relatively unexplored. In this paper, we consider a common strategy for improving protocol scheduling that has foundations in mathematical modelling, namely the concept of dose densification, whereby rest phases between drug administrations are reduced. To maintain a manageable scope in our studies, we focus on a single cell cycle phase-specific agent with uncomplicated pharmacokinetics, as motivated by 5-Fluorouracil-based adjuvant treatments of liver micrometastases. In particular, we explore predictions of the effectiveness of dose densification and other escalations of the protocol scheduling when the influence of toxicity constraints, cell cycle phase specificity and the evolution of drug resistance are all represented within the modelling. For our specific focus, we observe that the cell cycle and toxicity should not simply be neglected in modelling studies. Our explorations also reveal the prediction that dose densification is often, but not universally, effective. Furthermore, adjustments in the duration of drug administrations are predicted to be important, especially when dose densification in isolation does not yield improvements in protocol outcomes

Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis

Oncolytic virotherapy (OV) has been emerging as a promising novel cancer treatment that may be further combined with the existing therapeutic modalities to enhance their effects. To investigate how OV could enhance chemotherapy, we propose an ODE based model describing the interactions between tumour cells, the immune response, and a treatment combination with chemotherapy and oncolytic viruses. Stability analysis of the model with constant chemotherapy treatment rates shows that without any form of treatment, a tumour would grow to its maximum size. It also demonstrates that chemotherapy alone is capable of clearing tumour cells provided that the drug efficacy is greater than the intrinsic tumour growth rate. Furthermore, OV alone may not be able to clear tumour cells from body tissue but would rather enhance chemotherapy if viruses with high viral potency are used. To assess the combined effect of OV and chemotherapy we use the forward sensitivity index to perform a sensitivity analysis, with respect to chemotherapy key parameters, of the virus basic reproductive number and the tumour endemic equilibrium. The results from this sensitivity analysis indicate the existence of a critical dose of chemotherapy above which no further significant reduction in the tumour population can be observed. Numerical simulations show that a successful combinational therapy of the chemotherapeutic drugs and viruses depends mostly on the virus burst size, infection rate, and the amount of drugs supplied. Optimal control analysis was performed, by means of Pontryagin's principle, to further refine predictions of the model with constant treatment rates by accounting for the treatment costs and sides effects.Comment: This is a preprint of a paper whose final and definite form is with 'Mathematical Biosciences and Engineering', ISSN 1551-0018 (print), ISSN 1547-1063 (online), available at [http://www.aimsciences.org/journal/1551-0018]. Submitted 27-March-2018; revised 04-July-2018; accepted for publication 10-July-201

Addressing current challenges in cancer immunotherapy with mathematical and computational modeling

The goal of cancer immunotherapy is to boost a patient's immune response to a tumor. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumor microenvironment, immune-modulating effects of conventional treatments, and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modeling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumor classification, optimal treatment scheduling, and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modelers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumor-immune biology. We conclude the review with recommendations for modelers both with respect to methodology and biological direction that might help keep modelers at the forefront of cancer immunotherapy development.Comment: Accepted for publication in the Journal of the Royal Society Interfac

A theoretical study of the response of vascular tumours to different types of chemotherapy

In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drug’s potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs

Basal cell carcinoma: 10-year experience with electrochemotherapy

BACKGROUND: Electrochemotherapy (ECT), by combining manageable cytotoxic agents with short electric pulses, represents an effective palliative skin-directed therapy. The accumulated evidence indicates that ECT stands out as a safe and well-tolerated alternative treatment for patients with multiple or large basal cell carcinoma (BCC), who are not suitable for conventional treatments. However, long-term data and shared indications are lacking. METHODS: In this observational study, we retrospectively analyzed 84 prospectively collected patients with multiple, recurrent or locally advanced BCC who were not candidate for standard therapies and received bleomycin-based ECT according to the European Standard Operative Procedures of ECT, from 2006 to 2016. RESULTS: Disease extent was local, locally advanced and metastatic in 40 (48%), 41 (49%) and 3 (3%), respectively. Forty-four (52%) individuals had multiple BCCs. Grade 3 skin toxicity after ECT was observed in 6% of cases. Clearance rate was 50% (95% CI 39-61%). Primary presentation (p = 0.004), tumor size <3 cm (p < 0.001), well-defined borders (p = 0.021), absence of tumor ulceration (p = 0.001), non-aggressive BCC histology (p = 0.046) and age 6469 years were associated with higher complete response rate. In patients with local BCC, the clearance rate was 72.5 and 85% after one or two ECT cycles, respectively. In the laBCC group, 32 patients (78%) achieved an objective response. Five-year recurrence rate for local and laBCC was 20 and 38%, respectively (p 64 0.001). CONCLUSIONS: One or two ECT cycles with bleomycin may be a valuable palliative treatment in well-selected patients with multiple BCCs and favorable tumor features. Validation of predictive factors will be imperative to match patients with optimal ECT treatment modalities. Management of laBCC with ECT warrants further investigation. Trial registration ISRCTN14633165 Registered 24 March 2017 (retrospectively registered)

Novel actions of next-generation taxanes benefit advanced stages of prostate cancer.

PURPOSE: To improve the outcomes of patients with castration-resistant prostate cancer (CRPC), there is an urgent need for more effective therapies and approaches that individualize specific treatments for patients with CRPC. These studies compared the novel taxane cabazitaxel with the previous generation docetaxel, and aimed to determine which tumors are most likely to respond. EXPERIMENTAL DESIGN: Cabazitaxel and docetaxel were compared via in vitro modeling to determine the molecular mechanism, biochemical and cell biologic impact, and cell proliferation, which was further assessed ex vivo in human tumor explants. Isogenic pairs of RB knockdown and control cells were interrogated in vitro and in xenograft tumors for cabazitaxel response. RESULTS: The data herein show that (i) cabazitaxel exerts stronger cytostatic and cytotoxic response compared with docetaxel, especially in CRPC; (ii) cabazitaxel induces aberrant mitosis, leading to pyknotic and multinucleated cells; (iii) taxanes do not act through the androgen receptor (AR); (iv) gene-expression profiling reveals distinct molecular actions for cabazitaxel; and (v) tumors that have progressed to castration resistance via loss of RB show enhanced sensitivity to cabazitaxel. CONCLUSIONS: Cabazitaxel not only induces improved cytostatic and cytotoxic effects, but also affects distinct molecular pathways, compared with docetaxel, which could underlie its efficacy after docetaxel treatment has failed in patients with CRPC. Finally, RB is identified as the first potential biomarker that could define the therapeutic response to taxanes in metastatic CRPC. This would suggest that loss of RB function induces sensitization to taxanes, which could benefit up to 50% of CRPC cases