CANCER DEVELOPMENT AND TREATMENT
High overall incidence and associated mortality rate of cancer requires an accurate measure of multiple parameters. Mathematical models incorporating these parameters allow holistic design, that also acknowledge uniqueness of cancer respective organ. Cancer models in terms of disease development and treatment, have led to elaboration of different types of models \cite{Wang_2015,Weeber_2017,Zitvogel_2016,Annunziato_2016,Santiago_2017,Zitvogel_2017}. The following sections present recent mathematical models for cancers of breast and cervix.
Breast Cancer: Breast tumour size dynamics has been reviewed for theoretically analysed data based on clinical data \cite{Ribba_2014}, risk prediction models \cite{Cintolo_Gonzalez_2017}, and interplay of microenvironment factors dependant models\cite{Simmons_2017}. Breast cancer development is slow process and to achieve a diagnosable size, it has been theoretically estimated to take up to 8 years (reviewed in \cite{Ribba_2014}). Growth of both primary and secondary tumours in breast cancer was predicted through a consolidated model by Tyuryumina and Neznanov \cite{Tyuryumina_2018}. This model, referred to as CoMPaS, was made by using natural history of primary tumour (PT) and secondary distant metastases (MTS), and hence it echoed associations between PT and MTS. CoMPaS was able to accurately define the duration of growth of PT and MTS and 10-15-year survival of breast cancer patients. Importantly, the time taken is due to accumulation of mutations that manifest into a tumour. The number of mutation (hits) are measured as different stages viz. two-stage \cite{Giannakakis_2008} and two-six stage \cite{Zhang_2014} for clinical expansion and manifestation. Zhang et al., have postulated the genetic pathways that are due to three-stages of mutation. Initial 2-3 hits could be responsible for genetic stability (possible genes - BRCA1 and BRCA2), while later hits may be responsible for sporadic events of breast cancer development.
Oke and group utilized differential equations to develop breast cancer model \cite{Isaac_Oke_2018}. The group considered multiple parameters including presence / absence of anti-cancer drugs, immune-booster and ketogenic diet to develop a robust model for breast cancer. The analyses led to identification of an optimal drug concentration for high effectiveness. The results were validated through numerical simulations.
Another approach could be treatment specific modelling of cancer sub-type. McKenna et al specifically looked at doxorubicin treatment in triple negative breast cancer (TNBC) \cite{McKenna_2018}. Herein, the group coupled experimental results with simulations and formed an in vitro pharmacokinetic / pharmacodynamic (PK/PD) model. This model described the effects of doxorubicin regimen on a representative cell line (SUM-149PT) that define cellular population dynamics. However, this work needs to be evaluated through in vivo analysis for its clinical suitability. Apart from this work, other simulations discussed are not developed for different molecular subtypes and this limits their application for designing treatment based models. Hence, there is need to make sub-class specific models for improved understanding of its development which can be eventually used for designing therapy and improve survivability. Patient survival prediction models using data mining algorithms - artificial neural networks \cite{Delen_2005,Park_2013}, decision Trees \cite{Delen_2005}, logistic regression \cite{Delen_2005}, support vector machines \cite{Park_2013,Xu_2012} give ample examples of extent of application of programming languages. More recently, Kate and Nadig used SEER dataset for machine learning and used summary stages to make prediction models \cite{Kate_2017}. The work identified that evaluation of summary stages together causes least performance in comparison to models trained on specific summary stage.
Cervical cancer:
Simulations have been developed for cervical cancer for vaccination, diagnosis and treatment. Continuous expression of E6 protein makes it an ideal therapeutic target against cervical cancer. Khan et al., predicted peptide vaccine through immunoinformatics approach of high-risk human papillomaviruses (HPV) E6 protein \cite{Khan_2018}. Antibody Epitope Prediction tools (ElliPro and NetCTL) predicted B-cell and CTL epitopes for E6 proteins that were experimentally validated through systems biology. These sequences are predicted as vaccine against hrHPV. However, an in vitro, in vivo and clinical studies are warranted. An impact assessment for HPV vaccination on populations should follow this study. This necessitates a worldwide evaluation of vaccine. A population based study on impact of HPV vaccination to counter worldwide variation in HPV infection was performed using IACR transmission model \cite{Baussano_2018}. The analyses showed pre-vaccination HPV prevalence is positively correlates with herd immunity and is eventually responsible for vaccination effectiveness.
Clinical diagnosis is usually based on detection of HPV DNA through high-throughput system like PCR. Inclusion of high quality methods is expected to reduce number of steps involved in verification of true positive cases. Exercising these standards for all cases may be avoided due to costs involved. Beylerian and team simulated the typical distribution of HPV DNA test results that are achieved when using a 96-well plate format \cite{Beylerian_2018}. An algorithm was made that generated nearly 9,00,000 cases, roughly translating into 10,000 microplate assays, for simulation of results. The results were distributed into groups for assumed HPV prevalence rates of 12%, 13%, 14%, 15%, and 16% as per 96-well matrices. The analyses indicate that screening in areas with prevalence of 12% to 16% could anticipate 5 to 22 positive results per test plate in nearly 95% of all assays. Deviation from these results can be considered to be caused by well-to-well contamination. This can be applied effectively in areas where prevalence of HPV is known. However, in altered spatiotemporal situation, this research has limited application.
Kyroudis et al., had patient-specific tumor response to radio- and chemo-therapy as central objective to generate a very specific computational model \cite{Kyroudis_2019}. This model included a scoring mechanism that could compare regression profile of any two tumors and predict outcomes of therapy effectiveness. The small size of patient cohort necessitate validation in a large group until which this model stands within preliminary study. The efficacy of tumor growth subduing drugs is limited by effective range of immune cells, beyond which the response to treatment is inadequate. Considering immune evasive maneuvers in a typical tumor, Bayer et al. developed a two-phenotype model \cite{Bayer_2018}. This model showed that presence of “selfish” cells is more prominent in benign form while “cooperative” cells are more prominent in aggressive tumors.
The above discussed studies are defined by routine models of cell lines and population studies. Recently, limited volume systems, like microfluidic devices, have recently gained momentum as experimental systems of choice in cancer studies because various disease related processes can be understood at the cellular level and further modelling and simulations can be applied (Table 3).