Colorectal cancer (CRC) has formed a canonical example of tumourigenesis ever since its use in Fearon and Vogelstein's linear model of genetic mutation, and continues to generate a huge amount of research interest. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical and computational modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. The authors present a timely summary of the literature relating to CRC, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. The authors conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that theoretical modelling can provide.

Energetic efficiency is an important indicator of cardiac function in acute myocardial infarction. However, the relationship between cardiac energetic efficiency and infarct size is not perfectly elucidated. In this study, the relationship is analysed by means of simulation using a theoretical model of the guinea pig left ventricle. In simulation with varied ratios of infarct area, pressure–volume area (PVA), which is an index of total mechanical energy by ventricular contraction, and myocardial oxygen consumption (MVO₂) are calculated for each infarct ratio. Then, change of PVA when MVO₂ alters (PVA/MVO₂) as a well-known index of energy conversion efficiency is evaluated. In addition, PVA/VO₂, which represents a ratio of PVA change to alteration of mean oxygen consumption of myocytes except for infarct myocytes, is introduced as an index for real energetic efficiency. In simulation results, PVA/MVO₂ increases but PVA/VO₂ decreases as infarct area expands, because with expansion of infarct area PVA decreases but VO₂ remains almost unchanged because of larger shortening of myocytes. This implies that the enlargement of shortening of noninfarcted myocyte to compensate for depression of cardiac output is a potential cause of myocardial remodelling.

The authors propose a therapy consisting of a constant dosage of reverse transcription inhibitor and protease inhibitor to achieve long-term non-progressor (LTNP) status in human immuno-deficiency virus (HIV) patients. Based on the authors analyses of cytotoxic T lymphocyte precursor (CTLp) concentration at several equilibrium points and the bifurcation of these equilibrium points, they find that administration of drugs with an efficacy lower than a certain level induces a higher CTLp concentration. As a result, drug doses of moderate efficacy result in more patients with LTNP status than doses with high efficacy. In analyses of controllability, they show that a treatment of moderate efficacy is more efficient than one of very high efficacy in terms of controlling the immune system. Using simulations, they demonstrate that their proposed method results in LTNP status in HIV patients.