Figure 4.

BIC pen-like mathematical models: prioritizing the purpose of the model instead of its detailedness. BIC pens look like the simplest and cheapest ballpoint pen one can buy, but their apparent simplicity conceals features conceived to optimize them in economic, ergonomic, and safety terms. In Santos and coworkers 2016 [3], a similar strategy was followed to build a mathematical model accounting for anticancer dendritic cell (DC) vaccination composed of only two ordinary differential equations, far simpler than other published models [41]. (A) Simplicity in design: BIC pens have a characteristically simple hexagonal structure; this apparently naïve choice significantly reduces the material consumption of the pen and minimizes the required space for storage. An important aspect to consider in DC vaccine modelling is the bioavailability of the cells after their injection. There are much elaborated models describing this process [42], but for our purpose, it was sufficient to model DC bioavailability with a cyclic piecewise linear function that mimics the known overall behavior of injected DCs. (B) Mathematics behind design principles: compared to standard circular pens, BIC pens hardly roll on the surface of a table. This feature was explicitly desired when drafting their design. In Santos et al., we wanted a simple enough model that was still able to mimic the interaction between the tumor and both innate and adaptive immunity; to this end, the model contained two nonlinear kinetic rates in a single equation, which are still able to mimic the basics of the interplay between the tumor and the two branches of immunity. (C) Ability to solve problems: in the end, simplicity has to be reconciled with effectiveness. The design of a BIC pen, for example, integrates more characteristics like minimizing the risk of suffocation when swallowing the cap. The predictions made in Santos et al. (2016) in terms of which phenotypic features sensitize the tumor to the therapy were aligned with patient data from clinical trials; furthermore, the model predicted alternative phenotypes that promote therapy resistance. The figures about DC vaccine modelling are adapted from Santos et al. 2016 under the conditions of an open access publication (CC BY 4.0). The figures about the BIC pen were inspired by the content of the webpage www.bicworld.com. Fight by doing: A route map to good mathematical modelling in biomedicine.