Modeling Multiscale Necrotic and Calcified Tissue Biomechanics in Cancer Patients: Application to Ductal Carcinoma In Situ (DCIS) - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 366

Fig. 14 Preliminary continuum simulation of solid-type DCIS with comedonecrosis and
calcifications [ 17 ]. Legend: Green curve: deformed basement membrane. Red curve: viable
tumor boundary. Magenta curve: calcified necrotic debris. White shading: non-calcified necrotic
tissue
We plan to integrate these discrete and continuum approaches in a hybrid
model, as outlined in [ 43 , 50 ]. A key issue is determining the rate constants for the
continuum model. As water loss in necrotic cells does not occur at a fixed rate, it
may be best to simulate using the discrete model until most fluid has been lost,
then ''convert mass'' to the continuum model for the slower time scale processes.
A more detailed analysis of the full agent-based model could yield the correct
average per-volume rate of volume loss in the necrotic tissues, similarly to the
upscaling approach we developed in [ 23 , 54 ]. Other approaches may include
introduction of an age structuring variable, as is often used today in mathematical
ecology (e.g., [ 5 , 41 , 49 ]).
5.2 A Vision for Quantitative, Integrative
Computational Oncology
An integrative modeling approach—where clinicians, modelers, and biologists work
in close-knit teams throughout the modeling process—is necessary to push com-
putational oncology towards clinical application. Conversely, just as the space race
in the 1950s and 1960s fueled advances throughout engineering, physics, and
mathematics, efforts to push the envelope in patient-specific modeling are advancing
the state-of-the-art in mathematical modeling, computational algorithms, experi-
mental methods, and clinical practice. Moreover, quantitatively and explicitly stat-
ing our working biological hypotheses gives us the opportunity to rigorously and
systematically test and refine what can best be described as current cancer biology
orthodoxy. We close this chapter by outlining our vision of clinically-oriented
integrative computational oncology, and its possible impact beyond the clinic.
Model Design Clinicians and modelers jointly identify important unanswered
clinical questions. This helps modelers avoid investigating unnecessary tangents while