A statistical model to predict diffusion patterns in bone scaffolds and learn latent behaviours

Abstract

The fields of tissue engineering and regenerative medicine have been gaining traction in the recent decades. In the pursuit of better bone substitute, scaffolds, a porous matrix of a nanofibril network, are made, seeded with osteoblasts, and tested for their cell viability. Our data consist of live/ dead staining assays and AlamarBlue assays. From them, we identify the whereabouts of osteoblasts, osteoblasts’ concentration. With them, we reconstruct a model, showing the evolution of the osteoblasts’ concentration on the constructs over the course of 20 days. The model, described by Fick’s second law, captures the osteoblasts’ random movement in 3D over time. This movement is solely driven by the osteoblasts’ concentration gradient and is impeded by the diffusivity of the constructs. The definite integral of Fick’s second law is solved by finite element method so that the cell migration is reflected upon the change in the concentration values in 3D over time. Based on the data, the diffusivity could be found by using support vector regression models, one of many statistical learning theories, to approximate the inverse of the definite integral. Our results suggest that random movement may not be as significant as one thought and biological mechanisms could be largely at play when it comes to cell migration. However, convergence of the self-training algorithm, simplifications of the problem domain, and approximation of support vector regression models, suggest limitations in our method. As a result, a number of different approaches have been suggested including a weighting scheme on the data, and adaptation of other pertinent spatial statistics. The fundamental behaviours of the osteoblast’s sub-populations have been revealed by non-negative matrix factorisation in the form of concentrations which may have a deep biological root in the osteoblasts’ life cycles, proliferation, and quiescence. Cell migration could also be affected by external mechanical loadings such as in vivo hydrostatic stress. To this end, we have demonstrated how pressure dominates the previous cell diffusion pattern. However, validation of in vivo and in vitro pressures are objectives for future studies.