An explainable machine learning-based probabilistic framework for the design of scaffolds in bone tissue engineering.

Recently, 3D-printed biodegradable scaffolds have shown great potential for bone repair in critical-size fractures. The differentiation of the cells on a scaffold is impacted among other factors by the surface deformation of the scaffold due to mechanical loading and the wall shear stresses imposed by the interstitial fluid flow. These factors are in turn significantly affected by the material properties, the geometry of the scaffold, as well as the loading and flow conditions. In this work, a numerical framework is proposed to study the influence of these factors on the expected osteochondral cell differentiation. The considered scaffold is rectangular with a 0/90 lay-down pattern and a four-layered strut made of polylactic acid with a 5% steel particle content. The distribution of the different types of cells on the scaffold surface is estimated through a scalar stimulus, calculated by using a mechanobioregulatory model. To reduce the simulation time for the computation of the stimulus, a probabilistic machine learning (ML)-based reduced-order model (ROM) is proposed. Then, a sensitivity analysis is performed using the Shapley additive explanations to examine the contribution of the various parameters to the framework stimulus predictions. In a final step, a multiobjective optimization procedure is implemented using genetic algorithms and the ROM, aiming to identify the material parameters and loading conditions that maximize the percentage of surface area populated by bone cells while minimizing the area corresponding to the other types of cells and the resorption condition. The results of the performed analysis highlight the potential of using ROMs for the scaffold design, by dramatically reducing the simulation time while enabling the efficient implementation of sensitivity analysis and optimization procedures.

Light scattering by aggregated red blood cells.

In low flow rates, red blood cells (RBCs) fasten together along their axis of symmetry and form a so-called rouleaux. The scattering of He-Ne laser light by a rouleau consisting of n (2 < or = n < or = 8) average-sized RBCs is investigated. The interaction problem is treated numerically by means of an advanced axisymmetric boundary element--fast Fourier transform methodology. The scattering problem of one RBC was solved first, and the results showed that the influence of the RBC's membrane on the scattering patterns is negligible. Thus the rouleau is modeled as an axisymmetric, homogeneous, low-contrast dielectric cylinder, on the surface of which appears, owing to aggregated RBCs, a periodic roughness along the direction of symmetry. The direction of the incident laser light is considered to be perpendicular to the scatterer's axis of symmetry. The differential scattering cross sections in both perpendicular and parallel scattering planes and for all the scattering angles are calculated and presented in detail.