In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular “force isotropy” as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection–diffusion–reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations.

The microcirculation plays a major role in maintaining homeostasis in the body. Alterations or dysfunctions of the microcirculation can lead to several types of serious diseases. It is not surprising, then, that the microcirculation has been an object of intense theoretical and experimental study over the past few decades. Mathematical approaches offer a valuable method for quantifying the relationships between various mechanical, hemodynamic, and regulatory factors of the microcirculation and the pathophysiology of numerous diseases. This work provides an overview of several mathematical models that describe and investigate the many different aspects of the microcirculation, including geometry of the vascular bed, blood flow in the vascular networks, solute transport and delivery to the surrounding tissue, and vessel wall mechanics under passive and active stimuli. Representing relevant phenomena across multiple spatial scales remains a major challenge in modeling the microcirculation. Nevertheless, the depth and breadth of mathematical modeling with applications in the microcirculation is demonstrated in this work. A special emphasis is placed on models of the retinal circulation, including models that predict the influence of ocular hemodynamic alterations with the progression of ocular diseases such as glaucoma.

Objectives: A well-known drawback to the implementation of Convolutional Neural Networks (CNNs) for image-recognition is the intensive annotation effort for large enough training dataset, that can become prohibitive in several applications. In this study we focus on applications in the agricultural domain and we implement Deep Learning (DL) techniques for the automatic generation of meaningful synthetic images of plant leaves, which can be used as a virtually unlimited dataset to train or validate specialized CNN models or other image-recognition algorithms. Methods: Following an approach based on DL generative models, we introduce a Leaf-to-Leaf Translation (L2L) algorithm, able to produce collections of novel synthetic images in two steps: first, a residual variational autoencoder architecture is used to generate novel synthetic leaf skeletons geometry, starting from binarized skeletons obtained from real leaf images. Second, a translation via Pix2pix framework based on conditional generator adversarial networks (cGANs) reproduces the color distribution of the leaf surface, by preserving the underneath venation pattern and leaf shape. Results: The L2L algorithm generates synthetic images of leaves with meaningful and realistic appearance, indicating that it can significantly contribute to expand a small dataset of real images. The performance was assessed qualitatively and quantitatively, by employing a DL anomaly detection strategy which quantifies the anomaly degree of synthetic leaves with respect to real samples. Finally, as an illustrative example, the proposed L2L algorithm was used for generating a set of synthetic images of healthy end diseased cucumber leaves aimed at training a CNN model for automatic detection of disease symptoms. Conclusions: Generative DL approaches have the potential to be a new paradigm to provide low-cost meaningful synthetic samples. Our focus was to dispose of synthetic leaves images for smart agriculture applications but, more in general, they can serve for all computer-aided applications which require the representation of vegetation. The present L2L approach represents a step towards this goal, being able to generate synthetic samples with a relevant qualitative and quantitative resemblance to real leaves.