A deep learning generative model approach for image synthesis of plant leaves.

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.

Mathematical and numerical challenges in optical screening of female breast.

Diffuse optical tomography (DOT) is an emerging imaging technique which uses light for diagnostic purposes in a non-invasive and non-ionizing way. In this paper, we focus on DOT application to female breast screening, where the surface of the breast is illuminated by light sources and the outgoing light is collected on the surface. The comparison of measured light data with the equivalent field obtained from a relevant mathematical model yields the DOT inverse problem whose solution provides an estimate of the optical coefficients of the tissue. These latter, in turn, can be related to clinical markers for cancer detection. The goal of this work is to propose a mathematical and computational approach tailored to the concept of a DOT imaging device able to perform fast and accurate screenings at an affordable cost. Namely, we address two original points about the crucial issue of the solution of the severely ill-conditioned DOT inverse problem: (a) a computational approach based on Green's functions which do not require the exact knowledge of the tissue geometry, proposed here in the declination of the Method of Fundamental Solutions, which allows to enforce correct boundary conditions; (b) the elastic net regularization technique that shares the desirable properties of both the ℓ2 - and ℓ1 -norm penalization approaches and opens the possibility for sparsity recognition in the optical coefficients field and refinement procedures.

A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering.

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.

Blood flow mechanics and oxygen transport and delivery in the retinal microcirculation: multiscale mathematical modeling and numerical simulation.

The scientific community continues to accrue evidence that blood flow alterations and ischemic conditions in the retina play an important role in the pathogenesis of ocular diseases. Many factors influence retinal hemodynamics and tissue oxygenation, including blood pressure, blood rheology, oxygen arterial permeability and tissue metabolic demand. Since the influence of these factors on the retinal circulation is difficult to isolate in vivo, we propose here a novel mathematical and computational model describing the coupling between blood flow mechanics and oxygen ([Formula: see text]) transport in the retina. Albeit in a simplified manner, the model accounts for the three-dimensional anatomical structure of the retina, consisting in a layered tissue nourished by an arteriolar/venular network laying on the surface proximal to the vitreous. Capillary plexi, originating from terminal arterioles and converging into smaller venules, are embedded in two distinct tissue layers. Arteriolar and venular networks are represented by fractal trees, whereas capillary plexi are represented using a simplified lumped description. In the model, [Formula: see text] is transported along the vasculature and delivered to the tissue at a rate that depends on the metabolic demand of the various tissue layers. First, the model is validated against available experimental results to identify baseline conditions. Then, a sensitivity analysis is performed to quantify the influence of blood pressure, blood rheology, oxygen arterial permeability and tissue oxygen demand on the [Formula: see text] distribution within the blood vessels and in the tissue. This analysis shows that: (1) systemic arterial blood pressure has a strong influence on the [Formula: see text] profiles in both blood and tissue; (2) plasma viscosity and metabolic consumption rates have a strong influence on the [Formula: see text] tension at the level of the retinal ganglion cells; and (3) arterial [Formula: see text] permeability has a strong influence on the [Formula: see text] saturation in the retinal arterioles.

A poroelastic model for the perfusion of the lamina cribrosa in the optic nerve head.

In this work we present a mathematical model for the coupling between biomechanics and hemodynamics in the lamina cribrosa, a thin porous tissue at the base of the optic nerve head which is thought to be the site of injury in ocular neurodegenerative diseases such as glaucoma. In this exploratory two-dimensional investigation, the lamina cribrosa is modeled as a poroelastic material where blood vessels are viewed as pores in a solid elastic matrix. The model is used to investigate the influence on the distributions of stress, blood volume fraction (or vascular porosity) and blood velocity within the lamina cribrosa due to the application of different levels of the intraocular pressure (IOP) and the enforcement of different mechanical constraints at the lamina's boundary. The model simulations suggest that the degree of fixity of the boundary constraint strongly influences the lamina's response to IOP elevation. Specifically, when the boundary is mechanically clamped, IOP elevation leads to an increase in stress close to the lamina's boundary, making it more susceptible to tissue damage. On the other hand, when rotations are allowed at the boundary, the most vulnerable region appears to be located at the lamina's central axis, in proximity of the eye globe, where increased stress and reduced vascular porosity and blood velocity are predicted for increased levels of IOP.

A multiscale approach in the computational modeling of the biophysical environment in artificial cartilage tissue regeneration.

Tissue Engineering is a strongly interdisciplinary scientific area aimed at understanding the principles of tissue growth to produce biologically functional replacements for clinical use. To achieve such an ambitious goal, complex biophysical phenomena must be understood in order to provide the appropriate environment to cells (nutrient delivery, fluid-mechanical loading and structural support) in the bioengineered device. Such a problem has an inherent multiphysics/multiscale nature, as it is characterized by material heterogeneities and interplaying processes occurring within a wide range of temporal and spatial scales. In this context, computational models are useful to gain a quantitative and comprehensive understanding of phenomena often difficult to be accessed experimentally. In this paper, we propose a mathematical and computational model that represents, to our knowledge, the first example of a self-consistent multiscale description of coupled nutrient mass transport, fluid-dynamics and biomass production in bioengineered constructs. We specifically focus on articular cartilage regeneration based on dynamically perfused bioreactors, and we investigate by numerical simulations three issues critical in this application. First, we study oxygen distribution in the construct, since achieving an optimal level throughout the construct is a main control variable to improve tissue quality. Second, we provide a quantitative evaluation of how interstitial perfusion can enhance nutrient delivery and, ultimately, biomass production, compared with static culture. Third, we perform a sensitivity analysis with respect to biophysical parameters related to matrix production, assessing their role in tissue regeneration.

Breakthroughs in computational modeling of cartilage regeneration in perfused bioreactors.

We report about two specific breakthroughs, relevant to the mathematical modeling and numerical simulation of tissue growth in the context of cartilage tissue engineering in vitro. The proposed models are intended to form the building blocks of a bottom-up multiscale analysis of tissue growth, the idea being that a full microscale analysis of the construct, a 3-D partial differential equation (PDE) problem with internal moving boundaries, is computationally unaffordable. We propose to couple a PDE microscale model of a single functional tissue subunit with the information computed at the macroscale by 2-D-0-D models of reduced computational cost. Preliminary results demonstrate the effectiveness of the proposed models in describing the interplay among interstitial perfusion flow, nutrient delivery, and consumption and tissue growth in realistic scaffold geometries.

A multiphysics/multiscale 2D numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor.

In vitro tissue engineering is investigated as a potential source of functional tissue constructs for cartilage repair, as well as a model system for controlled studies of cartilage development and function. Among the different kinds of devices for the cultivation of 3D cartilage cell colonies, we consider here polymeric scaffold-based perfusion bioreactors, where an interstitial fluid supplies nutrients and oxygen to the growing biomass. At the same time, the fluid-induced shear acts as a physiologically relevant stimulus for the metabolic activity of cells, provided that the shear stress level is appropriately tuned. In this complex environment, mathematical and computational modeling can help in the optimal design of the bioreactor configuration. In this perspective, we propose a computational model for the simulation of the biomass growth, under given inlet and geometrical conditions, where nutrient concentration, fluid dynamic field and cell growth are consistently coupled. The biomass growth model is calibrated with respect to the shear stress dependence on experimental data using a simplified short-time analysis in which the nutrient concentration and the fluid-induced shear stress are assumed constant in time and uniform in space. Volume averaging techniques are used to derive effective parameters that allow to upscale the microscopic structural properties to the macroscopic level. The biomass growth predictions obtained in this way are significant for long times of culture.

Autocatalytic loop, amplification and diffusion: a mathematical and computational model of cell polarization in neural chemotaxis.

The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.