Biology often inspires engineering. We used dynamic models of leaf venations to assess the feasibility of plant-inspired infrastructure networks. The cost and performance of the leaf venation network was found to be comparable to that of a spanning tree, but the leaf venation program is an order of magnitude faster, which suggests that rapid leaf inspired solutions could be used to initialize more optimal spanning tree algorithms. To design networks that comprise an initial point or source, and branching points that are not necessarily attraction points, inspiration was taken from slime mold, a protist, amoeba-like organism that grows by foraging and forming a network. The DeeP MeLT also uses micro-macro geomechanics to find solutions to biological problems. In collaboration with Dr. Elsa Vennat at Ecole Centrale-Supélec (France), we proposed a micro-macro mechanical model of dentin, based on the homogenization scheme proposed by Hashin for hollow fibers embedded in a homogeneous solid matrix. The model was implemented in a FEM code, calibrated and validated against experimental force-displacement curves and strain fields obtained by Digital Image Correlation. In collaboration with Dr. Antonia Antoniou at Georgia Tech, a procedure was proposed to create dentin analogs with nano-copper, allowing calibration of numerical models from repeatable experimental tests.

- F. Patino-Ramirez, C. Arson, A. Dussutour, 2021. Substrate and cell fusion influence on slime mold network dynamics, Scientific Reports, DOI: 10.1038/s41598-020-80320-2.
- W. Jin, J. Aufrecht, F. Patino-Ramirez, H. Cabral, C. Arson, S. Retterer, 2020. Modeling root system growth around obstacles, Scientific Reports, DOI: 10.1038/s41598-020-72557-8.
- F. Patino-Ramirez, C. Arson, 2020. Transportation networks inspired by leaf venation algorithms, Journal of Bioinspiration and Biomimetics, DOI: 10.1088/1748-3190/ab7571.
- T. Ibru, S. Violante, E. Vennat, C. Arson, A. Antoniou, 2020. Structure and mechanical behavior of dentin-inspired nanoporous copper, Scripta Materialia, DOI: 10.1016/j.scriptamat.2019.09.034.
- C. Arson, Y. Yasothan, R. Jeanneret, N. Roubier, E. Vennat, 2020. An alternative to periodic homogenization for dentin elastic stiffness, Journal of Mechanics in Medicine and Biology, DOI: 10.1142/S0219519419500817.
- F. Patino-Ramirez, A. Broussard, C. Arson, A. Dussutour, 2019. Substrate composition directs slime molds behavior, Scientific Reports, DOI:10.1038/s41598-019-50872-z.

*Physarum Polycephalum*, commonly known as slime mold, is a protist, i.e. a unicellular organism that has no nervous system. Although brain-less, slime mold has proved to grow by forming approximate Steiner trees and is capable of changing network topology over time, depending on the environmental conditions. Additionally, slime mold can form networks that are more cost-effective than infrastructure facilities (e.g., railways) under the same constraints. Slime mold networks are made of a growth front forming a fan-like structure, the function of which is to explore the domain and search for nutrients, and a set of intersecting veins, which connect these fronts to all the other nodes or segments that belong to the cell.
Protoplasm growth fronts follow an oscillatory flow called "shuttle streaming". The oscillatory fluid transport distributes chemical signals, vital nutrients and oxygen all around the cell, while reshaping the network by a periodic and peristaltic movement of the veins and of the growing front, triggered by actin-myosin interactions. The oscillation frequency increases when the cell membrane is excited by the presence of attractants. The same mechanism controls the gradual retraction (thinning) of growth fronts at the vicinity of non-nutritive areas or repellents (such as salt). Despite the number of references on the pulsatile growth of slime mold networks, there is no clear understanding of the coupled processes that affect network development, and growth rates were never measured. We conducted experiments that shed light on the growth rate and topology evolution of slime mold networks in several controlled environments. The work was done in collaboration with Dr. Audrey Dussutour, worldwide expert on slime mold and collective behavior of biological organisms. We then used an algorithm that mimics slime mold foraging, growth and thinning to optimize a porous network for resource extraction.

*Pictures: Patino-Ramirez, Dussutour and Arson, 2019*

Biological systems have adapted to environmental constraints and limited resource availability. Here, we evaluate the algorithm underlying leaf venation (LV) deployment using graph theory. We seek to optimize the topology of an infrastructure network going from one source point to multiple destination points. We assess the feasibility of LV-inspired infrastructure networks by comparing the traffic balance, travel and cost efficiency of simply-connected LV networks to two optima: (i) the local optimum, which minimizes the travel distance between the source and each of the destination points (fan-like network); (ii) the global optimum, which minimizes the total graph length (Steiner tree). We use a Pareto front to show that the total length of leaf venations is close to optimal. Then we apply the LV algorithm to design transportation networks in the city of Atlanta. Results show that leaf-inspired models can perform similarly or better than computer-intensive optimization algorithms in terms of network cost and service performance, which could facilitate the design of engineering transportation networks.

*Pictures: Patino-Ramirez and Arson, 2020*

State-of-the-Art models of Root System Architecture (RSA) do not allow simulating root growth around rigid obstacles. Yet, the presence of obstacles can be highly disruptive to the root system. We grew wheat seedlings in sealed petri dishes without obstacle and in custom 3D-printed rhizoboxes containing obstacles. Time-lapse photography was used to reconstruct the wheat root morphology network. We used the reconstructed wheat root network without obstacle to calibrate an RSA model implemented in the R-SWMS software. The root network with obstacle allowed calibrating the parameters of a new function that models the influence of rigid obstacles on wheat root growth. Experimental results show that the presence of a rigid obstacle does not affect the growth rate of the wheat root axes, but that it does influence the root trajectory after the main axis has passed the obstacle. The growth recovery time, i.e. the time for the main root axis to recover its geotropism-driven growth, is proportional to the time during which the main axis grows along the obstacle. Qualitative and quantitative comparisons between experimental and numerical results show that the proposed model successfully simulates wheat RSA growth around obstacles. Our results suggest that wheat roots follow patterns that could inspire the design of adaptive engineering flow networks.

*Pictures: Jin, Aufrecht, Patino-Ramirez, Cabral, Arson and Retterer, 2020*

Dentin, the main tissue of the tooth, is made of tubules surrounded by peri-tubular dentin (PTD), embedded in a matrix of inter-tubular dentin (ITD). The PTD and the ITD have different relative fractions of collagen and hydroxyapatite crystals. The ITD is typically less rigid than the PTD, which can be seen as a set of parallel hollow cylindrical reinforcements in the ITD matrix. We extended Hashin and Rozen's homogenization scheme to a non-uniform distribution of hollow PTD cylinders, determined from image analysis. We related the transverse isotropic elastic coefficients of a Representative Elementary Volume (REV) of dentin to the elastic and topological properties of PTD and ITD. The model was calibrated against experimental data. Each sample tested was consistently characterized by Environmental Scanning Electron Microscopy (ESEM), nano- indentation and Resonant Ultrasound Spectroscopy (RUS), which ensured that macroscopic mechanical properties measured were correlated with microstructure observations. Despite the high variability of microstructure descriptors and mechanical properties, statistical analyses show that Hashin's bounds converge and that the proposed model can be used for back-calculating the microscopic Poisson's ratios of dentin constituents. Three-point bending tests conducted in the laboratory were simulated with the Finite Element Method (FEM). Elements were assigned transverse isotropic elastic prameters calculated by homogenization from the calibrated micro-mechanical parameters, with the microstructure parameters determined for each beam before testing. The vertical displacement field predicted by the FEM matches that measured by Digital Image Correlation (DIC) with a median error of 3 to 8%. Discrepancies were noted for horizontal (axial) deformation, which was attributed to plasticity. By contrast with previous studies, we fully calibrated and validated a closed form mechanical model against experimental data and we explained the testing procedures. In elastic conditions, the proposed homogenization scheme gives a better account of microstructure variability than micro-macro dentin models with periodic microstructure.

*Pictures: Arson, Yasothan, Jeanneret, Roubier, Vennat, Majnooni, 2020*