Multi-scale modeling of fluids, solids and cells for Biofabrication
Janaina de Andréa Dernowsek – PhD
[email protected] Division of 3D Technologies (DT3D) Center for Information Technology Renato Archer/CTI
Lecture overview • Multi-scale modeling • Mathematics methods • 3D multicell simulation during the self-formation of thyroid follicles
• Finite Element Modeling (FEM) approach • numerical method to evaluate engineering constitutive equations.
• Computational Fluid Dynamics (CFD) approach • Modeling and Simulation of Diffusion Process
Technologies (IT) to study systems at different levels Multiscale Modeling: combining models, methods and appoaches from different scales In all strategies the common GOAL is to CREATE constitutive LAWS and continuum-level EQUATIONS of a BIOLOGICAL SYSTEM •What is necessary and •What is not necessary
Multi-scale modeling This approach is so complicated because the processes involved are in different scales and are very dynamics.
To create a model of a single cell, it may require solving something between 100,000 to one million equations.
Wikswo Lab, available at http://news.vanderbilt.edu/2011/10/robot-biologist/
Mathematics methods for modeling
Boolean Networks
Flux Balance Analysis
Pi Calculus
Differential Eqs
Petri Nets
Computational Models for Biological Structures • Representation of the reality inside a non-material domain using In Silico resources, • Computational power raises the modeling aid capability, • Always a representation, never the same as real, • Anatomy and histology is highly complex.
Thyroid gland thyroid cancer is the 16th most commonly diagnosed form of cancer on the planet, with close to 300,000 new diagnoses in 2012 alone.
http://3dprint.com/54159/3d-printed-thyroid-mouse/
Thyroid gland Near future organ bioprint HYSTOLOGY & FISIOLOGY : Comprised of aggregates or lobules of spherical follicles that are filled with colloid Functional units, hormone Iodine + T3 + T4 + thyroglobulin synthesis. Single layer of follicular cells. θ=500μm aprox Parafollicular cells :Calcitonin producing. 50 – 55mm
2013. Terese Winslow LLC US. 25 – 30mm
The McGraw-Hill Companies, Inc. 3D Bioprinted Thyroid Gland by 2015, Kidney by 2018, Says Russian Scientists of 3D Bioprinting Solutions company.
Thyroid gland
Thyroid gland
This image illustrates the differentiation process of stem and endothelial cells into follicles and blood capillaries of the thyroid. Dernowsek et al., 2015 - Abstract
CompuCell 3D
• Open-source simulation environment for • multi-cell, • single-cell-based modeling of tissues, •organs and •organisms. • It uses Cellular Potts Model (CPM) to model cell behavior. •We can also make use Systems Biology Markup Language (SMBL) – a free and open interchange format for computer models of biological processes. https://www.youtube.com/watch?v=OiQ5qfTp7jo
3D multicell simulation during the self-formation of thyroid follicles: a computational approach for the biofabrication of tissues EC – Endothelial cell
ESC – Embrionic Stem Cells
Thyroid follicles
Vascularization 1. Simplified 3D multicell simulation of angiogenesis during the self-formation of thyroid follicles 2. It can be easily extended and adapted to describe other biological phenomena 3. This simulation allowed us to study how the cells interact each other and modulate the growth and morphology of the multicellular spheroids.
Finite Elements Technology • Finite elements method: a numerical method to evaluate engineering constitutive equations. • Evaluation of simplified equations using standard shape functions (polinomials); • Shape functions are used to interpolate values between mesh nodes; • Finite elements mesh is used to fit the problem domain (mesh x geometry);
Comercial FEM software • • • • • • •
NEi Nastran/FEMAP; MSC Nastran/Patran; ANSYS/Workbench; Comsol; Abaqus; Cosmos; Etc.
BioCAD - Concepts • Optimized models for Finite Element Analysis (FEM ) simulation
BioCAD
STL model (MIP) Surface model For FEM simulation
BioCAD Protocol •Mapping of anatomical landmarks
STL file from CT (InVesalius)
BioCAD
Surface and Solid
Finite Element Method - FEM
Mesh generation by geometry discretization in elements Nodal Calculation Color map results representation
FEM – Pre-processing • Geometry importation • Material characterization • Contact declaration between bodies.
• Mesh generation • Boundary conditions applying (displacement constraints, loadings)
FEM – Pre-processing • Geometry importation • Material characterization • Contact declaration between bodies. • Mesh generation • Boundary conditions applying (displacement constraints, loadings)
FEM – Pre-processing • Geometry importation • Material characterization • Contact declaration between bodies. • Mesh generation • Boundary conditions applying (displacement constraints, loadings)
FEM – Pre-processing • Geometry importation • Material characterization • Contact declaration between bodies.
• Mesh generation • Boundary conditions applying (displacement constraints, loadings)
FEM – Post-processing - results • Calculations on each node represented by color maps (Von Mises stress) • Structural static analysis (Von Mises, Shear stress, principal stress, deformation and displacement) • Criteria (which stress) according to the study objectives
• Results interpretation considering material resistance and mechanical behavior
Computational Fluid Dynamics (CFD)
CFD is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows.
Computational Fluid Dynamics Softwares FLUENT, TIDAL, C-MOLD, FLOTRAN SPLASH Tetrex ViGPLOT VGRID ANSYS – CFX STAR CCM++
Computational Fluid Dynamics (CFD) - Process Geometry of problem is defined . Volume occupied by fluid is divided into discrete cells. The Navier-Stokes equations are the fundamental partial differentials equations (PDE) that describe the flow of incompressible fluids.
Modeling and Simulation of Diffusion Process in Tissue Spheroids Encaged into Microscaffolds (Lockyballs) • The oxygen gradient formed in a spheroid is crucial to study the cell behavior during the tissue spheroid maturation •The diffusion kinetics is a major factor that influences cellular responses in 3D spheroids Brendan et al., 2014
Modeling and Simulation of Diffusion Process in Tissue Spheroids Encaged into Microscaffolds (Lockyballs) Computational models of OXYGEN GRADIENTS formed in a spheroid containing a constant number of cells with different circularity and compactness. The model predicts that as the spheroid elongates and becomes less circular, the average core-to-surface distance decreases and the oxygen gradient decreases with the spheroid becoming more evenly saturated with oxygen
Brendan et al., 2014
Modeling and Simulation of Diffusion Process in Tissue Spheroids Encaged into Microscaffolds (Lockyballs)
Four geometries were modelled to simulations. (A) Solid microscaffold without internal structure (original lockyball) (Danilevicius et al., 2015). (B, C, D) Solid microscaffolds with internal structures to improve the oxygenation cells Dernowsek et al., 2016
Dernowsek et al., 2016
Modeling and Simulation of Diffusion Process in Tissue Spheroids Encaged into Microscaffolds (Lockyballs) Conclusions • We demonstrated the advantages of a microscaffold and the limitations of tissue spheroids under inappropriate conditions for cell proliferation. • The design and the computational modeling of new microscaffolds described in this study new opportunities for tissue engineering. • As a future work, a validation will be necessary.
Thank you for your kind attention!
