Modeling of time dependent localized flow shear stress and its impact on cellular growth within additive manufactured titanium implants

Bone augmentation implants are porous to allow cellular growth, bone formation and fixation. However, the design of the pores is currently based on simple empirical rules, such as minimum pore and interconnects sizes. We present a three-dimensional (3D) transient model of cellular growth based on the Navier–Stokes equations that simulates the body fluid flow and stimulation of bone precursor cellular growth, attachment, and proliferation as a function of local flow shear stress. The model's effectiveness is demonstrated for two additive manufactured (AM) titanium scaffold architectures. The results demonstrate that there is a complex interaction of flow rate and strut architecture, resulting in partially randomized structures having a preferential impact on stimulating cell migration in 3D porous structures for higher flow rates. This novel result demonstrates the potential new insights that can be gained via the modeling tool developed, and how the model can be used to perform what-if simulations to design AM structures to specific functional requirements.

[1]  R. Atwood,et al.  Modeling of porosity formation in direct chill cast aluminum-magnesium alloys , 2002 .

[2]  A. Chorin.  Numerical solution of the Navier-Stokes equations , 1968 .

[3]  S. Cowin,et al.  A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. , 2001, Journal of biomechanics.

[4]  K. Pericleous,et al.  Numerical simulation of the effect of fluid flow on solute distribution and dendritic morphology , 2009 .

[5]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[6]  G. B. Fiore,et al.  Mechanobiology of engineered cartilage cultured under a quantified fluid-dynamic environment , 2002, Biomechanics and modeling in mechanobiology.

[7]  C P Chen,et al.  Enhancement of cell growth in tissue‐engineering constructs under direct perfusion: Modeling and simulation , 2007, Biotechnology and bioengineering.

[8]  Peter D. Lee,et al.  A new mechanism for freckle initiation based on microstructural level simulation , 2012 .

[9]  Robert E Guldberg,et al.  Effects of medium perfusion rate on cell-seeded three-dimensional bone constructs in vitro. , 2003, Tissue engineering.

[10]  Dominique Bernard,et al.  Non-destructive quantitative 3D analysis for the optimisation of tissue scaffolds. , 2007, Biomaterials.

[11]  K. Lau,et al.  Fluid flow shear stress stimulates human osteoblast proliferation and differentiation through multiple interacting and competing signal transduction pathways. , 2003, Bone.

[12]  Gabriele Dubini,et al.  Modeling evaluation of the fluid-dynamic microenvironment in tissue-engineered constructs: a micro-CT based model. , 2006, Biotechnology and bioengineering.

[13]  J A Frangos,et al.  Effect of flow on prostaglandin E2 and inositol trisphosphate levels in osteoblasts. , 1991, The American journal of physiology.

[14]  Roger Zauel,et al.  3-D computational modeling of media flow through scaffolds in a perfusion bioreactor. , 2005, Journal of biomechanics.

[15]  Francesco Migliavacca,et al.  The effect of media perfusion on three-dimensional cultures of human chondrocytes: integration of experimental and computational approaches. , 2004, Biorheology.

[16]  J. Wolff.  The Law of Bone Remodelling , 1986, Springer Berlin Heidelberg.

[17]  Cato T Laurencin,et al.  Human osteoblast-like cells in three-dimensional culture with fluid flow. , 2003, Biorheology.

[18]  Pascal Verdonck,et al.  CFD models for wallshear stress estimation; a comparitive study of two complete scaffold geometries , 2010 .

[19]  Larry L. Hench,et al.  Regeneration of trabecular bone using porous ceramics , 2003 .

[20]  Margherita Cioffi,et al.  The effect of hydrodynamic shear on 3D engineered chondrocyte systems subject to direct perfusion. , 2006, Biorheology.

[21]  Gretar Tryggvason,et al.  Numerical simulation of dendritic solidification with convection: two-dimensional geometry , 2002 .

[22]  Paola Causin,et al.  Breakthroughs in Computational Modeling of Cartilage Regeneration in Perfused Bioreactors , 2011, IEEE Transactions on Biomedical Engineering.

[23]  R Langer,et al.  Kinetics of chondrocyte growth in cell‐polymer implants , 1994, Biotechnology and bioengineering.

[24]  Peter D. Lee,et al.  Dendritic solidification under natural and forced convection in binary alloys: 2D versus 3D simulation , 2010 .

[25]  Nicola Elvassore,et al.  Mathematical Modeling of Three-Dimensional Cell Cultures in Perfusion Bioreactors , 2006 .

[26]  Peter D. Lee,et al.  Simulation of the columnar-to-equiaxed transition in directionally solidified Al-Cu alloys , 2005 .

[27]  J A Frangos,et al.  Fluid flow stimulates rapid and continuous release of nitric oxide in osteoblasts. , 1996, The American journal of physiology.

[28]  M. Bram,et al.  Characterization of the deformation behavior of intermediate porosity interconnected Ti foams using micro-computed tomography and direct finite element modeling. , 2010, Acta biomaterialia.

[29]  Julian R Jones,et al.  Hierarchical porous materials for tissue engineering , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[30]  A. Cliquet,et al.  Disuse Ostoporosis: Its relationship to Spine Cord Injuried Patient Rehabilitation , 2005 .

[31]  Francesco Migliavacca,et al.  Micro Fluid Dynamics in Three Dimensional Engineered Cell Systems in Bioreactors. , 2006 .

[32]  Lewis Mullen,et al.  Selective Laser Melting: a regular unit cell approach for the manufacture of porous, titanium, bone in-growth constructs, suitable for orthopedic applications. , 2009, Journal of biomedical materials research. Part B, Applied biomaterials.

[33]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[34]  K. Leong,et al.  A mathematical model for fluid shear-sensitive 3D tissue construct development , 2013, Biomechanics and modeling in mechanobiology.

[35]  F. Maes,et al.  Modeling fluid flow through irregular scaffolds for perfusion bioreactors , 2009, Biotechnology and bioengineering.

[36]  Julian R Jones,et al.  Evaluation of 3-D bioactive glass scaffolds dissolution in a perfusion flow system with X-ray microtomography. , 2011, Acta biomaterialia.

[37]  S. Yue,et al.  Non-destructive quantification of tissue scaffolds and augmentation implants using X-ray microtomography , 2011 .

[38]  Yaron Blinder,et al.  Modeling of flow‐induced shear stress applied on 3D cellular scaffolds: Implications for vascular tissue engineering , 2010, Biotechnology and bioengineering.

[39]  Antonios G. Mikos,et al.  Mineralized matrix deposition by marrow stromal osteoblasts in 3D perfusion culture increases with increasing fluid shear forces , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Lewis Mullen,et al.  Selective laser melting: a unit cell approach for the manufacture of porous, titanium, bone in-growth constructs, suitable for orthopedic applications. II. Randomized structures. , 2010, Journal of biomedical materials research. Part B, Applied biomaterials.

[41]  Peter D. Lee,et al.  A model of solidification microstructures in nickel-based superalloys: predicting primary dendrite spacing selection , 2003 .

[42]  D. Wendt,et al.  Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models. , 2008, Journal of biomechanics.

[43]  Daniela Cristina Leite de Carvalho,et al.  Osteoporose por desuso: aplicacao na reabilitacao do lesado medular , 2001 .

[44]  R. Dillaman,et al.  Fluid movement in bone: theoretical and empirical. , 1991, Journal of biomechanics.

[45]  J B WRAY,et al.  The vascular response to fracture of the tibia in the rat. , 1959, The Journal of bone and joint surgery. American volume.

[46]  Peter D. Lee,et al.  Multiscale modelling of solidification microstructures, including microsegregation and microporosity, in an Al–Si–Cu alloy , 2004 .

[47]  S. Cowin,et al.  A model for the excitation of osteocytes by mechanical loading-induced bone fluid shear stresses. , 1994, Journal of biomechanics.

[48]  P. Niederer,et al.  Experimental elucidation of mechanical load-induced fluid flow and its potential role in bone metabolism and functional adaptation. , 1998, The American journal of the medical sciences.

[49]  Aldo R Boccaccini,et al.  Scaffolds for vascularized bone regeneration: advances and challenges , 2012, Expert review of medical devices.

[50]  C. Engh,et al.  Porous-coated hip replacement. The factors governing bone ingrowth, stress shielding, and clinical results. , 1987, The Journal of bone and joint surgery. British volume.

[51]  E Jones,et al.  Hierarchical tailoring of strut architecture to control permeability of additive manufactured titanium implants. , 2013, Materials science & engineering. C, Materials for biological applications.