Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

Highlights - A representative volume element (RVE) size of 2 ×2 × 2 mm3 is sufficient to represent bovine trabecular bone microstructure and corresponding fluid flow properties. - Using periodic boundary conditions, with a mesh size >125,000 elements, provides the most accurate values for respective bone permeability data. - Comparison of bone specimens with respect to porosity does not provide accurate information about permeability. - For similarity between specimens based on mechanical properties, both magnitude of principal permeability and anisotropic ratio, need to be similar. - Comparison of permeabilities of our bovine sternum bone specimens with other bone samples from the literature, showed excellent agreement. Abstract In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens. For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 −8 m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies

Biofabrication of human articular cartilage: a path towards the development of a clinical treatment

Cartilage injuries cause pain and loss of function, and if severe may result in osteoarthritis (OA). 3D bioprinting is now a tangible option for the delivery of bioscaffolds capable of regenerating the deficient cartilage tissue. Our team has developed a handheld device, the Biopen, to allow in situ additive manufacturing during surgery. Given its ability to extrude in a core/shell manner, the Biopen can preserve cell viability during the biofabrication process, and it is currently the only biofabrication tool tested as a surgical instrument in a sheep model using homologous stem cells. As a necessary step toward the development of a clinically relevant protocol, we aimed to demonstrate that our handheld extrusion device can successfully be used for the biofabrication of human cartilage. Therefore, this study is a required step for the development of a surgical treatment in human patients. In this work we specifically used human adipose derived mesenchymal stem cells (hADSCs), harvested from the infrapatellar fat pad of donor patients affected by OA, to also prove that they can be utilized as the source of cells for the future clinical application. With the Biopen, we generated bioscaffolds made of hADSCs laden in gelatin methacrylate, hyaluronic acid methacrylate and cultured in the presence of chondrogenic stimuli for eight weeks in vitro. A comprehensive characterisation including gene and protein expression analyses, immunohistology, confocal microscopy, second harmonic generation, light sheet imaging, atomic force mycroscopy and mechanical unconfined compression demonstrated that our strategy resulted in human hyaline-like cartilage formation. Our in situ biofabrication approach represents an innovation with important implications for customizing cartilage repair in patients with cartilage injuries and OA

Handheld Co-Axial Bioprinting: Application to in situ surgical cartilage repair

Three-dimensional (3D) bioprinting is driving major innovations in the area of cartilage tissue engineering. Extrusion-based 3D bioprinting necessitates a phase change from a liquid bioink to a semi-solid crosslinked network achieved by a photo-initiated free radical polymerization reaction that is known to be cytotoxic. Therefore, the choice of the photocuring conditions has to be carefully addressed to generate a structure stiff enough to withstand the forces phisiologically applied on articular cartilage, while ensuring adequate cell survival for functional chondral repair. We recently developed a handheld 3D printer called Biopen . To progress towards translating this freeform biofabrication tool into clinical practice, we aimed to define the ideal bioprinting conditions that would deliver a scaffold with high cell viability and structural stiffness relevant for chondral repair. To fulfill those criteria, free radical cytotoxicity was confined by a co-axial Core/Shell separation. This system allowed the generation of Core/Shell GelMa/HAMa bioscaffolds with stiffness of 200KPa, achieved after only 10seconds of exposure to 700mW/cm2 of 365nm UV-A, containing \u3e90% viable stem cells that retained proliferative capacity. Overall, the Core/Shell handheld 3D bioprinting strategy enabled rapid generation of high modulus bioscaffolds with high cell viability, with potential for in situ surgical cartilage engineering

Multiscale coupling of X-ray physics and engineering mechanics, for supporting Computed Tomography-based orthopedics and bone remodeling

Abweichender Titel laut Übersetzung der Verfasserin/des VerfassersZsfassung in dt. SpracheObwohl die Computertomographie die Medizin, und dort insbesondere die biomechanische und werkstoffbezogene Forschung, durchdrungen hat, bleibt ein Grossteil der in CT-Bildern enthaltenen physikalischen und chemischen Informationen ungenutzt. Stattdessen werden Grauwerte von CT-Aufnahmen normalerweise direkt, mittels empirischer Methoden, mit Massendichten oder mechanischen Größen in Verbindung gebracht. Allerdings hat eine geeignete Kombination von strahlenphysikalischen und kontinuumsmikromechanischen Gesetzen in Verbindung mit der Finite Elemente Methode (Kapitel 1 liefert einen Überblick ber entsprechende Grundlagen) durchaus das Potential, die zuvor genannten, gleichsam versteckten physikalischen und chemischen Informationen zu verwenden, um Aufschlüsse über Gewebszusammensetzung und -mikrostruktur, deren heterogene Verteilung über das untersuchte Organ oder Implantat, und daraus folgende mechanische Eigenschaften zu erhalten. Die Kapitel 2 bis 5 beschreiben zunehmend ausgereifte Schemata zur Übersetzung von CT-Daten in mechanische Kenngrößen, welche auf verschiedenen Längenskalen auf verschiedene Biomaterialien und Organe angewendet werden. Kapitel 2 beschreibt die Bestimmung der Voxel-spezifischen Mineral-, Kollagenund Wassergehalte aus CT-Daten, auf Basis einer gewebsunabhängigen Regel für die Zusammensetzung extrazellulären Materials (J. Theor .Biol. 287, 115, 2011). Entsprechende Volumsanteile dienen als Input für eine mikromechanische Repräsentierung von Knochengewebe, zwecks Lieferung von Voxel-spezifischen Steifigkeitstensoren. Verwendung dieser Tensorfelder in einer FE Simulation macht deutlich, dass dieWahl adäquater Materialeigenschaften sowohl die Verzerrungsenergie in der extrazellulären Matrix massgeblich beeinflusst (und damit die vorhergesagte Stetigkeit des Organs), als auch den Diskretisierungsaufwand für konvergente Lösungen festlegt. Kapitel 3 ist ein Beitrag in Richtung quantitativerer Auswertungsmethoden für CT-Daten: Ein neuer Ansatz erlaubt die Rckbestimmung der für eine CTAufnahme verwendeten massgeblichen Photonenenergie, aus der Existenz eines eindeutigen Zusammenhanges zwischen Grauwerten und Röntgen- Abschwächungskoeffizienten, und der Energieabhängigkeit letzterer. Dies wird zur Bestimmung der Nanoporositätsverteilungen von resorbierbaren Tri-Kalzium-Phosphat-Keramiken für den Knochenersatz verwendet. Dieser Ansatz wird in Kapitel 4 modifiziert und weiterentwickelt, zwecks Studiums von klinischen CT-Daten eines Lendenwirbels. Dies liefert Voxel-spezifische Massendichten, sowie Mineral- und Kollagengehalte, und dann mittels eines kontinuumsmikromechanischen Modells (Ultrasonics 54: 1251, 2014), Voxel-spezifische Elastizitätstensorkomponenten als Input für ein FE Modell. Letzteres erlaubt die Bestimmung von typischen Spannungszuständen unter normaler physiologischer Belastung, welche dann zur Sicherheitsanalyse des Organs herangezogen werden. Dazu werden sie proportional gesteigert und ihre Auswirkungen auf die Knochenmikrostruktur mittels eines Mehrskalen-Elastoplastizitätsmodells untersucht: Bei Reißen der Kollagenfasern ist die Knochenmaterialfestigkeit erreicht. Zugehörige Simulationen mit räumlich gemittelten Materialeigenschaften unterschätzen das Bruchrisiko beachtlich, während die Berücksichtigung heterogener Materialeigenschaftsverteilungen realistische Sicherheitswerte liefert. Kapitel 5 behandelt einen analytischen Mehrskalenansatz, welcher mittels Mikromechanik die Stimulation von Knochenzellen quantifiziert, sowie die daraus erwachsenden Umbauten des Gewebes. Kombination dieses Verfahren mit den in Kapiteln 2 bis 4 beschriebenen Entwicklungen lässt neue Formen simulationsunterstützter Therapiemethoden in der Orthopädie erhoffen.While Computer Tomography has become a standard tool in clinical biomechanics and biomaterials studies, much of the physical and chemical information contained in such scans remain unused. Instead, the grey values of the Computed Tomographs are, as a rule, directly related, by some empirical functions, to mass density or to mechanical properties of interest. However, a suitable combination of X-ray physics fundamentals, multiscale continuum micromechanics, and Finite Element analyses, as reviewed shortly in Chapter 1, indeed bears the potential for transforming the aforementioned, somehow hidden information, into tissue composition and microstructure, its heterogeneous distribution across investigated organs or implants, and the corresponding mechanical properties resulting from microscopic interaction of material constituents across several length scales. Chapters 2 to 5 contain corresponding examples for increasingly mature CT-to-mechanics conversion schemes, dealing with bone biomaterials and bony organs at different scales. Chapter 6 provides an outlook for extending such studies even to evolving biological systems, by combining trabecular bone micromechanics with advanced bone remodeling algorithms. In Chapter 2, the voxel-specific volume fractions of mineral, collagen, and water are derived from the measured X-ray attenuation information quantified in terms of grey values , by accounting for tissue-independent bilinear relations between mineral and collagen content in extracellular bone tissue (J. Theor. Biol. 287: 115, 2011). The aforementioned volume fractions enter a micromechanics representation of bone tissue, so as to deliver elastic properties in terms of voxel-specific stiffness tensors. The insertion of these properties into a FE simulation reveals that the choice of appropriate material properties influences the strain energy density in the extracellular matrix (governing the stiffness of the organ), and also affects the discretization level needed for obtaining converged numerical results. In Chapter 3, driving the field of Computed Tomography towards more quantitative, rather than qualitative, approaches, a new evaluation method is presented, which uses the unique linear relationship between grey values and X-ray attenuation coefficients, together with the energy-dependence of the latter, in order to identify the average X-ray energy employed in the scanner, and the nanoporosity of a tricalcium phosphate scaffold. This approach is extended in Chapter 4 by re-constructing the linear relation between the clinically accessible grey values making up a Computed Tomograph and the X-ray attenuation coefficients quantifying the intensity losses from which the image is actually reconstructed. Therefore, X-ray attenuation averaging at different length scales and over different tissues is combined with recently identified -universal- composition characteristics of the latter. This gives access not only to the normally non-disclosed X-ray energy employed in the CT-device, but particularly to in vivo, patient- and location-specific bone composition variables, such as voxel-specific mass density, as well as mineral and collagen contents. This is shown by example of a third lumbar vertebra. The corresponding vascular porosity values enter a continuum micromechanics model for bone (Ultrasonics 54:1251, 2014), which thereupon delivers voxel-specific elastic properties. The latter are mapped onto a 3D Finite Element mesh developed from the same patient data. The stress states resulting from corresponding Finite Element analyses are inputs for a six-scale strength upscaling model for bone, so as to compute element-specific proportionality factors to material yield or material failure. The implementation of patient-specific material properties highlights that simulations with averaged properties underestimate the fracture risk in bone, while the new approach reliably considers the effect of the material heterogeneities arising from bone remodeling triggered by everyday spinal loading; and is also relevant for even more heterogeneous, pathological cases. The last work, presented in Chapter 5, is using a multiscale analytical approach, which combines bone structural information at multiple scales to the remodeling cellular activities, and more precisely the mechanical stimulus sense by the osteocytes, in order to form an efficient, accurate, and beneficial framework for the prognosis of changes in bone properties due to aging or pathologies. This latter approach, once combined with the CT-based technique covered in Chapters 2 to 4, holds the promise to establish new forms of simulation-supported therapeutic activities in orthopaedy.22

Effect of polyester and Plaster of Paris casts on determination of volumetric bone mineral density assessed by Peripheral Quantitative Computed Tomography (pQCT)

Peripheral quantitative computed tomography (pQCT) is a non-invasive, low-radiation tool for measuring volumetric bone mineral density. It has potential for use in fracture healing applications; however, the unknown attenuation effects of cast material on peripheral quantitative computed tomography have contributed to its limited use in this area. The effect of two common cast materials, polyester and Plaster of Paris was investigated by performing both in vitro and in vivo studies. The in vitro study tested the effect of increasing layers of cast material on bone density measurements performed on a hydroxyapatite phantom. Cast thickness was directly associated with a reduction in bone mineral density, with twelve layers of polyester and Plaster of Paris resulting in a 0.55 and 2.21 % decrease in bone density measurements. Precision error in situ with polyester cast material was 0.71 %, and 2.31 % with Plaster of Paris cast material. The in vivo study comprised a prospective trial with 28 healthy adult participants to evaluate the effect of the two cast materials. Trabecular bone mineral density was increased by 0.5 % in the presence of a polyester cast and decreased by 4.22 % in the presence of a Plaster of Paris cast. Cortical bone mineral density was decreased by 3.46 and 5.54 % for polyester and Plaster of Paris, respectively. This study quantified the effects of orthopaedic casts on pQCT-derived bone parameters. The results suggest applicability of commonly utilised cast materials in combination with pQCT to assess fracture healing

Numerical calculation of permeability of periodic porous materials: Application to periodic arrays of spheres and 3D scaffold microstructures

In this paper, an efficient numerical method is proposed to calculate the anisotropic permeability in porous materials characterized by a periodic microstructure. This method is based on pore‐scale fluid dynamic simulations using a static volume of fluid method. Unlike standard solution procedures for this type of problem, we here solve an average constitutive equation over both fluid and solid domain by use of a subgrid model to accurately capture momentum transfer from the fluid to solid interface regions. Using numerical simulations on periodic arrays of spheres, we first demonstrate that, by using the subgrid interface model, more accurate results can be produced, for the velocity and pressure fields, than via more conventional approaches. We then apply numerical upscaling over the unit cell to calculate the full anisotropic permeability from the pore‐scale numerical results. The obtained permeability values for a variety of periodic arrays of spheres in different arrangements and packing orders are in good agreement with semianalytical results reported in literature. This validation allows for the permeability assessment of more complex structures such as isotropic gyroid structures, or anisotropic cases, here modeled in their simplest form, the ellipsoidal inclusion

Comparison of the moulding ability of Plaster of Paris and polyester cast material in the healthy adult forearm

Objectives: To quantify the moulding ability of Plaster of Paris and polyester cast materials as assessed by the novel use of peripheral quantitative computed tomography. Methods: A prospective crossover study was performed in 25 healthy volunteers aged 18–65 years. Participants’ non-dominant wrist was immobilized using a synthetic polyester cast followed by a Plaster of Paris cast with three point moulding to simulate reduction of a dorsally angulated distal radius fracture. The novel use of peripheral quantitative computed tomography was used to measure the closeness of fit of each cast on an axial tomographic slice. Results and conclusions: Plaster of Paris casts were able to achieve a closer mould than polyester when measured between the bone and the cast (p = 0.002), as well as between the skin and the cast (p = 0.001). There was no difference when stratified on BMI. Using pQCT assessment, a closely moulded fit was able to be more consistently achieved when using Plaster of Paris when compared to polyester casts of the distal radius

The application of pulsed electromagnetic fields (PEMFs) for bone fracture repair: Past and perspective findings

Bone fractures are one of the most commonly occurring injuries of the musculoskeletal system. A highly complex physiological process, fracture healing has been studied extensively. Data from in vivo, in vitro and clinical studies, have shown pulsed electromagnetic fields (PEMFs) to be highly influential in the fracture repair process. Whilst the underlying mechanisms acting to either inhibit or advance the physiological processes are yet to be defined conclusively, several non-invasive point of use devices have been developed for the clinical treatment of fractures. With the complexity of the repair process, involving many components acting at different time steps, it has been a challenge to determine which PEMF exposure parameters (i.e., frequency of field, intensity of field and dose) will produce the most optimal repair. In addition, the development of an evidence-backed device comes with challenges of its own, with many elements (including process of exposure, construct materials and tissue densities) being highly influential to the field exposed. The objective of this review is to provide a broad recount of the applications of PEMFs in bone fracture repair and to then demonstrate what is further required for enhanced therapeutic outcomes. © 2018, Biomedical Engineering Society

Modal analysis of nanoindentation data, confirming that reduced bone turnover may cause increased tissue mineralization/elasticity

It is widely believed that the activities of bone cells at the tissue scale not only govern the size of the vascular pore spaces (and hence, the amount of bone tissue available for actually carrying the loads), but also the characteristics of the extracellular bone matrix itself. In this context, increased mechanical stimulation (in mediolateral regions of human femora, as compared to anteroposterior regions) may lead to increased bone turnover, lower bone matrix mineralization, and therefore lower tissue modulus. On the other hand, resorption-only processes (in endosteal versus periosteal regions) may have the opposite effect. A modal analysis of nanoindentation data obtained on femurs from the Melbourne Femur Research Collection (MFRC) indeed confirms that bone is stiffer in endosteal regions compared to periosteal regions (E̅endost = 29.34 ± 0.75 GPa > E̅periost = 24.67 ± 1.63 GPa), most likely due to the aging-related increase in resorption modeling on endosteal surfaces resulting in trabecularization of cortical bone. The results also show that bone is stiffer along the anteroposterior direction compared the mediolateral direction (E̅anteropost = 28.89 ± 1.08 GPa > E̅mediolat = 26.03 ± 2.31 GPa), the former being aligned with the neutral bending axis of the femur and, thus, undergoing more resorption modeling and consequently being more mineralized. © 2018 Elsevier Lt