Multiscale computational and experimental approaches to ... - IOS Press

Technology and Health Care 20 (2012) 363–378 DOI 10.3233/THC-2012-0686 IOS Press

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Multiscale computational and experimental approaches to elucidate bone and ligament mechanobiology using the ulna-radiusinterosseous membrane construct as a model system M.L. Knothe Tatea,b,∗ , A.E. Tamia , P. Netrebkoa , S. Milzc and D. Dochevad a Departments

of Biomedical Engineering and Mechanical & Aerospace Engineering, Case Western Reserve University, Cleveland, OH, USA b The Departments of Biomedical Engineering and Orthopaedic Surgery and the Orthopaedic Research Center, Lerner Research Institute, The Cleveland Clinic Foundation, Cleveland, OH, USA c Department of Anatomy, Ludwig Maximilians University, Munich, Germany d Department of Surgery (Laboratory for Experimental Surgery and Regenerative Medicine), Ludwig Maximilians University, Munich, Germany Abstract. An in vivo axial loading model of the rat ulna was developed almost two decades ago. As a minimally invasive model, it lends itself particularly well for the study of functional adaptation in bone and the interosseous membrane, a ligament spanning between the radius and ulna. The objective of this paper is to review computational and experimental approaches to elucidate its applicability for the study of multiscale bone and ligament mechanobiology. Specifically, this review describes approaches, including i) measurement of strains on bone tissue surfaces, ii) development of a three-dimensional finite element (FE) mesh of a skeletally mature rat ulna, iii) parametric study of the relative influence of mechanical constants and materials properties on computational model predictions, iv) comparison of experimental and computational strain distribution data, and analysis of the radius and interosseous membrane (IOM) ligament’s effect on axial load distribution through the ulna of the rat, and v) the effect of mechanical loading on transport through the IOM using different molecular weight fluorescent tagged dextrans. In the first stage of the study a computational stress analysis was performed after applying a 20 N single static load at the ulnar extremities, corresponding to values of experimental strain gauge measurements. To account for the anisotropy of the bone matrix, transverse isotraopic, elastic material properties were applied. In a parametric study, we analyzed the qualitative effect of different material properties on the global load and displacement behavior of the computational model. In a second stage, the same ulnar model used in the parametric study was extended to account for the interaction between the ulna, radius and IOM. The three-dimensional FE model of the rat forelimb confirms the influence of ulnar curvature on its deformation and underscores the influence of the radius and IOM on strain distribution through the ulna. The mode of strain, i.e. compression or tension, and strain distribution along the bone diaphysis correspond to those measured experimentally in vivo. When the radius and, indirectly, the IOM were loaded, the bone deformation shifted distally with respect to the diaphysis. In a final stage, the aforementioned ulnar model was used to study the permeability of fluorescent tagged dextrans with different molecular weights in the presence and absence of ulnar compression. Small molecular weight dextrans (3,000 Da) were distributed throughout the IOM in the absence of as well as after mechanical loading. Interestingly, no gradient in distribution was observed in either case. In contrast, very high molecular weight dextrans (1,000,000 Da) were observed only ∗ Corresponding author: M.L. Knothe Tate, Department of Biomedical and Mechanical & Aerospace Engineering, Case Western Reserve University, Cleveland, OH, USA. E-mail: [email protected].

0928-7329/12/$27.50  2012 – IOS Press and the authors. All rights reserved

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M.L. Knothe Tate et al. / Multiscale bone and ligament mechanobiology

within vascular and lymphatic spaces in the bone (as well as periosteum) and IOM, both in the absence of and after the application of mechanical loading via end load compression. Between the two extremes, both 10 and 70 kDa tracers were distributed throughout the IOM after application of compressive loading. Loading appears to dissipate the steep gradient of fluorescent 70 kDa tracer observed along the lateral surface of the unloaded IOM and its insertion into the radius and ulna. Hence, this combined computational and experimental analysis of the ulna compression model provides new insight into multiscale mechanobiology of the ulna-radius-interosseous membrane construct and may provide new avenues for elucidation of ligament’s remarkable structure-function relationships. Keywords: Bone, ligament, interosseous membrane, mechanobiology, multiscale modeling, molecular transport, tissue mechanics

1. Introduction 1.1. Role of mechanical loading in ligament biology Compared to the field of bone mechanobiology (see [1] for a recent review), elucidation of ligament mechanobiology is in its nascency [2–5]. However, given the functional and physiological role of ligaments that stabilize joints by connecting bones, elucidation of multiscale ligament mechanobiology is a key aspect to unraveling joint physiology in health and disease. Like bone, ligament exhibits the capacity to remodel, i.e. adjust mass and structure according to the prevailing mechanical stress level. Ligaments and tendons show growth in cross sectional area, as well as an increase in elastic modulus in response to exercise and opposite effects in response to immobilization [6]. Among mechanisms responsible for remodeling, direct mechanical stimulation of ligament fibroblasts by physical strain [7] and indirect mechanical shear stress imparted on cell membranes through mechanically induced interstitial fluid flow [8,9] have been postulated. Interstitial fluid transport is also particularly important given the relatively poor vascularization in tendons and ligaments, as discussed in detail below [10,11]. In addition, growth factors have been shown to modulate remodeling independent of mechanical loading [12–15], an effect that is particularly pronounced in ligaments of skeletally immature animals [13]. Furthermore, mechanical loading is a prerequisite for normal maturation and acquisition of adequate mechanical properties of the ligament [3,16]. 1.2. Ligament vascularization and healing Unlike bone, which heals without scarring, healing of tendon involves restoration of structure via “biologically and biomechanically inferior” scar tissue [2]. Bone healing involves an interplay of angiogenesis and osteogenesis that insures not only transport of cells to sites of injury but also transport of growth and other anabolic factors needed to support new tissue generation, effectively interweaving the new with the old bone [1,17–20] and thereby, enabling the creation of functionally competent repair tissue. Bone vascularization derives from the periosteum and endosteum (medullary cavity), with capillaries emanating from the outer and inner surfaces of the bone into the cortex [21–23]. In contrast, ligament vascularization derives from the “epiligamentous” (outer) surface layer and “merg[es] into the periosteum of the bone around the attachment sites of the ligament”, which contain proprioceptive nerves and exhibit high cellularity [2]. This surface layer envelops the parallel fibred ligament, comprised of collagenous matrix that is secreted by sparse ligament-specific cells, organized in a three dimensional network via long cellular processes, similar to bone [2,4,15,24]. Transverse permeability of ligament has been shown to increase and peak stress to decrease in the medial collateral ligament upon digestion of sulfated glycosaminoglycans (GAGs); while making up less than 1% of the tissue’s dry weight [26]. These data suggest that “GAGs may play a significant role in maintaining the apposition of collagen


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Fig. 1. In vivo loading model. Cyclic axial compression applied via caps (black arrows) to olecranon and flexed carpus results in cyclic tensile loading (white arrow, inset) of the interosseous ligament. Abbreviations: U – ulna, R – radius, IOM – interosseous membrane ligament.

fibrils in the transverse direction (90 degrees to the collagen fibrils, which are organized parallel to axial stretch), thus supporting dynamic compressive loads experienced by the ligament during complex joint motion.” [26,27]. 1.3. Matrix constituents, fluid and flow Also similar to bone, ligament is made up of approximately 2/3 water (wet ligament mass) and 1/3 “solid” organic components [2,4,17]. Ligament is composed of highly organized extracellular matrix, in which longitudinally arranged parallel collagen fibrils are interspaced with proteoglycans that imbibe water. Physiological strain in ligaments approaches magnitudes as high as 2.5–3% during physiological activity [28]. Much smaller magnitudes (an order of magnitude or less, i.e. 0.25–0.3%) of loading in bone provide for extensive convective interstitial fluid movement [1,17,22,23,29]. Poroelastic finite element models of interstitial fluid flow in ligaments have been developed [30,31] to investigate permeability as a function of interfibrillar spacing. However, the role of mechanical loading in ligament permeability and cell nutrition, matrix synthesis and multiscale ligament mechanoadaptation remains to be characterized. 1.4. The need for multiscale computational and experimental modeling approaches Development of models to unravel structure-function relationships in ligament is key to prevention and treatment of ligament injuries, which currently result in inferior tissue healing [2]. Multiple computational and experimental modeling approaches are necessary to elucidate the role of stress and strain as direct and indirect mechanotransducers underlying multiscale musculoskeletal mechanoadaptation. For instance, in bone, Rubin and Lanyon’s so-called “functionally isolated avian ulna model” paved the way for in vivo and in vitro models in which strain or some other manifestation of mechanical loading could be studied as a direct means for mechanotransduction at tissue and cellular length scales [1,17,32–37]. One challenge in implementing in vivo models that involve surgical intervention is that it is impossible to alter or control the mechanical environment without concomitantly changing the biological environment of a given system. For example, Turner et al.’s non-invasive four-point-bending model for in vivo studies of the rat tibia offers an elegant solution to this problem [38–46] but the model can not be classified

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as purely noninvasive due to periosteal pressure effects [47]. An experimental model developed by Torrance et al. [47] imparts an exogenous load to the proximal or distal end of the rat forelimb, i.e. applying a controlled compressive load between the olecranon and the flexed carpus, concomitant to cyclic tensioning of the IOM that joins the ulna and radius (Fig. 1). Regardless of whether invasive or non-invasive, all of these approaches are characterized by their integral, macroscopic nature, in that microscopic strains at a cellular level can only be inferred. Furthermore, in vivo studies are subject to certain limitations due to the inherent anisotropy of compact bone tissue. In contrast, in vitro studies are able to address microscopic strains at a cellular level, although extrapolation is necessary to interpret cell culture data at a tissue, organ and/or systemic level [48,49]. Hence, our goal was to combine multiscale musculoskeletal approaches to begin to elucidate ligament mechanobiology, from the organ to the molecular scale, in context of physiological musculoskeletal loading. Here, we develop and discuss multiscale computational and experimental approaches to elucidate ligament mechanobiology, using the interosseous ligament as an experimental model at the organ, tissue and super-cellular length scales. Specifically, to understand the effect of organ to tissue scale physiological mechanical loading (at the proximal and distal ends of the ulna) on ligament mechanobiology, we developed a finite element model of the radioulnar complex of the rat and effects of the IOM on load transfer between the radius and ulna. Implementing the same model in an in vivo study, we described the effect of mechanical loading on the permeability of the IOM to different molecular weight tracers. 2. Finite element prediction of radioulnar complex loading, accounting for the interosseous ligament 2.1. Background An understanding of radioulnar complex loading is not trivial due to the curvature of the ulna, the complex geometry of the ulna and radius as well as their interaction with and transfer of load through the interosseous ligament that joins them (Fig. 1). Load sharing between the ulna and radius has been shown in experimental strain gauge and finite element (FE) studies of the rat forearm. Without accounting specifically for the effect or presence of the interosseous ligament in the rat forelimb compression model, the ulna has been shown to carry 65% of the applied compressive force at the midshaft [50]. In the human forearm, the interosseous membrane (IOM) has been shown to play an important role not only in transferring load between the radius and ulna but also in maintaining the interosseous space between them. As such, it has been postulated that the IOM counteracts bending forces that result from compression of the curved ulna, providing resistance to the ulna’s lateral displacement and, thereby, decreasing the ratio of bending to compression [51,52]. Here, we develop an FE model to analyze the effect of the radius and interosseous membrane on axial load distribution through the ulna. 2.2. Approach and modeling methods The right limb of a skeletally mature (retired breeder) Sprague Dawley female rat was imaged in a high resolution computed tomography (µCT 40, Scanco Medical, Bassersdorf, Switzerland); 875 slices containing the sequential cross sections of ulna and radius were acquired longitudinally in 36 µm intervals with a resolution of 512 512 pixels. Thirty six slices were selected to generate the three dimensional mesh, i.e. one slice every 900 µm. The selected slices were cropped and imported using a custom written software to trace the endosteal and periosteal contour of each cross section. The resulting text files


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Table 1 Different ranges of mechanical properties used in the computational model parametric study Young’s moduli [GPa] [Gpa] Poisson ratio Shear moduli [GPa]

Elong Etrans1 Etrans2 ν12 ν13 ν23 G12 G13 G23

Main model 21.3 13.7 13.7 0.4 0.3 0.3 5 7 7

Isotropic 21.3 21.5 21.5 0.4 0.4 0.4 7 7 7

Highly anisotropic 42.6 13.7 13.7 0.4 0.2 0.2 5 7 7

(four for each cross section: ulna and radius periosteal and endosteal contours) containing the x and y coordinates were processed with an algorithm written using Matlab (Matlab 6.1, The MathWorks Inc., Natick, MA), to define an even distribution of points along the contours and to insert the z coordinates. The obtained text files served then as input file for the nodal coordinates of the solid mesh created with ABAQUS (ABAQUS 6.1, HKS Inc., Pawtucket, USA). The IOM was meshed manually because no information about the location of this soft tissue was available from the CT-scans. For that purpose we used the cross-sections from rats of exactly the same origin (i.e. same vendor, some age and same shipment) that were used in a parallel study carried out by our group. Comparing four sets (i.e. four forelimbs of four different rats) of 30 polymethylmethacrylate-embedded cross sections sectioned (Leica saw microtome SP 1600, Leica, Nussloch, Germany) at intervals of 500 µm, areas of contact between the IOM and ulna were identified and included in the solid mesh of the bone-ligament model described above. A stress analysis was performed using the “solid” element type (8 node hexahedral elements, quadratic displacement) of the ABAQUS finite element package. Stress and strain were calculated after imposing a single static deformation at the ulnar extremities as a result of a 20N load, thus corresponding to values of experimental strain gauge measurements performed in our group and reported in the literature [47], albeit higher than those reported in the previously published FE analysis of the ulna compression model in conjuction with adaptation to fatigue loading [50]. The tissue was modeled as a continuum, thereby neglecting the microscopic architecture of cortical bone. However, to take into account the anisotropy of the bone matrix, elasticity material parameters describing transverse isotropy were applied [53] (Table 1). In a parametric study (3 cases), we analyzed the relative effect of different mechanical properties on the global load – displacement behavior. The basic model was compared with two extreme conditions: isotropic material properties and marked anisotropy. In the first case the elastic moduli were set the same as the longitudinal elastic modulus of the main model, and in the second case the longitudinal stiffness was doubled. To account for the interaction between the ulna, radius and IOM, the ulnar model was adapted from that utilized in the parametric study. Boundary conditions were defined by constraining displacement in all directions for the nodes on the outer-most contour of the olecranon, and in the transverse direction for the nodes at the distal extremity, where the load was applied. The IOM was modeled using two-dimensional membrane elements that transmit purely tensile forces. Furthermore, thickness was defined for each membrane element. We investigated the influence of the radius and the IOM on stress and strain patterns through the ulna for i) axial load application to the distal end of the ulna, and ii) homogeneously load application to the distal ends of ulna and radius. For each case, the proximal end of the radius was either totally constrained or allowed to move freely in the longitudinal direction (Table 2).

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M.L. Knothe Tate et al. / Multiscale bone and ligament mechanobiology Table 2 Four scenarios used for predictive computational modeling, representing two loading and two boundary conditions. Abbreviations: U – ulna, R – radius, fx – fixed, fr – free Loaded bone(s) ulna (U ) ulna and radius (UR )

Boundary condition radius fix ( fx) radius free ( fr)

Fig. 2. Three dimensional (3D) mesh of ulna (orange), radius (blue) and interosseous membrane (green) of the rat forearm. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-2012-0686)

Fig. 3. Deformation of the ulna under axial load: distribution of strain in the longitudinal direction. Colors indicate strain (see legend, Fig. 5), with red depicting areas in tension and blue areas in compression. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-2012-0686)

2.3. Radioulnar complex loading predictions in context of the interosseous ligament Application of a static compression between the olecranon and the flexed carpus of the rat forelimb results in bending of the ulnar diaphysis, with maximal strain in the distal most region and relatively small magnitude compressive strains in the distal and proximal ends of the ulna (Figs 2 and 3, Table 3). A range of strains, up to several thousand microstrain (Fig. 4, Table 3), are observed in the cross sectional plane of the ulna, with predominantly compressive strains along the medial and tensile strains along the lateral aspects, respectively. Accounting for anisotropic material properties, transverse properties appear to exert less influence on mechanical deformation for a given compressive load than do longitudinal properties. Specifically, the transverse stiffness exerted no significant influence on either distribution or magnitude of strain in longitudinal direction. In contrast, doubling the Youngs modulus in the longitudinal direction reduced longitudinal strain by 41–44%. Interestingly, for the maximal load simulated, 20N, the FE model predicts a maximal displacement of 160 µm in the axial direction along the distal most contour, where the load was applied, which is significantly lower than that measured experimentally. During strain gauge measurements, the displacement of the actuator was approximately 400 µm, suggesting that the


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Table 3 Peak strains in axial direction resulting from the different loading scenarios of Tables 1,2, where compression and tension are indicated by negative (−) and positive (+) strain modes, respectively Elastic properties Strain mode Max Strain (με)

Main model − + 4300 2700

Isotropic − + 4300 2700

Highly Anisotropic − + 2400 1600

Fig. 4. Cross section of the ulna showing the medio-lateral strain gradient, with strain values depicted in the inset. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-2012-0686)

majority of the displacement is translated into deformation of soft tissue between the loading cups and the ulna. Furthermore, in the distal diaphysis where largest deformations occur under compression, the cross section’s neutral axis traverses from lateral-caudal to medio-cranial through the medullary cavity, due to the irregular shape of the bone and its intrinsic curvature. Of particular interest for the current study, for all loading and boundary conditions studied (Table 2), the radius and the interosseous membrane reduced stress and strain on the ulna by structurally stiffening the forelimb. The location of highest strain was almost identical to that in the analysis of the ulna alone and the distribution of compressive and tensile strain were similar to those found in the analysis of the ulna alone as well. The lowest deformation on the ulna was observed for the case where the load was applied homogeneously, distributed over the radius and ulna, and the radius was not allowed to displace (corresponding to physiological constraint of the humerus). Conversely, the highest ulnar deformation was induced when the load was applied only on the ulna and the radius was free to move proximally (calculated peak values for compressive and tensile strains, Table 4). The radius shows a curvature similar to the ulna, and therefore its deformation generated a pattern of strain distribution on the lateral and medial side comparable to those described for the ulna. Loading of the radius resulted in lower strains on the ulna, due mainly to the decrease in force applied directly on the ulna (half of the load was carried by the radius). The compressive strain was higher on the medial surface of the ulna, while the tensile strain was higher on the lateral surface of the radius. Constraining the radius proximally also reduced the strain on the ulna. Strains in the interosseous ligament are an order of magnitude smaller than those in the ulna and radius (Fig. 5). 2.4. Conclusions In summary, a new understanding of mechanical loading in the ulnar-radius-interosseous membrane construct has been achieved using the finite element modeling analysis. As previously noted, end loading of the ulna results in a combined compression-bending mode loading of the ulna and radius. Strains estimated by this technique were lower than those measured experimentally in ex vivo preparations. This

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M.L. Knothe Tate et al. / Multiscale bone and ligament mechanobiology Table 4 Peak values for compressive (−) and tensile (+)bone strains for the simulated scenarios depicted in Table 2. Abbreviations: U – ulna, R – radius, fx – fixed, fr – free Cases (cp. Table 2) Max strain (με)

– +

U fr 3400 1650

U fx 2500 850

UR fr 2200 500

UR fx 1500 350

Fig. 5. Cross-sections of ulna and radius at the location of maximal strain values in the distal diaphysis, resulting in order of magnitude smaller interosseous ligament strains. (Colours are visible in the online version of the article; http://dx.doi. org/10.3233/THC-2012-0686)

raises the possibility that we cannot understand loading of the ulna without taking into consideration effects of the radius and interosseous membrane on load distribution. Insights from this study may open up interesting avenues to further understanding of biomechanics of syndesmotic bones, e.g. radioulnar and tibiofibular complexes in humans. 3. Permeability of the interosseous ligament under ulnar compression loading 3.1. Background In a parallel study, we assessed permeability of the interosseous ligament to defined molecular weight tracers in vivo, as a function of mechanical loading. 3.2. Approach and experimental methods Loads were applied using the aforementioned rat ulna axial end loading model [47,50,54,56], which engenders cyclic tensile loads in the interosseous ligament, as described in the previous section. To assess selective permeability, fixable dextran-fluorophore conjugates (Molecular Probes, OR) and Procion Red tracer (Imperial Chemical, London) were used with molecular weights ranging 300 to 2,000,000 Da (Table 5). All studies were carried out with approval from IACUC. Sprague Dawley rats, weighing 215–240 g, were anaesthetized (0.5–3% isofluorane inhalation), while maintaining body temperature at 37◦ C. Prior


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Table 5 Summary of fluorescent tracers studied, their excitation/emission spectra, molecular weights and Stokes’ radii (∗ ), calculated after [57] Fluorophore Procion red Fluorescein Tetramethylrhodamine Tetramethylrhodamine Fluorescein Tetramethylrhodamine

Excitation/emission wavelengths 568 nm/ 580–620 nm 488 nm/ 510–550 nm 568 nm/ 580–620 nm 568 nm/ 580–620 nm 488 nm/ 510–550 nm 568 nm/ 580–620 nm

Molecular weight (Da) 300 Da 3,000 10,000 70,000 5 × 105 2 × 106

Stokes’ radius 4–5 Å 16.1 Å∗ 27.3 Å∗ 63.9 Å∗ 150.9 Å∗ 276.9 Å∗

to mechanical loading, a solution of fluorescent labeled dextrans in 0.9% saline or 0.8% Procion Red tracer in deionized water was injected slowly (0.1 ml/min) into the lateral tail vein at a volume ratio of 0.01 ml tracer solution per g body weight, according to published protocols [23]. Immediately after tracer injection, the right ulna was loaded in end-load bending with a 14 N load (peak surface strain approx. 0.3%) for 36 cycles at 4 Hz. The left ulna served as an unloaded contralateral control. Immediately after loading, the animals were euthanized and the ulnae and radii were carefully explanted and fixed in 40% ethanol (Procion Red) or 4% paraformaldehyde in 0.1 M phosphate buffer (Dextran tracers). All tissues were embedded in PMMA and undecalcified cross sections from the middiaphysis were prepared. Specimens were observed using confocal laser scanning microscopy (CSLM), with the excitation and emission spectra adjusted for each fluorophore used (Table 5). In addition, for each fluorophore, the microscope settings were held constant from specimen to specimen. Baseline control specimens from euthanized healthy adult rats were processed and examined using the same procedures. Confocal micrographs allow for qualitative assessment of size-dependent transport of the tracers in the ligament. For the smallest 300 Da tracer there was very high penetration through the ligament as well as the surrounding muscle and bone in both loaded and control limb. Loading led to increased and more homogeneous distribution of the tracer in the ligament. The 3,000 Da tracer showed high penetration of the ligament and surrounding tissue (Figs 6, 7A). Loading enhanced penetration of the tracer through the matrix (Figs 6, 7B). The 10,000 Da tracer showed moderately high penetration in ligament as well as in surrounding muscle and bone (Fig. 6E), with increased and more uniform penetration in the ligament of loaded limb (Fig. 6F). The 70,000 Da tracer shows much lower overall penetration with a minute amount located marginally and near the blood vessels in the unloaded limb (Fig. 6G). Mechanical loading resulted in an enhanced and more homogeneous distribution in the loaded limb (Fig. 6H). The 500,000 Da tracer remained mostly vessel-bound and did not penetrate the matrix of the ligament on the unloaded side. On the loaded side, there was slight penetration of this tracer in the vicinity of interosseous vessels but not in the IOM. The largest 2,000,000 Da tracer remained vessel-bound and did not penetrate the ligamentous matrix in either the loaded or unloaded limb (Figs. 6, 7CD). 3.3. Conclusions Taken together, our novel results demonstrated that ligament permeability increases upon mechanical strain and that the vessel-derived components (in our study – the molecular tracers) distribute throughout the ligament in uniform manner without the formation of a steep gradient. This suggests the following mechanism: as a result of the tensile mechanical stress, the vessels, which are in the epiligamentous layer or within the deeper sheets, are compressed, thereby releasing biochemical cues into the collagenous matrix of the ligament. Our novel observation regarding the lack of a steep molecular gradient within the

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Fig. 6. Confocal images of interosseous ligament in transverse plane with 20x objective (R – radius, U – ulna). High penetration of 3,000 Da tracer in matrix of unloaded ligament (A) was further enhanced by loading (B). Ultra high MW tracer 2,000,000 Da shows no permeation in matrix of both unloaded (C) and loaded (D) ligament. Interface between edge of ligament in transverse plane and apposing muscle fibres (MF) is depicted by the dotted line. Vascular canals (V) and further muscle fibres (MF) are visible on opposite side of ligament in transverse plane.

Fig. 7. Digital zoom of images from Fig. 6 showing higher magnification of tracer distribution with respect to particular musculoskeletal tissues and structures. The 3,000 Da tracer appeared pooled in certain areas of the ligament (perilymphatic spaces) and weakly distributed outside of vascular channels in the bone cortex (A, arrows) but was more distributed in the ligament, with concentration toward the ligament insertion to bone (blue arrows, B) and in the periosteocytic spaces of bone (white arrows, B) after loading. Similar effects were observed with the ultra high MW 2,000,000 Da tracer, but the tracer appeared not to penetrate the matrix of the ligament or the bone. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-2012-0686)


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Fig. 8. Confocal images of interosseous ligament in transverse plane with 20x objective (R – radius, U – ulna). Compared to unloaded limbs (E) and (G), respectively, loading dramatically increased permeation for 10 kDa (F) and 70 kDa (H) tracers. Interface between edge of ligament in transverse plane and apposing muscle fibres (MF) is depicted by the dotted line. Vascular canals (V) and further muscle fibres (MF) are visible on opposite side of ligament in transverse plane, although some MF were lost in processing for histology. Furthermore, these sections are in a somewhat distal or proximal plane (in or out of plane of page, closer to the junction of the radius and ulna) compared to the sections of Fig. 6, where the IOM is thinner.

ligament provides compelling evidence for efficient fluid flow in the ligament in the ligament interfibrillar spacing, allowing a quick penetration of biochemical cues even to the deeper cellar networks. Taken together, these data provide unique insight into the effect of mechanical strain on the permeability and cell nutrition of the ligament. 4. Discussion In this paper, we review computational and experimental approaches to elucidate the applicability of the ulna end loading compression model for the study of multiscale bone and ligament mechanobiology. A computational stress analysis of the radioulnar complex after application of static compression between the olecranon and the flexed carpus of the rat forelimb predicted maximal strain in the distal most region of the ulna, up to several thousand microstrain, with predominantly compressive strains along the medial and tensile strains along the lateral aspects, respectively. Interestingly, for all loading conditions studied, the radius and the interosseous membrane reduced stress and strain on the ulna by structurally stiffening the forelimb without alteration of strain distribution. The ligamentous tissue of the interosseous membrane showed permeability across two orders of magnitude molecular weight dextrans, from 3 to 70 kDa, with increased distribution in the ligament of the loaded limb. Very high molecular weight dextrans (500–2,000,000 Da) were observed only within vascular spaces including lymphatics, both in the absence of and after the application of end load compression. Taken together, this combined computational and experimental analysis of the ulna compression model provides new insight into

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multiscale mechanobiology of the ulna-radius-interosseous membrane construct and may provide new avenues for elucidation of ligament’s remarkable structure-function relationships. A three-dimensional finite element model of the rat forelimb was developed to investigate the deformation induced through end-load compression of the ulna, i.e. with the in vivo axial loading model, and to compare the calculated strain with strain gauge measurements from previous experimental studies. The results confirm the influence of the curvature of the ulna on its deformation, and also show the influence which the radius and interosseous membrane may have on the resulting strain. A continuum model was employed for the simulation of stress and strain through the cortical bone of the rat forelimb. The periosteal and endosteal contours of ulna and radius were accurately reconstructed from CT scans, and the interosseus membrane was defined by its insertion points on both bone surfaces. Neither the articular cartilage nor viscoelastic effects were taken into account: this is reasonable in the case of a static loading with force control. The predicted change in mode and relative magnitude of strain as a function of the location along the contour corroborate values resulting from in vivo measurements [47,56,58–61]. Maximal compressive strains were experienced on the medial surface of the ulna and maximal tensile strains on the lateral surface. Based on experimental data, it was thought that peak strains are engendered closer to the middiaphysis. Based on the data from this computational model, axial compression applied at the extremities of the ulna generates maximum deformation in a more distal part of the diaphysis. Assuming that the experimental data are correct, the location of maximal strain at the middiaphysis of the ulna cannot be explained by the intrinsic curvature of the ulna alone. Rather, surrounding anatomic structures may also play a role in strain distribution. Indeed, when the radius and, indirectly, the membrane were loaded, the deformation shifted to a more central location of the diaphysis. Despite limitations inherent to the computational model, studies on the human forearm show that the interosseous membrane transfers force from the radius to the ulna [11,51,62], whereby the distal radius carries almost 70% of the load and the proximal radius and ulna carry 50% respectively. More recent studies in human radioulnar joints show that an intact IOM provides superior joint stability in the neutral position while exerting no significant effect on joint stability in pronated and supinated forearm positions [63]. With regard to strain magnitude, in the longitudinal direction the degree of anisotropy influences strains less than stiffness, when considering the isolated ulna model. In the combined model (i.e. ulna, radius and IOM) strains are lower than those measured experimentally using strain gauges. Material property definitions were based on measurements on ex vivo, frozen [64] specimens reported in the literature [38,65]. Thus, the stiffness of the in vivo, fluid-perfused, warm tissue may be lower, which would be expected to cause a larger strain. The relative permeability of ligament was somewhat surprising given its lack of vascularity compared to, e.g. bone. Furthermore, similar trends in transport were observed in ligament compared to the pericellular space of bone. Namely, small molecular weight dextrans (3,000 Da) were distributed throughout the ligament in the absence of as well as after loading; no gradient in distribution was observed in either case. In contrast, very high molecular weight dextrans (500,000–1,000,000 Da) were observed only within vascular spaces including lymphatics, both in the absence of and after the application of end load compression. Between the two extremes, both 10 and 70 kDa tracers were distributed throughout the ligament after application of compressive loading. Loading appears to dissipate the steep gradient of fluorescent 70 kDa tracer observed along the lateral surface of unloaded ligament and its insertion into the radius and ulna. Lymph flow has been shown previously to be elevated with muscle activity, where muscle fiber stretch expands lymphatic spaces [66]; whether end load compression of the ulna results in muscle relaxation, in turn compressing lymphatic spaces in our experimental model, is not yet known.


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These data are consistent with Kanda et al.’s report that horseradish peroxidase (40 kDa) permeability is reduced in the anterior cruciate ligament of immobilized rabbit knees [67] and Weiss et al.’s study of GAGs’ role in decreasing transverse permeability of the medial collateral ligament [26,27]. The current paucity of studies investigating ligament permeability not only provided the impetus for the current study but also emphasizes the need to better understand the role of transport in ligament mechanobiology and healing. For study of musculoskeletal mechanobiology in general, and ligament mechanobiology in particular, the axial loading of the rat ulna offers many advantages over exogenous loading approaches [64,68–70]. First, the model is noninvasive in that it requires no surgical intervention. Secondly, axial loading of the curved ulna mimics the loads occurring during normal physiological activity. Finally, in comparison with the four-point bending model discussed previously, the location of the loading points with respect to the region of interest offers a higher degree of non-invasiveness, preventing artifacts in the biological response to hyper- and hypophysiological loads [42,47]. In the past decades, the ulna compression model has been used to study effects of strain magnitude, rate, frequency, distribution, and range, as well as the effect of number of loading cycles on growth, modeling and remodeling processes in long bones of skeletally immature and mature animals [54,58–61,71–74]. Recently this model has been successfully extended to recreate a consistent and reproducible fracture following fatigue [56], thus expanding the applicability of this experimental design to address other important aspects of bone behavior. Although strain gauge measurements have been made in and ex vivo [46, unpublished data from our group], these data give a measurement of strain at one location on the surface to which the gauge is applied and are highly dependent on alignment with respect to the neutral axis of the bone as well as practical issues such as adherence of the gauge to the bone surface. Computational predictions improve understanding of i.a. strain distribution through the ulna, and are important to infer actual strains imparted at a tissue and cellular level. In summary, a new understanding of bone and ligament mechanobiology in the ulnar-radiusinterosseous membrane construct has been achieved using multiscale computational and experimental approaches. As previously noted, end loading of the ulna results in a combined compression-bending mode loading of the ulna and radius. Strains estimated by this technique were lower than those measured experimentally in ex vivo preparations. This raises the possibility that we cannot understand loading of the ulna without taking into consideration effects of the radius and interosseous membrane on load distribution. Furthermore, end load compresssion of the ulna distributes uniformly molecular tracers through the ligament spanning the ulna and radius. This may open up interesting avenues to elucidate mechanobiology not only of ligaments but also of syndesmotic bones, e.g. radioulnar and tibiofibular complexes in humans. Acknowledgments We acknowledge Bruno Koller, PhD, from Scanco Medical (Bassersdorf, Switzerland) for his support and help in acquiring the CT-scans. In addition, we would like to acknowledge Professor Peter Niederer for his input and contributions to the work completed during Andrea Tami’s doctoral dissertation. We thank Jon Klingensmith (Vascular Imaging Group, Dep. Biomedical Engineering, Lerner Research Institute, The Cleveland Clinic Foundation, Cleveland, Ohio, USA) for sharing his software for tracing the contours of our images. This work was supported by the Swiss National Science Foundation, The Cleveland Clinic Foundation, and the Alexander von Humboldt Foundation.

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