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Strain distribution of intact and fractured human humeri was evaluated after simulation of three common physiological load situations for two different bone qualities. The muscle attachments were considered as simple points (nodes) where the corresponding loads (vectors) acted. The advantage of this simplified load representation is a fast evaluation of the muscle direction while its effect on the bone-joint strain behavior can still be retrieved. Its principal disadvantage is, however, to induce elevated punctual deformations in the nodes where the muscles were attached, including a small area of influence delimited for the position of the Gauss points8 used in the finite element analysis to evaluate the strain field. However, this study has demonstrated that the influence of the bone quality is more important for the straining than the theoretical effect of overestimation produced by the muscle attachments. This may be concluded because in the physiological situations analyzed, regions of higher deformations were observed at the bone surface in zones without muscles directly attached compared to regions with muscle attachments. This finding implies that the susceptibility of a region to suffer fractures correlates more closely with the local bone quality than with muscle attachments on it, and it could explain why fracture patterns are hardly predictable based only on a study of their local physiological load condition. As a result, this could clarify why in elder patients, whose bone quality is frequently affected by osteoporosis, spontaneous fractures could occur without the incidence of a predetermined or critical physiological situation.
However, a more realistic model should consider muscle attachments as surfaces of loads and the internal reconstruction of the trabecular bone network. Maybe the pattern of the straining, in the zones of influences where the muscles are attached, could be affected due to the possibility that such a zone could have a poor bone quality at the cortical but could be connected via trabecular network with a zone of a better mechanical quality. In this case its strain pattern could be better in comparison with the hypothetical situation, in which this cortical region has an acceptable mechanical quality but lacks a continuous trabecular network (osteoporosis). Considering a surface of load to simulate muscle attachments with a three-dimensional trabecular network reconstruction can show how large this effect will be. Thus, as was demonstrated in this study, the mechanical configuration (strain pattern) for particular patients under the same physiological conditions was primarily affected by bone quality.
In the model only proximal muscles were considered. This fact produced, as observed in Fig. 3.1, a remaining component of moment in each one of the three principal load directions in the distal region. However, the humeral bone should be in equilibrium and the sum of loads and moments in the center of rotations of bone should be zero (center of the bone head, and condyles). Since the CT scans of the bone were performed in the proximal region, information about the distal region was not available. Therefore the bone was extended and the points of rotation were translated to two points localized approximately at the same length as the condyle, but near the centerline of the bone shaft as encountered in reality. Thus, to achieve the moment of equilibrium an increase of the force was necessary. Equilibrium was then reestablished by imposing a pair of forces producing moments with the same magnitude and inverse directions as the remaining moments. This method generated a local distortion of the area containing the points of load application. However, this effect disappeared approximately in the first third of the distal humerus. So, this effect does not have any influence on the results of the straining obtained in the proximal region. The results and conclusions determined in this study are thus valid and sufficient to learn more about the bone – joint mechanics evaluated in intact and fractured humeri bones.
Differentiation was simulated by variation of the elastic modulus of Young. It is known that a relation between this mechanical parameter and the healthy state of the cartilage exists. Osteoarthrosis (OA), a common disease that affects the cartilage, could for example cause a diminution of the tensile properties of this tissue as shown in Table 4.1.
These variations have been associated with a disruption in the collagen fibrils in the solid matrix (Mow and Ratcliffe, 1997). Therefore, the selection of the elastic modulus of Young to represent the state of repair in osteochondral defects appears to be appropriate. Additionally, in an indirect manner it demonstrates the internal state of the collagen matrix by transmitting the mechanical signals after load application.
Moreover, most of the published tissue differentiation models used change Young’s elastic modulus as the parameter to represent growth or resorption during healing. This feature allows a comparison between the reported findings of these studies and the those encountered in this project.
In this project ABAQUS was used to simulate healing using the finite element method. The elastic modulus of Young was defined as a field variable. This implies that the mechanical stimulus for differentiation of each tissue is newly calculated when all tissue stiffnesses making up the joint region have been actualized after an iteration. However, in vivo studies do not determine the time of occurrence or the manner in which differentiation for each tissue type sets in. Moreover, to analyze how these changes take place requires considering a microenvironment that affects cells. Such environmental conditions at this microlevel are not yet precisely known. To assume continuous fields representing the joint and changing their mechanical properties at each tissue type was sufficient to demonstrate the hypotheses formulated in this project. In vivo experiments of osteochondral healing demonstrated that different tissues appear to have different rates to achieve each healing phase. The healing velocity depends on the type and number of cells in each tissue and their connectivity to cells of other tissues. In the created tissue differentiation model, the implementation of factors for growth and resorption calculated from numerical analysis of histological sections reproduce this fact.
More recently, interdisciplinary research of osteochondral healing is aimed to clarify how this cell communication pathway is initiated, maintained and when required, disabled. Simultaneously over the last years, the attention given to mechanical conditions influencing these cell communication-response pathways to stimulate healing has increased. In this project the tissues making up the joint were modeled as a continuum and its mechanical behavior was assumed to follow the rule of mixtures (a rule to explain the mechanical behavior of materials constituted by a fluid and a solid phase). This approach has been traditionally used in soil mechanics and more recently has been employed to describe and simulate the mechanical behavior of biphasic tissues.
To simulate differentiation, the biphasic mixture model of Mow and co-workers (Huang, et al., 2001;Huang, et al., 2003;Mow, et al., 1989) was used in this project. This model supposes cartilage to be a biphasic incompressible material composed of a solid and a fluid phase. This treatment is consistent with the cartilage composition (approx. 80% water, and 20% collagen matrix). Recent models have been published representing cartilage even as a triphasic material in which not only mechanical but also electrochemical events are taken into account. However, sufficient information that allows the usage of the corresponding electrical properties of the cartilage for simulation of healing still does not exist.
In the Mow theory, when a continuum is exposed to compressive loads, the fluids inside (e.g. 80% of cartilage consist of water) are exudated, thereby producing high hydrostatic pressures. This hydrostatic pressure is a mechanical response that counteracts the external acting load to avoid possible damage of the solid phase by overloading. This behavior has been observed in the cartilage, too. The fluid phase appears to be an important factor regulating the mechanical chondrocyte response under compressive loads. The biphasic behavior of cartilage could be analyzed using concepts from soil mechanics. Parameters defining biphasic cartilage properties have been well documented and measured in in vitro experiments. Thus, more realistic material properties for cartilage (biphasic) and the employment of a widely used theory (soil mechanics) to explain cartilage behavior were used in the present project.
Osmotic pressure is not taken into account in this theory. Basic concepts concerning the interaction of the ion charges between the collagen matrix and chondrocyte membrane has only recently been understood. Some cellular influx and efflux pathways have been identified. However, it is still unknown how mechanical signals in these pathways are transduced into biological responses. Experimental models and in vitro measurements of cell cultured chondrocyte stimulated with different patterns of mechanical loads (Lee, et al., 2002;Smith, et al., 2004;Suh, et al., 1995) (e.g. intermittent hydrostatic pressure, shear stresses) showed different responses in dependence of the type of load used. Intermittent hydrostatic pressure appears to increase matrix protein whereas shear stresses induce molecular changes related to apoptosis (Smith, et al., 2004). Mow and his group have proposed a triphasic theory or rule of mixtures to explain cartilage behavior. The absence of standard parameters (e.g. electrical response or its interaction with mechanical signals) describing triphasic composition of cartilage implies a difficulty in the incorporation of this mechanical behavior into a continuous joint model. Therefore, its usage in a differentiation model with predictive capabilities is obviously still not feasible.
Biphasic material properties on the other hand already reproduce the healing process observed in histology. Perhaps the use of a triphasic theory could be first tested experimentally and then incorporated into a computational approach in the future. Models evaluating the microenvironment of a chondrocyte or a determined tissue type as a triphasic material could be developed and compared with a biphasic one.
In order to guarantee convergence during simulated healing, an equation to calculate the minimal time limit allowed in an increment has been employed. This equation is recommended in the user manual of ABAQUS for models with highly non-linear mechanical behavior. The appropriate selection of this minimal time turned out to be important, because it avoids formation of singular points in the solution and thereby avoids the implementation of additional smoothing algorithms during healing simulation. Up to now, reported tissue differentiation models to simulate fracture healing (Lacroix and Prendergast, 2002) and osteochondral healing (Kelly and Prendergast, 2004;Kelly and Prendergast, 2004) used such smoothing algorithms in order to avoid drastic changes in the evolution of the tissue stiffness. Although the effect of this simplification on the healing pattern has not been clarified. Such a “tissue average” behavior does not exist in vivo.
In clinical practice, the influence of mechanical conditions on healing has until recently not been considered to be important, although some research groups have studied this topic alone in particular (Li, et al., 2001;Quinn, et al., 1998;Waldman, et al., 2003;Wang, et al., 2002;Wong and Carter, 2003), established a link between biomechanical and biochemical loads (Lai, et al., 1998) or determined a relation between biomechanical loads and gene activity (Valhmu, et al., 1998).
The influence of mechanical conditions during healing of osteochondral defects by animal models was corroborated; and at a more profound level, the microenvironment of chondrocytes cultures stimulated under controlled mechanical loads (bioreactors) was analyzed (Chen CT, et al., 2003;Martin, et al., 1999). In vitro studies have shown that cyclic compressive loading on chondrocytes appears to increase hydrostatic pressure, matrix deformation and fluid flow. These changes in the extracellular environment stimulate aggrecans and protein synthesis. In the present project, simulated compressive loads were applied and the corresponding tissue deformations, which are mechanically related to the strain fields, determined. The mechanical conditions imposed at the initial defect situation were maintained during repair. Gait analysis in the animal model demonstrated that the load transmission after and before defect creation was almost the same with a slight reduction during the first 6 days after surgery. Therefore no variations in the initial load were performed during healing simulation. Although the contact boundary condition during repair was not determined in the animal experimentation, it was supposed to be constant (frictionless) during simulated healing.
This study demonstrates the importance of mechanical conditions for understanding and evaluating healing, and hence justifies the usage of a differentiation model able to evaluate the influence of each parameter individually or simultaneously, which is impossible using in vitro experiments only.
The cases were selected according to the following criteria: 1. To answer controversial questions, such as the maximum defect size able to start spontaneous healing or the consequence of increased thickness, 2. To understand why osteochondral defects occur more frequently on specific geometrical surfaces and 3. To include recent treatments for osteochondral defect healing, such as the usage of defect fillings. After the validation of the tissue differentiation model, these selected examples showed the versatility of the algorithm developed in this project.
The selection of a specific area, TA in fig 2.6, to quantify tissues during healing allows a comparison of the effect of the mechanical conditions on repair for the different analyzed cases. Data from these areas complement the qualitative analyses (comparison of simulated healing to histology) giving more complete information about the healing state and its behavior after changes in the mechanical boundary conditions. The representation of the tissues is based on a continuous field in which the strain field was measured. This representation could even be extrapolated to show the active regions during healing without the requirement of a detailed geometrical representation of the subchondral bone or the different structural-related zones of the cartilage (superficial, middle and deep zone).
As shown in Figures 3.15 to 3.17, the algorithm is able to handle different ranges of stiffnesses for each tissue type. These stiffnesses can then be assigned to a specific tissue type more precisely. In this way, the effect of the cancellous bone quality on the quantity and quality of the newly differentiated cartilage can be determined. This ability to predict a widely heterogeneous distribution mitigates the possible effects on the simulated healing when an initial homogeneous characterization is used for the material properties of the model (instead of different stiffnesses as a function of cartilage depth).
This study has demonstrated that the usage of an algorithm to analyze the influence of mechanical conditions on healing can be applied successfully to simulated clinical situations. The principal advantages of the algorithm are 1. It allows the determination of the straining of each tissue type necessary for healing with adequate mechanical properties, which cannot be determined in vivo, and 2. It is able to predict the type and localization of each tissue during healing. On the other hand, a disadvantage of the model is the lack of a more precise correspondence between the increment step and the real time in which healing occurs. Although by comparing the histomorphometric analysis and the quantification of the simulated healing, it was possible to establish a correspondence between simulated iterations and the real time in which healing occurred during animal experimentation (days, weeks), it is not certain that the same relation may still be valid after months or years.
Generally, algorithms to simulate healing could be tested by their application to an intact situation. In such a case it is expected that remodeling should not take place. However, because this model uses the intact situation as equilibrium state, the minimum principal strains used as a basis for comparison with the current strain values in the defect model or evaluated model are the same.
For the selected bone specimens, the influence of bone quality and physiological loads on the magnitude and distribution of tissue strain was quantified. The strain magnitudes are influenced principally by bone quality and to a lesser degree by activity (0° neutral position, 90° abduction, 90° forward extension). The small average difference of only ± 6 % between the measured and the calculated stiffnesses shows that numerical tools can be used to analyze the influence of bone quality of fractured and intact humeri under physiological loads. Maximum strain values were found for 90° abduction. The strain magnitudes for this arm position were considerably larger (25%) in the weak bone with low values of density distribution (average 0.26 gm/cm2, DEXA) than in the reference humerus (average 0.49 gm/cm2, DEXA).
Comparing the total group of humeri, the specimen with low-density values (DEXA= 0.26gm/cm2) showed a low axial stiffness and average torsional stiffness. In contrast, the specimen with a better density distribution showed an average axial stiffness and a high torsional stiffness. The range of measured straining could be considered to represent the maximum and minimum strain values possible for different bone qualities under physiological loads. However, the analysis of more specimens could still allow a better description of the spectrum of the straining.
Even though the analyzed implant (LCP-PH) was quite flexible compared to conventional osteosynthetic devices for the proximal humerus (T-plate, nails), cancellous tissue straining increased due to osteosynthetic treatment. The weak bone stock was found to be more strained than the healthy counterparts. In this respect implant design considerations should not only account for implant stabilization in healthy but also in weak bone stock. Normally this aspect has not been considered in the pre-clinical evaluation of osteosynthese. Also specific or individual models created from QCT data allow to choose osteosynthetic devices which could guarantee an adequate load transmission avoiding strain peaks in the surrounding tissues and lead to homogeneous straining of the remaining trabecular network, especially in osteoporotic patients. Bone models that assume homogeneous material property distributions are not able to show critical conditions or regions of strain concentration. To know the localization of such regions could become important in the study of bone mechanics and their interaction with a selected predesigned osteosynthese. As a result, the consideration of bone density distribution for modeling bones appears to be important.
The study of physiological loads in human bones improved our understanding of their mechanical behavior, taking specific characteristics such as geometry and bone quality into consideration (Maldonado, et al., 2003). In the majority of biomechanical studies so far, the analysis of the different physiological activities was performed without consideration of bone quality. Normally the bone is modeled as being homogeneous, isotropic and with a linear elastic behavior defined by a unique value of Young’s modulus.
In the first part of this project, an analysis of different physiological loads using the finite element method in two humeral bones with inhomogeneous density distribution was performed. The results showed that the influence of the bone quality on the strain pattern was significant. Under the same mechanical conditions, a poor bone quality produces a higher strain concentration than a bone with a more favorable density distribution. After comprehension of the mechanical constrains which could influence bone behavior, the study of osteochondral defects at the joint was performed. Having demonstrated the influence of mechanical conditions on bone behavior, it was necessary to establish the local effects of mechanical conditions on healing, for example those of joint geometry.
In order to estimate the local effects on healing (joint curvature, defect geometry), osteochondral defects resembling the local joint geometry observed in the experiments were analyzed. The fact that different amounts of hyaline and fibrous tissue were formed when changes in the defect size, local joint geometry or stiffness of the defect fillings were made is evidence of the influence of mechanical conditions on healing.
Although ground reaction forces of all animals were registered during healing, its complex musculoskeletal load situation remains unknown. However, chondrocyte activity is principally promoted by compressive loads and therefore the assumption of only axial forces loading the model was considered to be sufficient to simulate osteochondral healing. How chondrocytes may respond under compressive loads is summarized in a theory supporting the tissue differentiation model developed in this project.
Stem cells operate as mechanotransducers that are differentiated and develop under hydrostatic pressures and high deformations. Since the first phase of the healing process of an osteochondral defect is characterized by an high percentage of fluids, which allows higher deformations and which are rich in osteoprogenitor and stem cells, it is imaginable that cells could respond to the corresponding mechanical conditions: higher pressures (80% water under compressive loads) as a reaction mechanism and higher deformations as consequence of the action of external loads. Due to the dependence of the defect size, only a limited number of cells exists. These cells feel the dynamically acting external loads so they necessarily need an evolution into a tissue with better stiffness, which allows transmission of the external loads without collapse of the newly formed tissues. Thereby stem cells are transformed to connective tissue, which is able to fulfill these specific mechanical conditions: The fluids in the soft tissues react to hydrostatic pressure and simultaneously allow maximal deformations. In this case an unstructured and laxed connective tissue is differentiated first to a structured and stiffer tissue, whose task is to transmit the external loads more efficiently, and finally, as response to the high pressure, into a tissue rich in fibroblast. This evolution of mechanical reaction could explain why the first cartilage formation is observed at the bottom and at the defect walls: The fluids inside the newly formed tissues under compression are moving laterally in a similar way as in the case of confined compression, moreover the deformations are maximal at the defect vertex (geometry, drastic changes in the elastic Young’s modulus). This combination of higher pressures and deformations stimulates differentiation from connective tissue to fibrous tissue. In this sense it is possible to identify characteristic values of hydrostatic pressures and deformations for each tissue type that allows differentiation of each tissue into the next stiffer one. In this manner, the elastic modulus of Young for each tissue will be increased or decreased depending on the current state of hydrostatic pressures and deformations. Cartilage consists of 80% water, and therefore, both the influence of the hydrostatic pressure and the action of mechanical deformations are important factors to be considered while analysing osteochondral repair. The cartilage cells seem to react faster in the first phases of the healing process, and decrease their rate of differentiation when the basis of the defect is filled with a stiffer tissue.
The numerical analysis of histological sections turned out to be a helpful tool to understand the biological response of the tissues under specific mechanical conditions. Additionally, the determination of factors for growth and resorption from in vivo data as well as the points of tissue-specific trilinear curves allowed a matching of simulated healing to the observed in vivo repair. The use of numerical analysis of histological sections represents an advance in the development of tissue differentiation models by reducing the necessity of initial assumptions (hypothetical factors for differentiation) or the use of additional procedures (smooth functions, stiffness averages, etc.).
A relation between the range of strains calculated during healing and the differentiated tissue type observed in histology was established. Hence, strain concentrations were registered at the interface cartilage-connective tissue and at the defect basis, in the same regions as those where the first newly differentiated tissues were observed in vivo.
Between the 4th week and the 6th week, a zone of high straining was observed at the resorption region in the defect basis. This could indicate the necessity to define another tissue type between connective tissue and the fibrous tissue. Between the 6th and the 12th week, another recognizable straining zone was detected between the newly formed cancellous bone tissue and the hyaline cartilage indicating that the definition of another transition - tissue type between these tissues, that is the pre-cancellous bone - was appropriate.
In the 12th week, the strain concentration at the interface between the newly formed cartilage and the remaining cartilage tended to disappear indicating the reestablishment of the continuity in the mechanical properties of the hyaline cartilage. The possible knowledge of the range of strains at each time step allowed the determination of a quantitative relation between the material properties and the mechanical behavior of each tissue type. The permanent strain concentration at the interface defect cartilage at the 4th and 12th week disappeared when, after centrifugal filling, the remaining connective tissue at the defect center was replaced by fibrous tissue. According to the simulation of bone marrow areas in the subchondral region, the strain distribution at the defect basis seems to be reduced in dependence on the size of the marrow areas. A reduction of 17% in the compressive strains at the defect basis was measured between the 6th and the 12th week.
The geometry of osteochondral defects appears to influence the pattern of cartilage repair. In no case was a total restoration of the defect observed. An increase in the defect depth leads to minor formation of hyaline cartilage than when the defect width was increased.
Some in vivo studies have already been performed in order to study the influence of defect size on healing (Brown, et al., 1991;Jackson, et al., 2001;Shahgaldi, 1998). While Brown and his group studied the influence of the defect width, Jackson und Shahgaldi have analyzed spontaneous repair in large defect models. These studies have established that certainly a maximal dimension (depth or width) exists in which after an initial defect filling with fibrous tissue, damage at the cartilage and hence, later even in the subchondral region is observed. In the case of large defects a direct proportional relation between depth and damage was established (large defects appear to produce more damage). Maybe this is related to the number of cells or BMU necessary to remodel and to repair injured tissues. Considering this possibility, the latest techniques for the treatment of large defect areas include the usage of biomaterials alone or in combination with cells to promote cartilage and subchondral bone restoration. Although the effect of the biological process on healing has not been taken into account in the differentiation model, it was possible to predict a low percentage of hyaline cartilage formation and a degradation of the surrounding subchondral bone for the initial model situation in agreement with in vivo observations. These results suggest that structural and mechanical conditions are important and could be responsible for the type of the tissues formed during healing. Mechanical conditions affecting healing should be evaluated for treatment of osteochondral defects.
The fact that no hyaline cartilage formation was observed when its thickness was increased, or that a minor percentage was formed after geometrical changes of the defect implies that the selection of a treatment should take into account the localization, size and shape of the defect and the joint region in which the defect is localized. Additionally, the lack of hyaline cartilage formation warned about the importance of an appropriate selection of the region in which the defect could be surgically created in animal experimentation. The usage of a region with a very thin cartilage thickness, for example, could produce a faulty healing outcome by fast transmission of the compressive loads to the subchondral bone, which could reduce the mechanical stimulus.
This study has demonstrated that changes in the local joint surface curvature alter the process of healing. The mechanical environment around the defect during healing causes strong variations in the mechanical signal, in accordance with changes in the joint curvature. Additionally it was shown that the simulated healing after defect filling using a biomaterial with the same mechanical stiffness as the native subchondral bone proved to be better than in the case of a biomaterial with a reduced stiffness (50% of the native bone). The effect of the stiffness of a predesigned biomaterial to fill the defect could be used as a parameter to analyze the healing outcome after biomaterial implantation.
Minimum principal strains selected as stimulus together with the usage of a factor (growth and resorption) for differentiation managed to reproduce the healing pattern observed in histology. In fact, the model agreed qualitatively with the histology and was quantitatively comparable to the histomorphometrical analysis (Duda, et al., 2005).
During healing, material frontiers are continuously in movement, reducing gradually the required stimulus to achieve the equilibrium state. Therefore the apparent “rate of healing” was reduced approximately after iteration 41, when the defect was filled to a higher percentage (Fig. 3.14). This behavior was comparable to the in vivo situation, where a higher percentage of the defect was filled between the 4th and the 6th week and was completely filled between the 6th and the 12th week. Thus, apparently the rate of filling depends on the current healing state: it was higher during the first weeks and was reduced at the final stages of healing.
The quality of the cartilage and its stiffness vary according to its localization, as indicated by others (Krishnan, et al., 2003;Laasanen, et al., 2003;Mow and Ratcliffe, 1997;Nieminen, et al., 2004;Wu and Herzog, 2002). So, different joints in the same individual entity (human or animal) have shown local variations in structure (geometry and material properties) and thereby in mechanical behavior. However, until today the more frequent occurrences of osteochondral defects at convex joint surfaces have not been related to the local mechanical environment. Although few clinical reports discuss the low rate of occurrence of osteochondral defects on concave surfaces, it is generally associated with mechanical factors without further explanation (Exner, et al., 1991;Hjelle, et al., 2002;Ueblacker, et al., 2004). This study is the first to demonstrate that this may be related to the mechanical stimulus for healing. In fact, the quantity of hyaline cartilage formation during healing simulation was affected by changes in the joint surface curvature (Fig. 3.14, Fig. 3.15, Fig. 3.16, Fig. 3.17).
After redefinition (subdivision) of the original stiffness ranges for the newly formed tissues in the defect area, it was demonstrated that a relation between the quality of the newly formed cancellous bone and its slope of differentiation (increments required to jump to another tissue type) and the quantity of the differentiated hyaline cartilage exists. Apparently changes in the joint curvature produce alterations in the differentiated cancellous bone tissue and in the rate of differentiation for the soft tissues. Higher quantities of differentiated tissues with better quality were formed under slower rates of differentiation. Concave joint surfaces showed a slower rate of differentiation for the cancellous bone and a higher quantity of hyaline cartilage with stiffnesses near to the upper limit (better quality) than observed in the case of convex joint surface (Fig. 3.15 vs. 3.16). Since the mechanical boundary conditions in a model with a flat joint “curvature”, taking into account the localization of the initial defect, are more similar to the convex joint curvature, the healing response observed for a flat model was comparable with the convex model. However, the rate of differentiation for the fibrous cartilage tissue was slower in the flat model. It is possible that a strong correlation between the mechanical conditions and the rate of differentiation for each tissue exists. If the mechanical conditions can be regulated during the healing process, the rate of differentiation could be regulated, too. Thereby the quantity and the quality of the newly formed hyaline cartilage, which is essential to avoid damage of the joint, could be improved. The mechanical response of different joint curvatures and therefore the quantity of the differentiated tissues appears to be remarkably different under the same loads. The algorithm allowed quantifying such differences (rate of differentiation, quantity of formed hyaline cartilage), establishing a link between the mechanical response of a specific joint curvature and the obtained simulated healing.
A continuity of material properties in the layers under an osteochondral defect, which operates as a basis for the newly formed cartilage, is important for the development of a tissue with adequate mechanical quality for load transmission. This process is indicated by the quantity of the hyaline cartilage formed during the defect healing (Fig. 3.20; Fig. 3.21). In fact, hyaline cartilage formation occurs earlier (approx. iteration 11), i.e., when plug and cancellous bone have the same stiffness as when a considerable difference in their elastic Young’s modulus exists (Fig. 3.20). Although the resorption was less than 5% at the subchondral bone basis of the defect for both models, the fact that this value was slightly higher in a plug with the same mechanical quality than the cancellous bone could imply the necessity for further analysis. Perhaps the definition of border conditions between the plug and the cancellous bone could be improved, for example the press-fit force, applyed to implant the plug, could be defined in dependence on the stiffness of the defect filling used or the plug porosity could be modeled heteregoneus depending on its stiffness distribution. The consideration of this last parameter should affects the response of the interface at the defect basis. A relation between the resorption areas and healing outcome (hyaline cartilage formation) could be thereby established.
Some differentiation models have been developed to study osteochondral healing (Duda, et al., 2005;Kelly and Prendergast, 2004), fracture repair (Bailon-Plaza and van der Meulen, 2001;Claes and Heigele, 1999;Lacroix and Prendergast, 2002) or remodeling around implants (Kerner, et al., 1999;van Rietbergen, et al., 1993). In these studies the influence of biomechanical conditions in combination with biological growth factors affecting healing have been established, as shown by Bailon-Plaza and co-workers. The healing patterns reported in the literature (Jackson, et al., 2001) were similar to the one obtained in the animal model of Bail et al. (Bail, et al., 2003). The resorption region or subchondral bone remodeling at the defect basis was a typical characteristic observed during the first stages of osteochondral repair (Jackson, et al., 2001). A differentiation model for osteochondral healing simulation should thus be able to reproduce this feature as well. The tissue differentiation model presented in this thesis is the only one that reproduces this effect. The predicted resorption agrees very well with the corresponding experiments.
Some studies have analyzed the usage of scaffolds and the incorporation of growth factors to generate collagen type II during osteochondral repair, which is present in hyaline cartilage. Lee J.W and co-workers (Lee, et al., 2004) found that TGF-ß1, BMP-2 and growth differentiation factor 5 (GDF–5) could “induce rapidly” type II collagen expression. Indrawattana (Indrawattana, et al., 2004) and Ma (Ma, et al., 2003) reported similar results using different growth factors applied alone or in combination. These studies have demonstrated the possibility of improving the quality of the repaired tissue. However, there is not enough information that can be incorporated in a tissue differentiation model to predict its effect on osteochondral repair. Using in vitro culture and by developing sophisticated bioreactors, the effect of mechanical conditions on chondrocytes has clearly been demonstrated: The type of load and form of application influences the viability of chondrocytes. Shear stresses, and overloading for example are responsible for apoptosis or cell degeneration whereas intermittent compressive loads appear to promote differentiation (Bueno, et al., 2004;D'Lima, et al., 2001;Smith, et al., 2004). However, a difficult point in this in vitro evaluation is the measurement of isolated effects for each load condition. It is very difficult not only to apply shear alone or bending alone without the incidence of an unexpected load component, but it is also possible that measurements in the media in which cells are stimulated to proliferate may induce an additional mechanical stimulus whose effect on differentiation can be determined only with difficulty.
The differentiation model developed in this project has so far not been used in the specific case of isolated cell groups. However, this point is discussed in order to show that maybe the study of mechanical conditions on healing through the usage of such models seems to be more promising for determining which mechanical environment has a considerable effect to improve healing.
In a pilot study fluid flow and pore pressure, used as mechanical stimulus for differentiation, were incapable of reproducing the qualitative and quantitative healing process observed in vivo lacking the characteristic resorption region at the defect base observed in histology. Only minimum principal strains were able to cause this effect of resorption. The mechanical stimuli of the fluid related parameters were obviously not sufficient to produce resorption, generating an imbalance between the resorption and the growth region defined in the trilinear curve. Hence, the consideration of only compressive loads acting at the joint might be insufficient to recreate the complex mechanical environment present in a joint. Additionally, the amount of growth stimulus was higher in comparison with the values obtained when minimum principal strains were used as stimuli producing an effect of apparent “accelerated” healing. In fact, defect filling was completed after only 25 iterations, which was very quick in comparison with 166 iterations required in the case of minimum principal strains. However, with improved boundary conditions for the fluids these parameters should principally reproduce resorption as well.
An aspect to be considered is the relation between strain and permeability during healing simulation. Permeability is a property that involves microstructural aspects of cellular activity as shown in recent investigations. Its effect on the mechanics of the joint tissues is measurable and well known. Changes in the cartilage’s permeability have a remarkable influence on its capacity to support compressive loads by generating hydrostatic pressures. Some researchers concluded that for degenerative diseases, changes in the porosity of the cartilage tissue are associated with losses of the water content, which leads to a reduction in its permeability. The consideration of this parameter in the development of a tissue differentiation model turned out to be very important in analyzing how changes in the elastic properties occur, inducing changes in the strain fields. These changes can be considered as an indirect indicator of healing. In the present study a correspondence between the state of healing and the current permeability was established. However, for two reasons, it was not possible to find a more exact relation between the state of tissue permeability and its healthiness. First, the material properties during healing were not measured in the animal experimentation, and second, because permeability was defined in dependence of the current elastic modulus of Young at each iteration and not with the current strain at each material point. Some studies have focused on establishing a relationship between strains and permeability based on in vitro experiments allowing the development of a theory of this biological process. In initial results, an explicit mathematical relation of these factors was proposed. However, further in vitro studies would be necessary to implement the corresponding equations in a tissue differentiation model.
The resorption regions in the cancellous bone are strongly influenced by variations in the joint curvature. Based on the quantity of the newly formed cartilage, this study has shown that concave curvatures could provide a more favorable environment for healing compared to convex surfaces. The concave model showed minor areas of resorption forming during healing simulation. The fact that areas of cartilage and fibrous tissue observed in the cancellous bone during defect healing are higher in a convex curvature compared with the concave one might suggest that mechanical conditions are responsible for the creation and maintenance of these regions (Z1, Z2 and Z3: Fig 3.18). Perhaps a relationship exists between the mechanics of differentiation, the mechanical quality of the underlying subchondral bone and the quantity of hyaline cartilage that could be differentiated during spontaneous repair.
Prendergast developed a differentiation model to simulate fracture healing. His group made an extension of the initial proposed model and applied it to analyze osteochondral healing treated with grafts. The related work was published some months after the first results of this thesis. Prendergast used his differentiation model to investigate the possible optimal mechanical properties of a material to be used as defect filling. The differentiation model proposed by the Prendergast group presents not only some weaknesses in the concept but also lacks relevant characteristics observed in histological analysis of animal models. Comparing the results obtained in this work to the model proposed by Kelly and Prendergast, a predetermined combination of fluid velocity and shear strains to predict the differentiated tissue during repair results not only in a strong dependence on the initially selected material properties but also, as was our own experience using fluid flow as mechanical stimulus, makes it impossible for the model to reproduce resorption at the defect basis. Additionally, the usage of two parameters (fluid velocity versus shear strains) as stimuli for tissue differentiation during healing makes it difficult to extrapolate such a linear relation between the fluid velocity and the shear strain to an in vivo situation. The tissue differentiation model used in the present study has shown that the usage of only minimum principal strains as mechanical stimuli achieves an acceptable correlation with the histomorphometrical data and reproduces the histological findings in animal models of osteochondral repair. Additionally, our differentiation model allows a large spectrum of strains to be defined only by the initial configuration. A redefinition of the limiting values for strains associated with specific tissue types during the run of the model is thus not necessary.
Huiskes’s model has been widely used to study bone behavior. Its description of growth and remodeling simulation during and after medical device implantation has shown results very close to the observed findings in medical practice. In this study it was demonstrated that cartilage differentiation certainly could be explained as well according to the same principles as those developed by Huiskes with only some modifications. An important point was the determination of factors for growth and resorption from numerical analysis of the histological sections which were used in combination with a mechanical stimulus as proposed by Huiskes’s to simulate differentiation. The selection of compressive strains as mechanical stimulus indubitably demonstrated a strong influence in the course and rate of the healing outcome.
The models analyzed in this thesis should also help to explain why osteochondral defects are more frequently reported in joints with convex surfaces. In fact, it was found that the local mechanical environment affects the type of tissues after differentiation tissues. A validated tissue differentiation model is able to predict how the mechanical stiffness of a biomaterial influences the quality and quantity of the newly formed tissues during healing, allowing to choose the appropriate biomaterial with matching mechanical properties for joint functionality.
Patient specific models taking into account the different regions, thicknesses and radii of the cartilage for joint reconstruction, as well as the specific physiological loads could be helpful in developing a more profound link between the mechanical conditions and the complex biological process during osteochondral healing.
Alternatively it could be possible to determine for a specific patient (given geometry, density bone distribution, and cartilage mechanical properties) the external load required to obtain the greatest percentage of hyaline cartilage formation. In this case, physiological load conditions must be simulated.
To date, some methods exist to determine the state of the repair process such as arthroscopic examinations to verify if the defect is filled or if the graft is integrated with the surroundings tissues. Latest techniques include biomarkers in joint fluids in combination with MRI to check joint damage, quantity of collagen type II, or to look for the presence of macromolecules such as a cartilage oligomeric protein, which is normally interpreted as pathological changes during healing (Poole, 2003), as indirect indicators of the healing state. However, in practice it should be desirable to develop technical procedures to measure the mechanical properties of engineered cartilage during healing in order to compare and improve the treatment of osteochondral defects.
8 Gauss points: points of interpolation inside of a finite element in which the equilibrium equation are applied.
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