Individual-specific multi-scale finite element simulation of cortical bone of human proximal femur

Abstract

We present an innovative method to perform multi-scale finite element analyses of the cortical component of the femur using the individual’s (1) computed tomography scan; and (2) a bone specimen obtained in conjunction with orthopedic surgery. The method enables study of micro-structural characteristics regulating strains and stresses under physiological loading conditions. The analysis of the micro-structural scenarios that cause variation of strain and stress is the first step in understanding the elevated strains and stresses in bone tissue, which are indicative of higher likelihood of micro-crack formation in bone, implicated in consequent remodeling or macroscopic bone fracture. Evidence that micro-structure varies with clinical history and contributes in significant, but poorly understood, ways to bone function, motivates the method’s development, as does need for software tools to investigate relationships between macroscopic loading and micro-structure. Three applications – varying region of interest, bone mineral density, and orientation of collagen type I, illustrate the method. We show, in comparison between physiological loading and simple compression of a patient’s femur, that strains computed at the multi-scale model’s micro-level: (i) differ; and (ii) depend on local collagen-apatite orientation and degree of calcification. Our findings confirm the strain concentration role of osteocyte lacunae, important for mechano-transduction. We hypothesize occurrence of micro-crack formation, leading either to remodeling or macroscopic fracture, when the computed strains exceed the elastic range observed in micro-structural testing.

Introduction

The structure of bone changes across macro- and micro-structural scales, affording bone seemingly contradictory characteristics of rigidity, strength, toughness, flexibility, lightness and porosity. Macro-level finite element (FE) models of the human femur, based usually on scanning by one or the other of magnetic resonance imaging (MRI) or quantitative computed tomography (QCT), have addressed the trabecular and cortical components, supplemented in the case of trabeculae by microQCT [1], [2], [3], [4], [5], [6], [7], [8]. Because cortical bone forms 80% of the adult skeleton and makes a corresponding contribution to bone strength [9], [10], [11], we focused the multi-scale modeling on the cortex of the human femur. The computation of material properties from the grey scale values, calibrated during imaging preparation, in terms of bone mineral density (BMD), yields isotropic material properties of the macro-structural model. However, morphometric studies of bone indicate heterogeneity of orientation of Haversian system [12], [13]. At the micro-level, although the anisotropy due to the orientation of collagen and of apatite has been included in micro-FE models adjacent to osteocyte lacunae and elsewhere in the lamellae, we here address this anisotropy for the first time in individual-specific and experimentally verified multi-scale models of bone [14], [15], [16], [17], [18], [19]. Such osteon groups, and in particular single osteons, show specificity of distribution of collagen orientation to regions of tension or compression due to physiological mechanical stimulation as optimized to support function, with variations in the presence of bone disease [20], [21], [22], [23], [24], [25].

Although the processes by which genetic, environmental and clinical factors affect bone structure at various levels of the multi-scale remain inadequately understood, the well-grounded understanding that in aggregate they do affect the structure of bone at various levels of the multi-scale motivates the preparation of individual-specific, multi-scale FE models. Indeed, current patient-specific FE models prepared from a patient’s CT scan, that address only the macro-level, can predict hip fractures only as well as, or just slightly better than epidemiological data based on clinical history or bone density, none of which are satisfactory [4], [5], [26], [27], [28], [29], [30], [31], [32]. One source of the limited value of the macro-level FE models is their reliance on material properties obtained from local values of BMD. Because such values are isotropic, the material properties used are isotropic. However, cortical bone tissue shows direction-dependent properties, some of which are independent of BMD, and that previously have been found to affect the mechanical response to loading. This motivates inclusion of the anisotropy of the micro-structure in order to improve fracture prediction [33], [34]. As a partial step towards addressing anisotropy, non patient-specific macro-FE models of the cortical components of long bones, have employed either orthotropic or transversely isotropic material properties at the macro-level so as to account for the preferential orientation of the Haversian system, hypothesized to provide reinforcements to the structure along orientation of greater strain or stress (see e.g. [8], [12], [13], [35]). However, the orientation of collagen within the Haversian system, which follows the experimentally observed distributions adjacent to the osteocyte lacunae and elsewhere in the lamellae, has not previously been modeled in conjunction with the osteon-specific degree of calcification within a hierarchical macro-micro simulation of long bone. We undertake such modeling here.

The macro- and micro-structures of the human femur have not yet been biomechanically linked with attention to the main micro-structural variables, nor has their interaction yet been well explored. Micro-level structural analysis of bone specimens isolated from the human femur has established that the orientation of collagen and of carbonated hydroxyapatite needles (here called apatite), as well as the local degree of calcification, are fundamental micro-structural variables [9]. Specifically, such variables form patterns at the macro-structural level and at the micro-structural level, differently so around osteocyte lacunae locally and elsewhere in the tissue. Such patterns affect the strain and stress distributions at the micro-level [17]. In particular, strains are significantly amplified at the osteocyte lacunae, augmenting the strain perceived by the osteocytes, important for bone remodeling signaling [36], [37], [38], [39]. Micro-cracks in bone (1) occur when strain exceeds the elastic limit; (2) locally parallel collagen orientation; (3) show density and length that differ between regions mechanically stimulated under tensile vs. compressive loading; (4) accumulate faster with higher strains; (5) trigger resorption of tissue; and (6) lead to impaired mechanical properties that can cause suffering of the individual or even death of the elderly [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52]. At the micro-level, although the anisotropy due to the orientation of collagen and of apatite has been included in micro-FE models, it has not heretofore been addressed in patient-specific, multi-scale models of bone [17], [36]. Further, we model specifically the osteon groups that we observe in the bone tissue of the individual at the region of interest.

The objective of this research was to develop individual-specific multi-scale models, experimentally validated at each structural level, that take into account collagen-apatite anisotropy and presence of osteocyte lacunae. The application of such models will serve to investigate the micro-structural strains in response to physiological loading in terms of age, sex, and ethnicity (e.g. [35], [53], [54]), as well as clinical factors including presence of disease and pharmacological treatment that affect the bone tissue (e.g. [55], [56]). We here present the modeling method and three examples of its application that point to new findings in agreement with previous experimental and modeling results. The method can simulate types of physiological loading different from the ones presented. It can also incorporate alternative mechanical properties obtained from different experiments.