Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis

Journal Pre-proof Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis

Takane Suzuki, Yusuke Matsuura, Takahiro Yamazaki, Tomoyo Akasaka, Ei Ozone, Yoshiyuki Matsuyama, Michiaki Mukai, Takeru Ohara, Hiromasa Wakita, Shinji Taniguchi, Seiji Ohtori PII:

S8756-3282(19)30508-3

DOI:

https://doi.org/10.1016/j.bone.2019.115212

Reference:

BON 115212

To appear in:

Bone

Received date:

29 July 2019

Revised date:

18 December 2019

Accepted date:

19 December 2019

Please cite this article as: T. Suzuki, Y. Matsuura, T. Yamazaki, et al., Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis, Bone(2019), https://doi.org/10.1016/j.bone.2019.115212

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© 2019 Published by Elsevier.

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Biomechanics of callus in the bone healing process, determined by specimen-specific finite element analysis Authors Takane Suzuki, MD., PhD., 1) Japan, [email protected] Yusuke Matsuura, MD., PhD.,2) Japan,

[email protected]

2)

Takahiro Yamazaki, MD. Japan, [email protected] ３)

Japan, [email protected]

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Ei Ozone, MD. 2) Japan, [email protected]

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Tomoyo Akasaka, MD., PhD.

Yoshiyuki Matsuyama, MD. 2) Japan, [email protected] [email protected]

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Michiaki Mukai, MD. 2) Japan, 2)

Takeru Ohara, MD. Japan, [email protected]

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HiromasaWakita, MD. 2) Japan, [email protected] Shinji Taniguchi, MD. 2) Japan, [email protected]

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Seiji Ohtori, MD., PhD., 2) Japan, [email protected] 1) Department of Bioenvironmental Medicine, graduate school of medicine, Chiba

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university. 1-8-1 Inohana, chou-ku chiba city, chiba. 2) Department of Orthopaedic Surgery, graduate school of medicine, Chiba

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university. 1-8-1 Inohana, chou-ku chiba city, chiba. 3) Department of Rehabilitation Medicine, graduate school of medicine, Chiba university. 1-8-1 Inohana, chou-ku chiba city, chiba.

Corresponding author. Yusuke Matsuura

[email protected]

Department of Orthopaedic Surgery, graduate school of medicine, Chiba university. 1-8-1 Inohana, chou-ku chiba city, chiba.

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Abstract As fractures heal, immature callus formed in the hematoma is calcified by osteoblasts and altered to mature bone. Although the bone strength in the fracture-healing process cannot be objectively measured in clinical settings, bone strength can be predicted by specimen-specific finite element modeling (FEM) of quantitative computed tomography (qCT) scans. FEM predictions of callus strength would enable an objective treatment plan. The present study establishes an equation that converts material properties to bone density and proposes a specimen-specific FEM. In 10 male New Zealand white rabbits,

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a 10-mm long bone defect was created in the center of the femur and fixed by an

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external fixator. The callus formed in the defect was extracted after 3–6 weeks, and formed into a (5 × 5 × 5 mm3) cube. The bone density measured by qCT was related to

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the Young’s modulus and the yield stress measured with a mechanical tester. For validation, a 10-mm long bone defect was created in the central femurs of another six

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New Zealand white rabbits, and fixed by an external fixator. At 3, 4, and 5 weeks, the femur was removed and subjected to Computed tomography (CT) scanning and

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mechanical testing. A specimen-specific finite element model was created from the CT data. Finally, the bone strength was measured and compared with the experimental

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value. The bone mineral density σ was significantly and nonlinearly correlated with both the Young’s modulus E and the yield stress σ. The material-property conversion

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equations were E = 0.2391e8.00ρ and ρ = 30.49σ2.41. Moreover, the experimental bone strength was significantly linearly correlated with the prospective FEM. We demonstrated the Young’s moduli and yield stresses for different bone densities, enabling a FEM of the bone-healing process. An FEM based on these material properties is expected to yield objective clinical judgment criteria.

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1. Introduction To ensure the correct clinical decisions for fracture patients, orthopedic surgeons must determine the load-bearing capacity, appropriate time of hardware removal, and comeback to work and/or sporting activities of their patients. Therefore, a valid and standard definition of fracture union should be an essential and fundamental goal in orthopedics. Clinically, radiographic assessment has remained a crucial tool in determining fracture healing. In an international survey of 444 orthopedic surgeons in 2002, Bhandari et al.

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found that 39.7%–45.8% of surgeons always assess tibial fracture healing (callus size,

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cortical continuity, and progressive loss of fracture line) from radiographic data [1]. However, a few studies have investigated the reliability of plain radiography in

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detecting fracture healing. According to these studies, radiographs define union with insufficient accuracy and cannot (in general) conclusively determine the stage of the

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union [2–4]. Therefore, healing assessment remains a largely subjective topic and physicians significantly disagree on when a fracture has healed [1,5,6].

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Bone stiffness increases as the fracture healing progresses from the early phases of callus formation to union [7, 8]. In some studies, bone stiffness in fracture healing has

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been evaluated by measuring the displacement angle across the fracture. [9,10]. However, such tests are not commonly applied in clinical settings

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Other researchers have developed numerical models that simulate the fracture-healing process [11–18], but none of these models can predict the characteristics of a

specimen-specific callus that changes over time and is unevenly distributed. Subject-specific FEM is an effective and non-invasive tool for assessing the strength and stiffness of mature bone. CT)based FEMs can accurately predict the bone strength at various sites such as femurs [19–21], vertebrae [22–24], the radial diaphysis [25], and the distal radius [26,27]. Because CT-based FEMs account for the bone geometry, architecture, and heterogeneous mechanical properties of bone, models based on qCT data can predict the bone strength more accurately than clinical bone mineral density by dual-energy X-ray absorptiometry. Mechanical properties such as Young’s modulus and the yield stress of a regional bone can be calculated from CT DICOM data via the Hounsfield unit (HU) value using the equations which were published in previous studies [28–30]. However, since these equations have been obtained through studies

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using elderly fresh frozen cadavers, it cannot be applied to callus with biological activity in the bone-healing process. Orthopedic surgeons must judge fracture fusion by the presence of callus bridge from X-ray and CT scan and subjective symptoms such as pain and tenderness. Therefore, we do not know the amount and duration of an activity that would be limited to the patient. If the bone strength in healing process will be evaluated using FEM, it may be able to assist the orthopedic surgeon’s decision. However, the material properties of callus with biological activity in the bone-healing process have not been known.

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We considered that the mechanical properties of regional calluses can also be calculated

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by a Hounsfield transformation of CT DICOM data. We hypothesized that the bone stiffness during the fracture-healing phase of callus formation to union can be measured

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in CT-based FEMs. The aim of this study was to evaluate the mechanical properties of the callus per HU value in a rabbit model and to create a specimen-specific FEM of

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2. Materials and Methods

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callus during the fracture-healing process.

2.1. Relationship between the material properties of callus and mineral density

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Animals

All protocols for animal procedures were approved by the ethics committees of our

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institutions following the National Institute of Health’s Guidelines for the Care and Use of Laboratory Animals (1996 revision). The experimental animals were 16 male New Zealand white rabbits weighing 3000 to 3200 g. All rabbits were maintained in cages with free access to food and water. They were housed in a temperature-controlled room (22°C ± 2°C) under a 24-h light cycle (lights on 12:00 h). Surgical procedure This procedure was performed on 10 male New Zealand white rabbits. Animals were anesthetized with ketamine (10 mg/kg i.m.) and xylazine (0.2 mg/kg i.m.) and treated aseptically throughout the experiments. The femur was approached through a lateral incision and dissected between the quadriceps and biceps femoris. The periosteum was longitudinally incised maintaining its continuity, and the cortex of the femur was reviled. The femur was stabilized by an external fixator made from resin cement (Unifast Trad, GC, Tokyo, Japan). Four 2.0-mm diameter external fixator pins (DePuy Synthes,

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Raynham, MA, U.S.) were inserted in the femur, which was also encircled with 0.8-mm diameter stainless steel soft wire near the pin. A 10-mm bone section at the center of the femur was resected to avoid injuring the periosteum (Fig. 1). The resected femurs were stored at −82°C for later mechanical testing. The periosteum was sutured by 6-0 Ethilon (Ethicon, Somerville, NJ, USA). The cut tissue layers were then approximated and the skin was closed with 4-0 Ethilon suture (Ethicon, Somerville, NJ, USA). Specimens

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Every three rabbits were euthanized at 3 and 4 weeks postoperation, and four rabbits

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were euthanized at 5 weeks postoperation because our pilot study demonstrated that all phases of bone healing were included 3–5 weeks postoperation. The rabbits were

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anesthetized with ketamine (10 mg/kg i.m.) and xylazine (0.2 mg/kg i.m.) and euthanized with sodium pentobarbital. The tissue at the bone defect, which would

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eventually become callus, was then resected and pulled into a cuboid with approximate side lengths of 5 mm (Fig. 2). The heights and sectional areas of the specimens were

Computed tomography

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Kawasaki, Japan).

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measured using a digital Vernier caliper (Digimatic Caliper; Mitutoyo Corporation,

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All specimens, including the resected femur, were immersed in water with a calibration phantom (QRM-BDC, QRM, Möhrendorf, DE) containing three hydroxyapatite rods (0, 100, and 200 mg/cm3) and imaged by CT (Aquilion ONE; Toshiba Medical Systems, Tokyo, Japan, 320-row detector, 120 kV, 200 mA, slice thickness 0.5 mm, pixel width 0.3 mm, pitch 0.516) (Fig. 3 a, b, and c). The bone mineral density of each specimen was calculated from the HU value measured from the CT DICOM data of the specimen using FEM software: (Mechanical Finder, Research Center for Computational Mechanics, Tokyo, Japan) (Fig.3d).

Mechanical testing All specimens, including the resected femur, were compressed in a universal testing machine (Autograph AG-20kN X Plus; Shimadzu, Kyoto, Japan) operated at 5 mm/min

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until failure (Fig. 4). The magnitudes of the applied load and displacement were continuously recorded and the force–displacement curves were plotted. The stress– strain curves were then derived from the force–displacement curves, initial heights, and cross-sectional areas. The yield stress was defined as the peak on the stress–strain curve. The Young’s moduli were calculated from the slopes of the stress–strain curves between 0 and 0.1 strain. The yield stresses and Young’s moduli were compared with the bone mineral density using Pearson’s correlation coefficient. A p value of 0.05 was

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considered as statistically significant.

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Histological evaluation

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Four typical specimens with different HU values were reserved for histological evaluation. Each specimen was fixed with 4% paraformaldehyde in phosphate buffer

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(0.1 M, pH 7.4) for 48 hours at 4°C and demineralized with 10% EDTA at 4°C for 12 days. The fixed specimens were embedded in paraffin with Tissue-Tek V.I.P6 (Sakura

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Finetech Japan CO.LTD, Tokyo, Japan), and sectioned by a sliding microtome LS113 (YAMATO-KOHKI industrial CO.LTD, Asaka, Saitama, Japan). Next, they were

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stained with hematoxylin eosin (HE) and toluidine blue (TB), and photographed by a Moticam Pro 252A (Motic, Hong Kong, China) for histological analysis (Fig. 5a, b).

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Histological measurement

Images for the histological measurements were continuously taken by a DP-21 photomicroscope (OLYMPUS, Tokyo, Japan) using a 100-power magnifying lens and composited by CellSence (OLYMPUS, Tokyo, Japan) to create tiling images. The areas of the section, cartilage, and mineralized tissue were measured by the imaging analysis software WinROOF Ver.7.2 (Mitani-shoji, Fukui, Japan) under the following criteria. (1) Area of section: the area of the tissue outlined by the HE stain (Fig. 5c). (2) Area of cartilage: the area of the metachromasia region in which the chondrocytes and chondroblasts produce acid slime polysaccharides, evidenced by TB staining. (3) Area of mineralized bone: because the cartilage transformed into bone is difficult to identify, the areas of the cartilage and mineralized bone regions were measured on the

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HE-stained tissues. The mineralized bone area was calculated as the area covered by cartilage and mineralized bone regions (identified by HE staining) minus the area covered by the metachromasia region (identified by TB staining). The cartilage ratio and mineralized bone ratio were respectively calculated as follows: cartilage ratio (%) = (area of cartilage / area of section) × 100,

Surgical procedure

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2.2. Validating the material properties of callus

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mineralized bone ratio (%) = (area of mineralized bone / area of section) × 100.

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This procedure was performed on six female New Zealand white rabbits. The surgery

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was performed as described above. The cut tissue layers were then approximated and

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the skin was closed with 4-0 Ethilon suture (Ethicon, Somerville, NJ, USA). Specimens

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At 3, 4, or 5 weeks postoperation, the rabbits were anesthetized with ketamine (10 mg/kg i.m.) and xylazine (0.2 mg/kg i.m.) and euthanized with sodium pentobarbital. All implants were removed from the femur and proximal, and the extant 2 cm of each

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femur end was potted in resin bone cement to aid gripping during mechanical testing. Nonlinear FEM

All specimens were immersed in water with a calibration phantom (QRM-BDC, QRM, Möhrendorf, DE) and imaged by CT (Aquilion ONE; Toshiba Medical Systems, Tokyo, Japan, 320-row detector, 120 kV, 200 mA, slice thickness 0.5 mm, pixel width 0.3 mm, pitch 0.516). The CT data were imported by an FEA software package (Mechanical Finder, Research Center for Computational Mechanics, Tokyo, Japan) for constructing nonlinear, subject-specific, three-dimensional models. In the femur segmentation stage, the region of interest of outer surface of femur was defined as the pixels with intensity exceeding 100 HUs. The bone was meshed by linear tetrahedral elements with global edge lengths of 0.6–1.2 mm, and the outer surface of the cortical bone was modeled using 0.6–1.2-mm triangular shell elements to compensate for the strength losses

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resulting from CT resolution effects (Fig. 6). The virtual thickness of the shell element was set to 0.5 mm. The resin cement caps on the femur ends were meshed by linear tetrahedral elements with global edge lengths of 0.6–1.2 mm. The heterogeneity of the callus was modeled by defining the mechanical properties of each element based on the corresponding HU value at its location, obtained in subsection 2.1. The femur was assigned the same equations as the callus. The ash density of each element was set as the average ash density of the voxels contained in the space of that element. The Young’s modulus of the shell was assigned as the value of the next tetrahedral element

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with an HU value of at least 1200. The Poisson’s ratio in each element was set to 0.3, as

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mentioned in previous reports (Muller et al. 2008). Young’s modulus and Poisson’s ratio for each element of resin cement were set as 4.0 GPa and 0.4, respectively.

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Adhesive contact between resin and bone was established. The elements were assumed to be bilinear elastoplastic with an isotropic hardening modulus set to 0.05.

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A compression test was performed on all femurs. A uniform displacement was applied to the resin cement at the distal end of the femur. The displacement was ramped at

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0.01-mm increments until the failure criteria were reached (Fig. 7a). The resin cement elements at the proximal end of the femur were restraint. Each element was assumed to

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yield when its Drucker–Prager equivalent stress reached the element yield stress. After plotting the force–displacement curve from the FEA results, the fracture load was

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identified by a rapid decline in load (Fig. 7b). Quasi-static uniaxial compressive load testing To assess their actual mechanical behavior, the specimens were compression-loaded in a universal testing machine (Autograph AG-20kN X Plus; Shimadzu, Kyoto, Japan). The force was applied to the distal cement block, while the proximal cement block was completely constrained. The actuator was driven at 5 mm/min under displacement control (Fig. 7c). The magnitudes of the applied load and displacement were continuously recorded and the force–displacement curves were plotted (Fig. 7b). The stiffness predicted by FEM was compared with that measured from the slope of the force–displacement curve using a paired t-test and Pearson’s correlation coefficient. A p value of 0.05 was considered as statistically significant.

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3. Results 3.1. Relational expressions between the material properties of callus and bone mineral density We obtained the 95 cuboidal callus specimens from 10 rabbits. Among 95 cuboidal callus specimens, we reserved four specimens for histological evaluation and the other specimens for mechanical evaluation. The average (SD, range) HU value and mineral density (m/cm3) of the specimens were 333.4 (212.2, 13.2–895.9） and 0.314 (0.203,

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0.014–0.915), respectively.

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Histological findings (Figs. 8, 9, Table 1) Specimen 1 (bone mineral density = 0.052 mg/cm3)

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Almost all of the tissue contained fibroblasts and no cartilaginous ossifications were observed. Immature cartilage callus was forming in all small areas. The cartilage and

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mineralized bone ratios (%) were 0.55 and 0.00, respectively. This specimen

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characterized the early reparative phase.

Specimen 2 (bone mineral density = 0.220 mg/cm3)

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Irregular cancerous bone was formed by endochondral ossification (Fig. 8b). Whereas the cartilage part was clearly observed in the regenerated bone trabeculae (Fig. 9b), the

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ossification part was relatively scarce. Osteoclasts were aggregated around the bone trabeculae (Fig. 8b arrows). Conversely, the area between the bone trabeculae was occupied not by bone marrow cells, but by fibroblasts and macrophages. The cartilage and mineralized bone ratios (%) were 11.8 and 4.11, respectively. This specimen characterized the reparative phase. Specimen 3 (bone mineral density = 0.310 mg/cm3) Regenerated bone trabeculae occupied a large callus space in this specimen, and the callus was fibrous in the part (Figs. 8c, 9c). The cartilage and mineralized bone ratios (%) were 35.5 and 5.40, respectively. This specimen represented the reparative phase. Specimen 4 (bone mineral density = 0.432 mg/cm3)

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An irregular thin cancellous bone was the main element in this specimen, but the bone trabeculae were partially fused, thickened, and similar to cortical bone (Fig. 8d). A cartilage ingredient appeared in the bone trabeculae, but there were relatively many ossification parts. A lamellar bone structure was also seen in the bone matrix (Fig. 9d). The cartilage and mineralized bone ratios (%) were 8.53 and 21.5, respectively. This specimen characterized the late reparative phase to the remodeling phase. Summary of histological findings: in the specimens assigned to mechanical testing, the

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callus had progressed to the early reparative phase to remodeling phase (Fig. 10). Mechanical evaluation and 5.32 (5.16) MPa, respectively.

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The mean (SD) Young’s modulus and yield stress of the callus were 97.9 (808.8) MPa

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The bone mineral density σ was significantly nonlinearly correlated with both the Young’s modulus E (r = 0.8212) (Fig. 11) and with the yield stress ρ (r = 0.8016) (Fig.

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ρ = 30.49σ

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E = 0.2391e8.00σ

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12). The relationships are given by Eqs. 1 and 2, respectively. (1) (2)

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3.2. Validating the material properties of callus The mean (SD) fracture load of femur was determined as 48.1 (20.2) N in the experiment and 49.2 (15.5) N in the prospective FEA. The experimental values and prospective FEA values were significantly linearly correlated (r = 0.965) (Fig. 13). 4. Discussion We demonstrated that the Young’s moduli and yield stresses of callus are as strongly correlated with bone mineral density as those of bone. Furthermore, our FEM study validated the equation that converts bone density values to material properties. Various past researches have proposed equations for converting bone density to Youngs’s moduli and yield stresses of bone [29–31]. Besides clarifying the relationships between bone mineral density and the Young’s modulus and yield stress of callus, we compared our results with those of previous conversion equations of bone

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material properties (Fig. 14). The Young’s modulus equation was a power function for bones, and approximated an exponential function for callus. We surmise that the Young’s modulus of bone is maintained when the HU value is low, whereas callus is softer than bone and has a significantly lower Young’s modulus. Histological studies revealed callus with a low HU value in the reaction phase; moreover, most of reaction phase was occupied by the cartilage component. Therefore, structural weakness was expected. When the HU value increased, the bone density increased accordingly, and trabecular and lamellar bone structures were formed. These changes might explain the

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exponential increase in Young’s modulus. Moreover, the Young’s modulus of mature

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callus was nearly identical to that of bone. On the other hand, the yield stress of callus followed a power function, as also observed in bone. In fact, the yield stresses of callus

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and bone exhibited the same tendency.

Perren reported that fractures do not heal when the strain exceeds 0.1 [31]. The yield

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strains obtained from the experimental results are plotted as diamonds in Fig. 14. Although the variation is large, when the bone mineral density is 0.2–0.5 g/cm3, the

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callus does not yield until the strain reaches approximately 0.4. The individually measured values obtained from the experimental results were similar to those obtained

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by dividing the yield stress by the Young’s modulus (gray plot in Fig. 15). As the bone density increases, the yield strain decreases. The maturing callus approaches

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approximately 0.1 of the bone’s yield strain. Clinically, unstable fractures lead to hypertrophic nonunion. Early in the reaction phase, the immature callus is matured rather than destroyed by large strains. However, a mature callus may be destroyed by a large strain. This phenomenon is the likely cause of hypertrophic nonunion.

We demonstrated that bone strength during the bone-healing process can be quantitatively predicted by FEM based on the proposed conversion equation from HU values to the material properties of bone. Furthermore, by performing FEA using this equation, the bone strength of the patient’s bone-healing process can be estimated. Thereby, it can be expected that the patient’s individualized treatment plan, for example, the establishment of objective judgment criteria for the fixed period of the cast, and the time when the patient’s sports and work activities can be resumed can be estimated. We

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believe that this information obtained using FEM will be useful for the doctors’ objective criteria. This study has certain limitations. First, since the specimens handled in the mechanical tests are extremely small and irregular, experimental errors can occur. Therefore, we attempted to reduce the impact by increasing the number of specimens. Second, in particular, the research objects were rabbits rather than humans. As collecting the callus during the fracture-healing process in a living human body is extremely difficult, animal experiments were necessary. Whether the derived equations are directly applicable to

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humans is debatable. In future work, the clinical appropriateness of the

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material-property conversion equations must be examined in repeat cases. Third, the number of subjects (animals) used herein was small. We used only 10 rabbits for

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creating equation, and six rabbits for validation. However, good correlation was observed between the prediction values measured using FEM and the experimental

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values in validation study.

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References

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Funding: This work was supported by JSPS KAKENHI Grant Number JP 30513072.

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(26) Edwards WB, Troy KL. 2012. Finite element prediction of surface strain and fracture strength at the distal radius. Med Eng Phys. 34:290–298. (27) Matsuura Y, Kuniyoshi K, Suzuki T, Rokkaku T, Hiwatari R, Murakami K, Hashimoto K, Okamoto S, Shibayama M, Iwakura N, Yanagawa N, Takahashi K. Accuracy of specimen-specific nonlinear finite element analysis for evaluation of distal radius strength in cadaver material. J Orthop Sci. 2014 19(6):1012-8 (28) Carter, D.R., Hayes, W.C., 1977. The compressive behavior of bone as a two-phase porous structure. J. Bone Joint Surg. Am. 59, 954–962. (29) Keller, T.S., 1994. Predicting the compressive mechanical behavior of bone. J. Biomech. 27, 1159–1168.

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(30) Keyak, J.H., Lee, I.Y., Skinner, H.B., 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. J. Biomed. Mater. Res. 28, 1329–1336. (31) Perren SM. The concept of biological plating using the limited contact-dynamic compression

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plate (LC-DCP). Scientific background, design and application. Injury. 1991;22 Suppl 1:1-41.

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cartilage Specimen

Bone mineral

area of section

No

density (mg/cm3)

(μm2)

mineralized bone

area of cartilage

cartilage ratio

area of bone

area of mineralized bone

mineralized bone

(μm 2) ･･･(2)

(%)

(μm2) ･･･(3)

(3) - (2) (μm 2)

ratio (%)

0.052

51837256.5

289917.6

0.6

0.0

0.0

0.0

2

0.220

6400800.3

759169.0

11.9

1022385.4

263216.4

4.1

3

0.310

11503277.9

4086682.1

35.5

4708365.7

621683.6

5.4

4

0.432

27396069.9

2336775.6

8.5

8236808.2

5900032.7

21.5

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Highlights We established an equation that converts material properties to bone density The equations were E = 0.2391e8.00ρ and ρ = 30.49σ2.41.

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The conversion equations enabled FEA for the bone healing process.

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