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

Highlights

• We established an equation that converts material properties to bone density.

• The equations were E = 0.2391e^8.00ρ and ρ = 30.49σ^2.41.

• The conversion equations enabled FEA for the bone healing process.

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, a 10-mm long bone defect was created in the center of the femur and fixed by an 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 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 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 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 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 equations were E = 0.2391e^8.00ρ and ρ = 30.49σ^2.41. 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.

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. found that 39.7%–45.8% of surgeons always assess tibial fracture healing (callus size, cortical continuity, and progressive loss of fracture line) from radiographic data [1]. However, a few studies have investigated the reliability of plain radiography in detecting fracture healing. According to these studies, radiographs define union with insufficient accuracy and cannot (in general) conclusively determine the stage of the union [[2], [3], [4]]. Therefore, healing assessment remains a largely subjective topic and physicians significantly disagree on when a fracture has healed [1,5,6].

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

Other researchers have developed numerical models that simulate the fracture-healing process [[11], [12], [13], [14], [15], [16], [17], [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], [20], [21]], vertebrae [[22], [23], [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], [29], [30]]. However, since these equations have been obtained through studies 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.

We considered that the mechanical properties of regional calluses can also be calculated 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 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 callus during the fracture-healing process.