Measuring bone stiffness using spherical indentation

Abstract

ObjectivesBone material properties are a major determinant of bone health in older age, both in terms of fracture risk and implant fixation, in orthopaedics and dentistry. Bone is an anisotropic and hierarchical material so its measured material properties depend upon the scale of metric used. The scale used should reflect the clinical problem, whether it is fracture risk, a whole bone problem, or implant stability, at the millimetre-scale. Indentation, an engineering technique involving pressing a hard-tipped material into another material with a known force, may be able to assess bone stiffness at the millimetre-scale (the apparent elastic modulus). We aimed to investigate whether spherical-tip indentation could reliably measure the apparent elastic modulus of human cortical bone.Materials and methodsCortical bone samples were retrieved from the femoral necks of nineteen patients undergoing total hip replacement surgery (10 females, 9 males, mean age: 69 years). The samples underwent indentation using a 1.5 mm diameter, ruby, spherical indenter tip, with sixty indentations per patient sample, across six locations on the bone surfaces, with ten repeated indentations at each of the six locations. The samples then underwent mechanical compression testing. The repeatability of indentation measurements of elastic modulus was assessed using the co-efficient of repeatability and the correlation between the bone elastic modulus measured by indentation and compression testing was analysed by least-squares regression.ResultsIn total, 1140 indentations in total were performed. Indentation was found to be repeatable for indentations performed at the same locations on the bone samples with a mean co-efficient of repeatability of 0.4 GigaPascals (GPa), confidence interval (C.I): 0.33–0.42 GPa. There was variation in the indentation modulus results between different locations on the bone samples (mean co-efficient of repeatability: 3.1 GPa, C.I: 2.2–3.90 GPa). No clear correlation was observed between indentation and compression values of bone elastic modulus (r = 0.33, p = 0.17). The mean apparent elastic modulus obtained by spherical indentation was 9.9 GPa, the standard deviation for each indent cycle was 0.11 GPa, and the standard deviation between locations on the same sample was 1.01 GPa. The mean compression apparent elastic modulus was 4.42 GPa, standard deviation 1.02 GPa.DiscussionSpherical-tip indentation was found to be a repeatable test for measuring the elastic modulus of human cortical bone, demonstrated by a low co-efficient of repeatability in this study. It could not, however, reliably predict cortical bone elastic modulus determined by platens compression testing in this study. This may be due to indentation only probing mechanical properties at the micro-scale while platens compression testing assesses millimetre length-scale properties. Improvements to the testing technique, including the use of a larger diameter spherical indenter tip, may improve the measurement of bone stiffness at the millimetre scale...

Computed tomography porosity and spherical indentation for determining cortical bone millimetre-scale mechanical properties

“…Wide variability in bone stiffness, as measured by micro-indentation, was found in the porous cortical bone samples. This variation in stiffness measured by indentation led to indentation values not correlating with compression testing values 25 . We hypothesised that a larger indenter tip would be less prone to the variability of conventional micro-indentation as the larger contact area would include some of the porosity, leading to indentation results that closer correlate with compression testing.…”

“…Various indentation techniques have been investigated as potential tools for measuring the mechanical properties of bone in vivo , without having to extract a bone sample 22 . Indentation techniques can calculate the mechanical properties of bone at the micro-scale 23,24 in carefully prepared samples but, until now, indentation techniques on their own have not reliably predicted millimetre-scale bone mechanical properties 22,25–27 .…”

“…Bone stiffness, the ability of the bone to resist deformation 34 , is also important, particularly in the field of cementless joint replacement surgery; Bone stiffness plays an important role both in the initial press-fit insertion of a cementless implant 25,35 , and in long-term bone remodelling around the implant 36,37 . To determine the safe impaction force range during cementless hip replacement the bone stiffness must be known to calculate the “safe elastic range” of bone deformation during insertion of an implant 25 . Too little strain in the bone around the implant will lead to a reduced “elastic grip” 35 , potentially leading to implant loosening, and too much strain can lead to fracture 38 .…”

“…Too little strain in the bone around the implant will lead to a reduced “elastic grip” 35 , potentially leading to implant loosening, and too much strain can lead to fracture 38 . Bone stiffness, implant stiffness and implant impaction force all determine this safe elastic range 25,39 . In addition, it has been demonstrated that bone ingrowth into a bone scaffold can be improved by first determining the local bone stiffness of the site the scaffold will be inserted and then designing a scaffold with stiffness properties closely representing the local bone stiffness 40,41 .…”

3D Imaging of Indentation Damage in Bone

“…One other factor that needs to be considered in terms of indentation testing is the size of the indenter [28]. The inferred mechanical properties of the bone are likely to depend on the indent size due to the scale of the microstructural features such as pores and cracks within the bone structure sampled during the indentation process [29]. In the present study, the indent size is not a critical concern since the main focus of the study is to generate and visualise sub-surface crack networks to understand the crack propagation and fracturing behaviour of bone rather than to examine the mechanical properties (e.g., hardness and modulus) by implementing indentation under X-ray CT.…”