Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

Abstract

Background: Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

Results: Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K₂HPO₄) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K₂HPO₄ and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

Conclusions: This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.

Keywords: Bone density; Finite element analysis; Mechanical properties; QCT.

Fig. 1

Ash and QCT equivalent density (a: dipotassium phosphate; b: calcium hydroxyapatite) relationships used in reviewed studies. Relationships from: ^a (Keyak et al. 1994) – 140 kVp, 70 mA; ^b (Les et al. 1994) – 140 kVp, 30 mA; ^c Unknown – used in (Eberle et al. 2013a, b); ^d (Keyak et al. 2005) – 80 kVp, 280 mAs

Fig. 2

Apparent and ash density to CT number relationships reported by reviewed studies. Peak tube voltage and phantom type are reported when available. The relationship ρ_ash = 0.6ρ_app is assumed (Schileo et al. 2008)