Finite Element Model-Computed Mechanical Behavior of Femurs with Metastatic Disease Varies Between Physiologic and Idealized Loading Simulations

Abstract

Background and objectives: Femurs affected by metastatic bone disease (MBD) frequently undergo surgery to prevent impending pathologic fractures due to clinician-perceived increases in fracture risk. Finite element (FE) models can provide more objective assessments of fracture risk. However, FE models of femurs with MBD have implemented strain- and strength-based estimates of fracture risk under a wide variety of loading configurations, and "physiologic" loading models typically simulate a single abductor force. Due to these variations, it is currently difficult to interpret mechanical fracture risk results across studies of femoral MBD. Our aims were to evaluate (1) differences in mechanical behavior between idealized loading configurations and those incorporating physiologic muscle forces, and (2) differences in the rankings of mechanical behavior between different loading configurations, in FE simulations to predict fracture risk in femurs with MBD.

Methods: We evaluated 9 different patient-specific FE loading simulations for a cohort of 54 MBD femurs: strain outcome simulations-physiologic (normal walking [NW], stair ascent [SA], stumbling), and joint contact only (NW contact force, excluding muscle forces); strength outcome simulations-physiologic (NW, SA), joint contact only, offset torsion, and sideways fall. Tensile principal strain and femur strength were compared between simulations using statistical analyses.

Results: Tensile principal strain was 26% higher (R ² = 0.719, P < .001) and femur strength was 4% lower (R ² = 0.984, P < .001) in simulations excluding physiologic muscle forces. Rankings of the mechanical predictions were correlated between the strain outcome simulations (ρ = 0.723 to 0.990, P < .001), and between strength outcome simulations (ρ = 0.524 to 0.984, P < .001).

Conclusions: Overall, simulations incorporating physiologic muscle forces affected local strain outcomes more than global strength outcomes. Absolute values of strain and strength computed using idealized (no muscle forces) and physiologic loading configurations should be used within the appropriate context when interpreting fracture risk in femurs with MBD.

Keywords: Metastatic bone disease; femur strength; finite element model; physiologic loading; strain.

Figure 1.

Cross-section of a sample femur geometry with lytic metastasis and elastic modulus distribution acquired from computed tomography scans (left), and the 9 loading configurations simulated using finite element models (right). The normal walking, stair ascent, and stumbling physiologic simulations included the abductor (ABD), proximal and distal ilio-tibial tract (ITTP, ITTD), proximal and distal tensor fascia lata (TFLP, TFLD), vastus medialis (VM), and vastus lateralis (VL) muscle forces, in addition to the hip joint contact force (CF). Posterior view shown. Please refer to the online version for interpretation of color.

Figure 2.

Average calibration relationship relating CT Hounsfield units to density using a calibration phantom included in each femur CT scan. Dotted line indicates a linear fit.

Figure 3.

Femur strength and lesion tensile principal strain relationships between normal walking joint contact only and physiologic loading configurations (left column). Dashed lines indicate y = x relationship and dotted lines indicate linear fit. Outcome bias between loading configurations was evaluated using Bland-Altman plots (right column). Solid lines indicate means of the differences and dotted lines indicate 95% confidence interval limits.

Figure 4.

Distribution of femur strengths according to the weakest (33rd), middle, and strongest (67th) percentiles for physiologic, offset torsion, and sideways fall loading configurations. Surgically and non-surgically treated femurs are indicated. Error bars indicate percentile standard deviation. LSR – load-to-strength ratio, a – weakest percentile average significantly different from middle, b – weakest percentile average significantly different from strongest, c – middle percentile average significantly different from strongest, all P < .001. The insets show force-displacement curves from a sample femur. Please refer to the online version for interpretation of color.

Figure 5.

Distribution of lesion tensile principal strains according to the strongest (33rd), middle, and weakest (67th) percentiles for physiologic loading configurations. Surgically and non-surgically treated femurs are indicated. Error bars indicate percentile standard deviation. a – weakest percentile average significantly different from middle, b – weakest percentile average significantly different from strongest, c – middle percentile average significantly different from strongest, all P < .001. The insets show distribution of tensile principal strain through the cross-section of a sample femur. Please refer to the online version for interpretation of color.

Figure 6.

Relationship between femur strength and lesion tensile principal strain for normal walking physiologic loading, showing a moderate correlation. Dotted line indicates a linear fit. ρ – Spearman correlation coefficient.

Figure 7.

Relationship between femur strength and load-to-strength ratio for normal walking physiologic loading, showing a strong correlation. Dotted line indicates a power fit. ρ – Spearman correlation coefficient.