Sensitivity Analysis of the Bone Fracture Risk Model Beth Lewandowski, PhD, NASA Glenn Research Center Jerry Myers, PhD, NASA Glenn Research Center Jean Sibonga, PhD, NASA Johnson Space Center Introduction • The probability of astronaut bone fracture before, during and after spaceflight is quantified with the NASA Bone Fracture Risk Module (BFxRM)* • The BFxRM uses a probabilistic modeling approach with distributions of model parameters which introduce uncertainty into the probability results • This uncertainty masks the ability to quantify the effect of countermeasures on fracture probability * Nelson et al., “Development and validation of a predictive bone fracture risk model for astronauts,” Ann. Biomed. Eng., 37(11), 2337–59, 2009. 2 Introduction • We hypothesize that the large uncertainty is due to the inability to measure key contributors to bone strength with areal bone mineral density (aBMD) techniques* • This presentation reports the results of a sensitivity analysis of the BFxRM in order to identify the parameters which contribute the most to the uncertainty * Zyssetet al., “Clinical Use of Quantitative Computed Tomography-Based Finite Element Analysis of the Hip and Spine in the 3 Management of Osteoporosis in Adults: The 2015 ISCD Official Positions-Part II,” J. Clin. Densitom., 18(3), 359–92, 2015. BFxRM Model Components • A biomechanical model to estimate applied loads from a loading event • An algorithm for spaceflight bone mineral density (BMD) loss and a mathematical relationship between BMD and bone strength • The fracture risk index (FRI) which is the ratio of applied load to bone strength • An algorithm to convert FRI to bone fracture probability Monte Carlo Simulation Probability Estimate Est. fx Most likely and relative probability probability magnitude skeletal by load to of fracture of loading strength strength for event + event ratio uncertainty 4 BFxRM Model Parameters • Environmental factors – Gravity level – EVA suit/no EVA suit • Factors associated with the fall event – Fall height – Translational velocity – Attenuation • Mass and anthropometric values of the astronaut – Body mass – Effective hip mass – Hip spring and damping characteristics • BMD characteristics – Preflight BMD value – Rate of BMD loss during spaceflight – Maximum BMD loss – Recovery half-life • Characteristics of the relationship between BMD and bone strength – Slope of the relationship – Intercept of the relationship • Bone fracture characteristics – Parameters associated with the conversion between FRI and fracture probability 5 Sensitivity Analysis • Performed to determine which parameters cause the most variation in model results • Fracture probability for pre-flight, 0 days post-flight and 365 days post-flight is calculated 100,000 times as the parameter distributions are sampled • A correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities • Each parameter’s contribution to the variance is found by: – Squaring the correlation coefficients – Dividing by the sum of the squared correlation coefficients – Multiplying by 100% 6 Results • The top five most sensitive parameters: Preflight 0 days 365 days Post-flight Post-flight Parameters % Variance % Variance % Variance Hip Spring Constant (k ) 36.7 37.7 37.4 H Probability Equation Midpoint FRI 35.5 29.0 33.4 Value (μ) Preflight Trochanter BMD (BMD ) 19.9 21.7 20.6 Pre Trochanter Bone Strength Equation 4.56 5.16 4.7 Intercept (B ) BS Effective Hip Mass Multiplier (h ) 1.65 1.50 1.58 m 7 Future Work • Updates to the BFxRM are planned – Update the applied load model with any additional hip spring and damping constant information from new journal articles – Perform a Baysian update to the BMD to bone strength relationship using FEM bone strength data – Update the relationship between FRI and fracture probability with data sets that include fracture outcomes – Identify additional validation tests that can be performed and update the NASA-STD-7009A compliance matrix for the BFxRM 8 Thank you Questions? 9