Lumbar Spine Response of Computational Finite Element Models in Multidirectional Spaceflight Landing Conditions

Abstract

The goals of this study are to compare the lumbar spine response variance between the hybrid III, test device for human occupant restraint (THOR), and global human body models consortium simplified 50th percentile (GHBMC M50-OS) finite element models and evaluate the sensitivity of lumbar spine injury metrics to multidirectional acceleration pulses for spaceflight landing conditions. The hybrid III, THOR, and GHBMC models were positioned in a baseline posture within a generic seat with side guards and a five-point restraint system. Thirteen boundary conditions, which were categorized as loading condition variables and environmental variables, were included in the parametric study using a Latin hypercube design of experiments. Each of the three models underwent 455 simulations for a total of 1365 simulations. The hybrid III and THOR models exhibited similar lumbar compression forces. The average lumbar compression force was 45% higher for hybrid III (2.2 ± 1.5 kN) and 51% higher for THOR (2.0 ± 1.6 kN) compared to GHBMC (1.3 ± 0.9 kN). Compared to hybrid III, THOR sustained an average 64% higher lumbar flexion moment and an average 436% higher lumbar extension moment. The GHBMC model sustained much lower bending moments compared to hybrid III and THOR. Regressions revealed that lumbar spine responses were more sensitive to loading condition variables than environmental variables across all models. This study quantified the intermodel lumbar spine response variations and sensitivity between hybrid III, THOR, and GHBMC. Results improve the understanding of lumbar spine response in spaceflight landings.

Introduction

The National Aeronautics and Space Administration (NASA) has identified the analysis and mitigation of injury risk due to dynamic spaceflight loading as a priority. Growing interest in commercial spaceflight has also highlighted the need for not only protecting NASA crewmembers but also civilian pilots and passengers during spacecraft launches and landings [1,2]. The increased interest in commercial spaceflight travel, as well as the exposure to blunt trauma injuries has imposed a design challenge for commercial spaceflight development. Acute seat pan angles, nonextended legs, combined axis loading, as well as other restraint and loading scenarios may induce unforeseen changes in occupant injury risk.

Finite element models have been used widely to study occupant response in automotive and military conditions. These models have proved extensible to loadings in spaceflight conditions [3–8]. Anthropomorphic test device (ATD) models provide valuable information to investigate the occupant kinetics and kinematics in a cost- and time-effective manner; human body models, such as the global human body models consortium (GHBMC) model, provide more biofidelic response and have been used as an important tool for improving injury and mortality outcomes [9,10]. The GHBMC model has been validated in occupant postures for motor vehicle crash loading conditions [10–12]. However, the sensitivity and extensibility of ATD and human body models have not yet been examined across a full spectrum of multidirectional spaceflight landing scenarios.

Despite improvement in vehicle crashworthiness, the incidence of thoracolumbar spine fractures in motor vehicle crashes has increased over time [13–15]. In aerospace conditions, lumbar spine injury has also been a concern for astronauts, given the multitude of boundary conditions and restraint systems [2]. As previous studies and injury criteria of the lumbar spine mostly relate lumbar response to vertebral body fractures, this study focuses on lumbar vertebral body fractures as the predominant mode of injuries. Given the prevalence of lumbar spine injuries, questions arise regarding: (1) the response variation across multiple loading and environmental factors, (2) the response sensitivity to perturbations in boundary conditions, and (3) the associated lumbar vertebral body fracture risk.

This study aims to quantify the lumbar response variance in the hybrid III, test device for human occupant restraint (THOR), and GHBMC finite element models, and to determine the sensitivity of lumbar spine injury metrics to a selected set of parameters in multidirectional spaceflight landing scenarios.

Methods

Finite Element Models.

This utilized the 50th percentile hybrid III ATD v.7.1.8 (Humanetics, Plymouth, MI), the 50th percentile THOR ATD v.2.1 from the National Highway Traffic Safety Administration (NHTSA), and the 50th percentile GHBMC simplified occupant model (M50-OS, v1.8.4.1). The two ATD models were previously validated against experimental tests with a 90 deg–90 deg–90 deg seat in the following spaceflight-relevant loading directions: −X (frontal), +X (rear), ±Y (lateral), and +Z (vertical) [4,5]. Resultant accelerations of head, chest, and pelvis accelerations, as well as shoulder and lap belt forces were compared to match testing data for model validation for the two ATD models. The GHBMC model was previously validated against experimental data using braced volunteer tests in a 90 deg-90 deg-90 deg seat at the Air Force Research Laboratory (Dayton, OH) in the aforementioned loading directions [3]. Resultant head and chest accelerations, as well as belt forces were measured and compared to volunteer testing data for model validation. Lumbar spine data was not available from referenced volunteer tests, but the lumbar force and displacement of the GHBMC model was compared and validated against postmortem human subjects (PMHS) tests data previously [16].

In the current study, each of the three models was positioned in a rigid 90 deg-90 deg-90 deg seat model with a five-point seatbelt (Appendix A; Fig. 1). Belt pretension ranged from 22.2 to 155 N (5–35 lbf) according to the design of experiments (DOEs) below, with the belt system locked prior to applying the seat acceleration. The seat model was created to represent the test seat used by Wright-Patterson Air Force Base, which also included side guards (a head guard with padding, a shoulder guard with padding, a hip guard without padding, and a right knee guard without padding). Side guards were modeled as rigid parts and *MAT_LOW_DENSITY_FOAM was used as the padding material. For the GHBMC model, a segment-based contact was applied between the lumbar spine vertebral bodies using *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE and SOFT  = 2. This modification from the original contact proved to be the most stable, and alleviated penetration issues between vertebral bodies originally observed in some severe loading cases. The same material property of the intervertebral disks (*MAT_ELASTIC) and the 1D joint beams between the vertebrae (*MAT_GENERAL_NONLINEAR_6DOF_DISCRETE_BEAM) was maintained for the GHBMC model.

Fig. 1.

Landing orientation with respect to gravity

Design of Experiments.

Acceleration pulses were generated using a Latin hypercube DOE approach. To mimic the multidirectional spaceflight landing scenarios, linear and rotational deceleration components in longitudinal (±X), lateral (±Y), and vertical (±Z) directions with respect to the occupant were simulated. Two nominal acceleration pulse shapes characteristic of space capsule dynamics during landing were supplied by NASA, which represent two acceleration pulses the spacecraft may experience during a water landing phase. The first is a direct impact pulse with a 32.5 ms rise time, followed by an attenuated, cyclic acceleration phase (Fig. 2(a)). A second pulse shape, characterized as an indirect pulse, has a 120 ms rise time with a sinusoidal shape (Fig. 2(a)). In the sensitivity study, a pulse shape parameter ranging from 0 to 1 was defined for the acceleration pulse in each direction (X, Y, Z). A morphing algorithm was used to vary the pulse rise time and shape within the parameter space bounded by the NASA-defined direct and indirect pulses, while a normalized peak pulse acceleration value was maintained (Fig. 2).

Fig. 2.

Acceleration morphing algorithm diagram. (a) Direct acceleration pulse (cyclic) and indirect acceleration pulse (sinusoidal) with morphing illustrated by arrows and (b) examples of two intermediate shaped pulses produced by the morphing algorithm.

To represent the landing direction and magnitude, the shape and magnitude parameters of the X, Y, and Z directional components of the pulse were randomly generated, with the shape factor varying from 0 to 1, and the magnitude factor varying from 0 to 25 G. The resultant peak acceleration ranged between 5 G and 25 G. The range of the acceleration was determined based on related NASA standards and was chosen close to the upper limit of tolerable acceleration profiles for spaceflight crewmembers [17]. This method ensured a random distribution of peak accelerations, and independently created acceleration curves in five directions (±X, +Y, ±Z), which covered a wide variety of spaceflight landing scenarios.

Wind, waves (in water landings), and descent trajectory may all affect the orientation of the space capsule with respect to gravity during landing. As a result, pitch and roll angles were varied by altering the gravity vector during the acceleration phase of the simulations. Rotation about the occupant's local Y-axis and Z-axis were varied from −45 deg to 45 deg, and 0 deg to 20 deg, respectively (Fig. 1). Additionally, to account for the uncertainty in occupant positioning, the position of the occupant model was varied by 20 mm in the forward and rearward directions and 20 mm in the upward and downward directions. The position of the occupant's H-point with respect to the seat back and the relative angle of the H-point with respect to the seat bottom were measured at the onset of acceleration loading and used as independent variables in the regression analysis evaluating lumbar injury metric sensitivity (described in Data Analysis section).

The test matrix included a total of 1365 simulations for the three models, with 13 independent variables included in the sensitivity DOE study (Table 1). These variables were categorized as six loading condition variables and seven environmental variables. It is hypothesized that lumbar spine injury metrics are more sensitive to changes in loading condition variables than environmental variables. The distribution of loading conditions was developed to provide relevant data for nominal and off-nominal loading conditions relevant to NASA's Commercial Crew Program. While some of the loading conditions are unlikely or would be catastrophic, the data would provide valuable information to apply risk-weighted adjustment factors based on the probability of a given landing scenario.

Table 1.

Summary of input variables and ranges for the simulations

Variable type	DOE input	Minimum	Maximum	Derived analysis variables
Loading condition variables	X (longitudinal) pulse shape	0	1	X pulse duration(1) (32.5–120 ms)
	Y (lateral) pulse shape	0	1	Y pulse duration(2) (32.5–120 ms)
	Z (vertical) pulse shape	0	1	Z pulse duration(3) (32.5–120 ms)
	X acceleration(4)	−1 (eyeballs out)	1 (eyeballs in)	Peak X, Y, Z component acceleration (G)
	Y acceleration(5)	0	1
	Z acceleration(6)	−1 (eyeballs up)	1 (eyeballs down)
	Resultant acceleration(7)	5 G	25 G
Environmental variables	Seat Y-rotation(8)	−45 deg	45 deg
	Seat Z-rotation(9)	0 deg	20 deg
	X-offset of occupant from seat	0 mm	20 mm	Hip H-point X position(10), hip H-point Z position(11), and hip angle(12)
	Z-offset of occupant from seat	0 mm	20 mm
	Belt pretension force(13)	22.2 N	155 N

Superscript number notations refer to the 13 independent variables included in the study.

Data Analysis.

The hybrid III model was equipped with two lumbar load cells modeled as zero-length beams on the upper (EID 1500380) and lower (EID 1500002) aspects of the lumbar spine. The original THOR model from NHTSA is not equipped with a lumbar load cell. This study used a lumbar load cell modeled as a zero-length beam element (EID 784621) which was previously incorporated into a version of the THOR model used by NASA [18,19].

The lumbar spine in the GHBMC M50-OS is comprised of rigid vertebrae with six degree-of-freedom intervertebral joints. Load cells are modeled at the intervertebral joints using zero-length beams. Force and moment measurements from the beams were collected at the intervertebral disk locations. Additionally, contact force was extracted from the defined contact between lumbar vertebral levels. To maintain consistency in anatomical measurement location, the element between the L1 and L2 vertebrae (EID 610238, CID 600002) of the GHBMC model was used for lumbar spine response comparisons to the upper lumbar spine load cell in the hybrid III model, and the lumbar spine load cell in the THOR model (Fig. 3). Contact forces and beam forces were extracted across all vertebral levels of the GHBMC lumbar spine (Appendix B). Force and moment data extracted from the load cells of the three models was filtered using a channel frequency class 600 Hz filter [20].

Fig. 3.

Lumbar load cell locations for each model

The Brinkley dynamic response criterion, also known as the dynamic response index (DRI), was used to assess thoracolumbar spine injury risk [21,22]. The DRI injury risk function was developed by the Air Force using existing seat performance data in aircraft ejections, and injury data in cadaver tests [23].The DRI injury risk function does not specify injury severity or injury type, so it was used to represent the risk range of any abbreviated injury scale (AIS) 1+ spinal injury [22]. The AIS is an anatomical-based system created to classify and describe the severity of injuries. The AIS code is on a scale of one to six, one being a minor injury and six being maximal [24]. In this current study, DRI is derived from spinal axial force,$\hspace{0.17em}Fz$ (Eq. (1)), and used to calculate the probability of spinal injury (Eq. (2)). The average and peak DRI and injury risk were calculated for all three finite element models across all simulations.

$$\mathrm{DRI}=3.62\mathrm{*}{F}_z-2.59$$ (1)

$$p\left(\mathrm{AIS}\hspace{0.17em}\ge 1\right)={10}^{\left(\frac{\mathrm{DRI}-15.8}{3.73}\right)}$$ (2)

A sensitivity analysis was performed to compare the lumbar response of the three finite element models with respect to the boundary conditions. Lumbar forces and moments for each model were regressed against the 13 independent variables (seven loading condition variables and six environmental variables) from the DOE study, as well as the interaction terms between these 13 variables using second-order polynomial equations (Table 1) [25]. All the polynomial regression variables were normalized by magnitude. The objective of normalization was to observe which boundary condition variables most affect the lumbar forces and moments and to remove the size effect for each variable. For the loading condition and environmental variables which had values in both the positive and negative range (X acceleration, Z acceleration, Y-axis model rotation) in the DOE study, the scaled range was defined from −1 to 1. The remaining variables were scaled from 0 to 1. The coefficients for each variable of the polynomial regression were then fit with an objective function to minimize the residual sum of squares, and lasso regularization was used to avoid overfitting [25]. The absolute value for all coefficients associated with each variable (independent and interactive terms) in the regression model was summed, which represented the weighting for the variable. Larger weighting indicated a higher sensitivity of the corresponding variable to the change in lumbar force and moment. An example of the sensitivity calculation is detailed in Appendix C.

Results

Intermodel Comparisons.

Hybrid III (mean±SD: 2.2 ± 1.5 kN) and THOR (2.0 ± 1.6 kN) exhibited similar lumbar axial compression forces across all simulations (Fig. 4). The peak hybrid III upper lumbar compression force was 8.5 kN, while the peak THOR lumbar compression force reached 7.3 kN. The GHBMC model resulted in much lower lumbar compression forces (L1-L2 mean±SD: 1.3±0.9 kN), with peak force falling below 4 kN in most of the simulations. The hybrid III and THOR models had comparable peak lumbar forces, with forces in the THOR being 12% less than hybrid III on average (R ² = 0.66). The GHBMC lumbar compression forces were 45% less than the hybrid III (R ² = 0.55) and 51% less than the THOR (R ² = 0.87).

Fig. 4.

Intermodel comparison of peak lumbar axial compression force for all simulations. Solid lines indicates the linear regressions, the dashed line indicates the reference line y = x, and circle shading represents crash acceleration directions indicated by the legend.

Intermodel comparisons were also examined by acceleration direction in +X (rear), −X (frontal), +Z (up), and −Z (down) quadrants (Appendix D). A direction-dependence trend was noticed across the three models. For the +X (rear) and −Z (down) quadrants, which corresponded to the nominal landing directions where the majority of spaceflight landing occurs, hybrid III had higher lumbar compression forces, and GHBMC sustained much lower lumbar compression forces compared to the two ATD models. For the −X (frontal) and +Z (up) quadrants, which corresponded to the off-nominal landing directions, hybrid and THOR had similar lumbar compression forces which were consistently higher than the GHBMC lumbar compression forces.

Lumbar shear forces ($Fx$ and $Fy)$ were generally lower than the lumbar compression force for hybrid III and THOR (Appendices E and F). THOR sustained much higher forward shear force compared to the hybrid III, but lower rearward shear force, which indicated a tradeoff in shear force between these two models. Similarly, a directional trend was noticed in the shear force $Fy$. Hybrid III sustained a 39% higher left shear force $Fy$ compared to THOR, while THOR predicted a 34% higher right shear force than hybrid III. Compared to the ATD models, GHBMC sustained relatively lower shear forces, with the predominant peak shear forces in the forward ($Fx$) and right $\left(Fy\right)$ directions (Appendices E and F).

THOR sustained much higher lumbar extension moments than hybrid III (Fig. 5). On average, the THOR lumbar extension moment was 436% higher than hybrid III (R ² = 0.69), with high lumbar extension moments observed primarily in the +X (rear) and −Z (down) directions. The average lumbar spine extension moments for THOR and hybrid III were 254.9 N·m and 43.1 N·m, respectively. A strong linear correlation (R ² = 0.91) was observed between the hybrid III and THOR peak lumbar flexion moments, demonstrating the moment measurement similarity between the two ATD models. The average lumbar spine flexion moments for THOR and hybrid III were 73.7 N·m and 50.2 N·m, respectively. Notably, the highest flexion moments were observed in the loading regimes comprised of +Z (up) and −X (frontal) accelerations. The THOR sustained an average 64% higher lumbar spine flexion moment than the hybrid III, as indicated in the linear regression.

Fig. 5.

Hybrid III versus THOR comparison of peak lumbar extension and flexion moment $My$. Circle shading represents crash acceleration directions indicated by the legend in Fig. 4.

Compared to the two ATD models, GHBMC sustained much lower lumbar spine bending moment in the same loading conditions, with an average L1–L2 extension moment of 2.2±1.6 N·m and flexion moment of 3.5±5.4 N·m, respectively (Fig. 6). The peak extension moment reached 7.9 N·m, while the peak flexion moment reached 31.7 N·m.

Fig. 6.

Hybrid III versus GHBMC comparison of peak lumbar extension and flexion moment $My$. Circle shading represents crash acceleration directions indicated by the legend in Fig. 4.

The DRI quantified the lumbar injury risk based on lumbar axial compression force. Most of the THOR simulations sustained relatively low thoracolumbar spinal injury risk, with an average risk of 1.02% (Appendix G). However, the highest DRI in the THOR simulations was 23.7, corresponding to 100% spinal injury risk. Similarly, most of the hybrid III simulations also resulted in low spinal injury risk, but the average injury risk increased to 11.4% compared to THOR. The highest DRI for hybrid III reached 28.3. When applying the DRI threshold of 18.4 for nominal spacecraft landings, 4.0% (18 of 455) of THOR simulations and 3.5% (16 of 455) of hybrid III simulations exceeded the threshold value [22]. GHBMC resulted in the lowest spinal injury risk of the three models, with most of the simulations producing a spinal injury risk near 0%. The highest DRI of the GHBMC simulations was 14.5, which corresponds to 0.5% spinal injury risk.

Sensitivity Analysis.

Based on the sensitivity analysis, the lumbar forces and moments were more sensitive to loading condition variables compared to the environmental variables, across all three models. Relative sensitivity of the injury metric to each variable was calculated as percentage out of 100% (Table 2). The lumbar compression force had similar sensitivity trends across three models, when accounting for all loading condition variables and environmental variables. The hybrid III lumbar compression force was most affected by changes in Z acceleration (37.8%), followed by changes in resultant acceleration (26.2%), and Y acceleration (17.3%). Z acceleration was also the predominant factor to affect the THOR and GHBMC lumbar compression force and accounted for 49.4% and 37.7% of the sensitivity, respectively.

Table 2.

Sensitivity (reported in percentage) of the lumbar forces and moments to loading condition and environmental variables

Variable type	Independent variables regressed against lumbar injury metrics	Upper lumbar compression force	Upper lumbar flexion moment	Upper lumbar extension moment	Lumbar compression force	Lumbar flexion moment	Lumbar extension moment	L1-L2 compression force	L1-L2 flexion moment	L1-L2 extension moment
		Hybrid III			THOR			GHBMC
Loading condition variables	X pulse duration(1)	0.0	0.7	4.8	0.1	0.9	1.3	0.0	0.0	1.0
	Y pulse duration(2)	0.3	0.4	0.2	0.0	0.1	0.3	0.0	0.0	0.1
	Z pulse duration(3)	2.3	1.2	0.0	3.4	0.5	1.5	2.2	0.1	0.6
	X acceleration(4)	5.7	26.9	19.0	14.7	30.4	30.7	17.6	47.8	44.2
	Y acceleration(5)	17.3	2.8	22.1	6.2	1.5	15.8	14.5	5.0	3.8
	Z acceleration(6)	37.8	27.8	16.8	49.4	31.7	19.1	37.7	36.6	36.9
	Resultant acceleration(7)	26.2	32.4	24.5	18.3	21.9	21.2	20.4	6.5	7.2
Environmental variables	Seat Y-rotation(8)	0.4	1.9	2.7	0.4	7.9	0.1	0.4	0.5	0.7
	Seat Z-rotation(9)	0.9	0.7	0.9	1.3	1.5	0.5	1.4	1.8	0.8
	Hip H-point X position(10)	4.6	3.3	5.1	5.1	2.5	5.1	5.2	0.6	2.5
	Hip H-point Z position(11)	1.3	1.8	1.6	0.0	1.2	2.6	0.2	0.2	0.0
	Hip angle(12)	0.5	0.0	0.0	0.0	0.0	0.0	0.0	0.4	0.0
	Belt pretension force(13)	2.7	0.1	2.2	1.0	0.1	1.7	0.3	0.4	2.3
Total		100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

Loading variables, especially the X, Z, and resultant accelerations were the primary variables to affect lumbar flexion moment for all three models. For hybrid III, resultant acceleration contributed to 32.4% of the changes in upper lumbar flexion moment, followed by Z acceleration (27.8%) and X acceleration (26.9%). Compared to loading condition variables, all environmental variables had minimal effect (<5%): hip H-point X position was the variable to mostly affect the hybrid III upper lumbar flexion moment (3.3%). For THOR, X and Z acceleration were the leading variables to affect lumbar flexion moment, which accounted for 30.4% and 31.7% of the sensitivity, respectively. For GHBMC, lumbar flexion moment was also mostly affected by X acceleration (47.8%) and Z acceleration (36.6%).

The lumbar extension moment sensitivity resembled lumbar flexion moment, in terms of relative contribution from loading and environmental variables. For hybrid III, resultant acceleration accounted for 24.5% of the relative sensitivity, followed by Y acceleration (22.1%) and X acceleration (19.0%). For THOR, X acceleration was the leading variable to affect lumbar extension moment, with a sensitivity of 30.7%. For GHBMC, X and Z acceleration were the predominant variables, which accounted for 44.2% and 36.9% of the lumbar extension moment sensitivity, respectively.

Linear Regression Analysis.

Lumbar force and moment were also linearly regressed against the 13 loading condition and environmental variables. R-squared values were used to quantify the goodness of fit for each regression (Fig. 7). Consistent with the results from the sensitivity analysis, loading condition variables, specifically the acceleration magnitude, predominantly affected the lumbar response. For hybrid III simulations, increases in −Z (down) or +Z (up) acceleration both resulted in an increase in lumbar compression force. Additionally, an increase in −X (frontal) or +X (rear) acceleration was also linearly correlated with an increase in lumbar flexion or extension moment. THOR and GHBMC simulations showed similar lumbar response trends as a function of acceleration, while the rest of the variables resulted in minimal effect (Appendix H).

Fig. 7.

Linear regression of hybrid III lumbar response and pulse accelerations for simulations with different acceleration directions: (a) lumbar compression force versus −Z (down) acceleration; (b) lumbar compression force versus +Z (up) acceleration; (c) lumbar flexion moment versus −X (frontal) acceleration; and (d) lumbar extension moment versus +X (rear) acceleration

Discussion

Lumbar axial force has been used as a criterion to evaluate vertebral fracture risk in military seats, with a maximum compressive load of 6.7 kN (1500 lbs) between the pelvis and lumbar spine defined for 50th percentile ATD models [26]. In spaceflight, the lumbar compression force thresholds for nominal and off-nominal capsule landings in deconditioned astronauts are 4.6 kN and 5.3 kN, respectively [27]. These axial force thresholds correspond to 5% risk of AIS 1+ lumbar spine injury for nominal and off-nominal landings, respectively, as NASA intends to protect astronauts from sustaining even minor injuries. The GHBMC model predicted much lower lumbar forces compared to the hybrid III and THOR models, and the GHBMC lumbar compression forces were below 5.3 kN in all simulations. Lumbar compression forces exceeded 5.3 kN in 5.1% of the THOR simulations (23 of 455). Although the hybrid III model experienced the highest average lumbar compression force of three models, only 4.8% of the simulations (22 of 455) sustained a lumbar compression force greater than 5.3 kN. It should be noted that space capsules typically land with the crew in a combined +X and +Z primary loading direction, with the crewmember in a seated position 90 deg from vertical on their back as the “nominal” direction. Therefore, some of the simulations with high lumbar compression forces represented “off-nominal” directions or worst-case scenarios of spaceflight landings, with the loading direction mainly in the −X and −Z directional quadrants.

To date, there remains a gap in the development of robust injury criteria to quantify lumbar vertebral fracture risk [28]. Combined axial load and bending moment can contribute to lumbar vertebral fractures; however, most studies only consider axial loading for injury tolerance criteria even though bending is present and restricted in vertical accelerative environments. One of the previous studies performed drop-tower tests using cadaveric vertebrae, and indicated a peak force of 3.4 kN was associated with 50% risk of injury for the upper and lower thoracic spine, and a peak force of 3.7 kN corresponded to 50% injury risk when data were combined with lumbar spine tests [29]. A lumbar vertebral fracture force range of 5.2–7.9 kN was also noted from the previous lumbar column drop tower tests [30–32]. Although the loading condition differs from the current study, the results revealed the majority of simulations in the nominal landing direction fell below this lumbar fracture force range. In terms of lumbar bending moment, another study used the total human model for safety human body model to reconstruct 11 real-world motor vehicle crashes and examined the lumbar force and moment across the L1–L5 vertebrae. Consistent with lumbar fracture occurrence in 6 out of the 11 cases, the average flexion bending moment for occupants with lumbar spine fractures (L1–L3: 23.7, L4–L5: 60.0 N·m) was higher than occupants without lumbar spine fractures (L1–L3: 19.8, L4–L5: 52.7 N·m) [33]. Dynamic postmortem human subject compression tests have found a lumbar failure flexion moment of 165–237 N·m based on whole lumbar spine testing, and a failure flexion moment of 47–88 N·m based on lumbar functional unit (segment consisting of two vertebrae) testing, as a result from concentrated loading and bending of anterior aspects of the vertebral bodies [34]. Simulation results in the current study were comparable with this lumbar bending moment range, with 5.7% of the hybrid III simulations falling within the failure bending moment range of 165–237 N·m. Similarly, 4.4% of the THOR simulations sustained a lumbar flexion moment in the range of 165–237 N·m. All of the GHBMC simulations also resulted in a bending moment less than this threshold of 237 N·m, although the acceleration pulse direction and boundary conditions varied from the previous studies, so a direct comparison was not feasible. Another study with cadaveric tests reported a lumbar extension moment of 120–350 N·m under 15 degrees of extension, which showed a stiffer response compared to the flexion moment [35]. The average THOR extension moment fell within this range, but both hybrid III and GHBMC had a much lower average extension moment.

Additionally, the lumbar spine of the GHBMC was modeled as rigid vertebral bodies and kinematic joints, which is a simplification of the human spine structure. The bending moment-rotation angle was also defined as a linear curve in the GHBMC lumbar beam joints, which was also a simplification of the spine material property. Both hybrid III and THOR predicted much higher bending moments, which could be a result of structural difference and material variation between the ATD and human body models. The hybrid III lumbar spine was simplified as rigid rings coated by a lumbar spine rubber block and connected with two zero-length beam elements representing load cells [36]. The THOR lumbar spine was modeled by two rigid rectangular blocks, connected by a zero-length beam element representing a load cell. The GHBMC spine captured more anatomical curvature and included load cell beams at each L1–L5 vertebral level. As a result, the GHBMC spine was more compliant, and sustained higher excursion compared to the ATD models. Given the same boundary condition inputs, the GHBMC sustained the highest excursion of the lumbar spine, followed by the hybrid III and THOR. The excursion magnitude reflected the stiffness of the spine structure across the three models and corresponded to the lumbar bending moment magnitudes (Appendix I).

The DRI was used as an injury metric to quantify the lumbar spine injury severity of the human occupant. The derived injury risk based on DRI indicated that the majority of the simulations fell below the injury threshold, which was consistent with the acceptable AIS 1+ injury risk of less than 5% for nominal spacecraft landings proposed by NASA [27]. This study could be used as a reference framework to evaluate lumbar spine response in spaceflight configurations and also reveals the need to develop injury criteria to consider combined loading and better quantify the lumbar spine injury severity, similar to the lower neck injury criterion and the lumbar spine index [33,37].

The sensitivity analysis of the lumbar spine injury metrics (compression force and flexion/extension moments) indicated that loading variables, especially the X and Z accelerations, predominantly affected the lumbar response, compared to environmental variables. This supported the original hypothesis and indicated the need to optimize the loading orientation of the capsule as an approach to reduce lumbar spine injury risk. Additionally, the analysis elucidated the independent and interactive variable effects on lumbar spine response and provided a consistent manner to cross-compare differences across three finite element models. Only first and second-order polynomial terms (interactive terms between two variables) were included in the regression; the effect of multiple variables or higher-order interactive terms was not considered at this juncture. This prevented overfitting of the regression model, while highlighting the relative sensitivity of each variable in the DOE.

Several limitations exist. Further improvement to the GHBMC spine is warranted, including changing the material property from rigid to deformable and implementing load cells in vertebral body cross section to better measure the bending moment and make the response more accurate. Additionally, the parametric study was performed in a simplified boundary condition with a rigid seat and five-point harness. As a result, the magnitude of the simulations output, other than the general trends of comparison, should be considered in the context of the simplified setup. Future testing using PMHS in the same loading conditions will also be valuable to provide matched data for model comparison and validation. The crew deconditioning effect was also not considered, as several physiologic changes, including changes in muscle strength and loss in bone mineral density could affect the occupant response and injury tolerance [38,39].The anthropometric variation in spaceflight occupants was not evaluated; future studies could investigate the lumbar spine response using subject-specific occupant models accounting for height, weight, and anthropometry. The current study serves as a starting point to elucidate the existing variations between ATD and human body model responses. The current GHBMC model is a first step toward a more biofidelic representation of the human spine anatomy, compared to ATD models. The results can be used to develop transfer functions that relate ATD and human body model responses. Additionally, the current study only focused on vertebral fractures of the lumbar spine and did not consider the loading of the facet joints, while future work could extrapolate the findings to evaluate disk herniation or facet fractures. Most disk bulging and herniations are the result of long-term degeneration and not of a single, brief, acute event, so follow-up studies could extend the time scope to incorporate these injuries [40,41].

Conclusions

In conclusion, this study elucidated that the hybrid III and THOR models exhibited the most similar lumbar compression forces in the +Z loading direction quadrant, followed by the +X loading direction. When combining all loading directions, the average lumbar compression force was 45% higher for hybrid III (2.2±1.5 kN) and 51% higher for THOR (2.0±1.6 kN) compared to GHBMC (1.3±0.9 kN). The results also revealed the large variations in lumbar moment across three models. Compared to hybrid III, THOR sustained an average 64% higher lumbar flexion moment, and an average 436% higher lumbar extension moment. The GHBMC model sustained much lower bending moments compared to both ATD models. Response variations among the three models indicate the need to further improve the biofidelity of the lumbar spine, and consideration of various landing scenarios during spacecraft landing for evaluation of lumbar response. The study also indicated that lumbar response was more sensitive to changes in loading variables, particularly the acceleration magnitude, than environmental variables. Results inform further improvement of spaceflight occupant safety, and the prevention of lumbar spine injuries in aerospace environments.

Appendix A. Belted and Gravitationally Settled Hybrid III, THOR, and GHBMC M50-OS Models

Appendix B. Beam Elements and Contact IDs Used for GHBMC Lumbar Load Measurements

Vertebral Joint Level	Beam element ID	Contact ID
T12-L1	400000	600001
L1-L2	610238	600002
L2-L3	610239	600003
L3-L4	610240	600004
L4-L5	610241	600005

Hybrid III linear regressions
	Z Acc. (G)		Res Acc. (G)			X Acc. (G)				X Acc. (G)
+Z Sim	A	B	A	B	+Z Sim	A	B	+Z Sim		A	B
Compression force (kN)	0.53	0.26	0.20	0.17	Flexion moment (N·m)	81.68	−7.77	Extension moment (N·m)		30.35	2.22
	($R_{\text{adj}}^2$ = 0.72)		($R_{\text{adj}}^2$ = 0.33)			($R_{\text{adj}}^2$ = 0.61)				($R_{\text{adj}}^2$ = 0.65)
−Z Sim	A	B	A	B	−Z Sim	A	B	−Z Sim		A	B
Compression force (kN)	0.39	−0.16	0.11	0.11	Flexion moment (N·m)	20.32	−2.38	Extension moment (N·m)		56.23	2.05
	($R_{\text{adj}}^2$ = 0.54)		($R_{\text{adj}}^2$ = 0.29)			($R_{\text{adj}}^2$ = 0.56)				($R_{\text{adj}}^2$ = 0.33)
	Z Acc. (G)		Res Acc. (G)			X Acc. (G)				Res Acc. (G)
+X Sim	A	B	A	B	+X Sim	A	B	+X Sim		A	B
Compression force (kN)	2.17	0.08	0.14	0.14	Extension moment (N·m)	27.54	3.91	Extension moment (N·m)		21.37	2.57
	($R_{\text{adj}}^2$ = 0.23)		($R_{\text{adj}}^2$ = 0.23)			($R_{\text{adj}}^2$ = 0.53)				($R_{\text{adj}}^2$ = 0.24)
	X Acc. (G)		Z Acc. (G)			Res Acc. (G)				Z Acc. (G)
−X Sim	A	B	A	B	−X Sim	A	B	−X Sim		A	B
Flexion moment (N·m)	20.43	−8.52	95.95	6.58	Compression force (kN)	0.24	0.13	Extension moment (N·m)		25.27	−1.78
	($R_{\text{adj}}^2$ = 0.26)		($R_{\text{adj}}^2$ = 0.48)			($R_{\text{adj}}^2$ = 0.32)				($R_{\text{adj}}^2$ = 0.34)
THOR linear regressions
	Z Acc. (G)		Res Acc. (G)			X Acc. (G)				X Acc. (G)
+Z Sim	A	B	A	B	+Z Sim	A	B	+Z Sim		A	B
Compression force (kN)	0.82	0.26	0.34	0.18	Flexion moment (N·m)	135.76	−13.26	Extension moment (N·m)		185.65	15.54
	($R_{\text{adj}}^2$ = 0.81)		($R_{\text{adj}}^2$ = 0.41)			($R_{\text{adj}}^2$ = 0.57)				($R_{\text{adj}}^2$ = 0.72)
	X Acc. (G)		Res Acc. (G)			X Acc. (G)		Z Acc. (G)		Res Acc. (G)
−Z Sim	A	B	A	B	−Z Sim	A	B	A	B	A	B
Compression force (kN)	1.02	−0.06	−0.09	0.08	Extension moment (N·m)	323.52	8.76	168.59	−17.60	112.03	13.67
	($R_{\text{adj}}^2$ = 0.47)		($R_{\text{adj}}^2$ = 0.26)			($R_{\text{adj}}^2$ = 0.33)		($R_{\text{adj}}^2$ = 0.36)		($R_{\text{adj}}^2$ = 0.25)
−Z Sim	A		B
Flexion moment (N·m)	16.22		−2.29
	($R_{\text{adj}}^2$ = 0.32)
	X Acc. (G)		Res Acc. (G)			Z Acc. (G)
+X Sim	A	B	A	B	+X Sim	A	B
Extension moment (N·m)	152.43	24.16	81.82	18.05	Compression force (kN)	1.69	0.13
	($R_{\text{adj}}^2$ = 0.72)		($R_{\text{adj}}^2$ = 0.42)			($R_{\text{adj}}^2$ = 0.69)
	Z Acc. (G)		Res Acc. (G)			Z Acc. (G)				Z Acc. (G)
−X Sim	A	B	A	B	−X Sim	A	B	−X Sim		A	B
Compression force (kN)	2.32	0.09	0.08	0.15	Extension moment (N·m)	150.08	−11.69	Flexion moment (N·m)		146.71	13.53
	($R_{\text{adj}}^2$ = 0.38)		($R_{\text{adj}}^2$ = 0.31)			($R_{\text{adj}}^2$ = 0.63)				($R_{\text{adj}}^2$ = 0.59)
GHBMC linear regressions
	Z Acc. (G)		Res Acc. (G)			X Acc. (G)				X Acc. (G)
+Z Sim	A	B	A	B	+Z Sim	A	B	+Z Sim		A	B
Compression force (kN)	0.64	0.14	0.28	0.11	Flexion moment (N·m)	2.27	0.18	Extension moment (N·m)		6.03	0.55
	($R_{\text{adj}}^2$ = 0.71)		($R_{\text{adj}}^2$ = 0.41)			($R_{\text{adj}}^2$ = 0.78)				($R_{\text{adj}}^2$ = 0.56)
	X Acc. (G)		Res Acc. (G)			X Acc. (G)				X Acc. (G)
−Z Sim	A	B	A	B	−Z Sim	A	B	−Z Sim		A	B
Compression force (kN)	0.73	−0.03	0.06	0.04	Extension moment (N·m)	2.29	0.07	Flexion moment (N·m)		2.16	−0.26
	($R_{\text{adj}}^2$ = 0.30)		($R_{\text{adj}}^2$ = 0.23)			($R_{\text{adj}}^2$ = 0.37)				($R_{\text{adj}}^2$ = 0.62)
	Z Acc. (G)					X Acc. (G)				Z Acc. (G)
+X Sim	A	B			+X Sim	A	B	+X Sim		A	B
Compression force (kN)	1.12	0.08			Extension moment (N·m)	2.54	0.12	Flexion moment (N·m)		0.62	0.09
	($R_{\text{adj}}^2$ = 0.66)					($R_{\text{adj}}^2$ = 0.30)				($R_{\text{adj}}^2$ = 0.23)
	Z Acc. (G)		Res Acc. (G)			X Acc. (G)				Z Acc. (G)
−X Sim	A	B	A	B	−X Sim	A	B	−X Sim		A	B
Compression force (kN)	1.45	0.05	0.32	0.07	Flexion moment (N·m)	1.97	−0.65	Flexion moment (N·m)		7.36	0.36
	($R_{\text{adj}}^2$ = 0.35)		($R_{\text{adj}}^2$ = 0.21)			($R_{\text{adj}}^2$ = 0.29)				($R_{\text{adj}}^2$ = 0.32)

All linear regressions followed the form y = A + B*x, where A is the intercept (first column), B is the slope (second column). Adjusted R-squared indicated the goodness of fit. All regressions included resulted in a goodness of fit $R_{\text{adj}}^2$ > 0.20.

Appendix C. Regression Analysis Example

The following summarizes an example of the sensitivity calculation for the upper lumbar compression force in hybrid III simulations. Raw regression coefficients for this injury metric are shown in Eq. (C1).

(C1)

Subsequently, Eq. (C2) described the nonzero terms with the absolute values of these coefficients, which were color coded from low magnitude in green to high magnitude in red.

(C2)

An example of the raw sensitivity for the Z-acceleration component was calculated as a weighted sum of coefficients (indicated by the boxes in Eq. (C2)) using Eq. (C3). The terms that contain only the Z-acceleration variable were given full weight of 1, while the interactive terms that contain Z-acceleration and another variable were given 1/13 weight (the number of model input variables).

$$Z-\mathit{Acceleration}\hspace{0.17em}\mathit{Sensitivity}=\hspace{0.17em}[10.23\hspace{0.17em}+\frac{1}{13}(0.07\hspace{0.17em}+\hspace{0.17em}0.46\hspace{0.17em}+\hspace{0.17em}1.05\hspace{0.17em}+\hspace{0.17em}1.10\hspace{0.17em}+\hspace{0.17em}0.30\hspace{0.17em}+\hspace{0.17em}1.11)]\hspace{0.17em}=\hspace{0.17em}10.54$$ (C3)

These sensitivity values were calculated for each variable and summed. The summed total of sensitivity scores for all 13 variables was 27.89. Therefore, the relative sensitivity was 37.8% (10.54/27.89) for the Z-acceleration component in the regression analysis of the hybrid III upper lumbar compression force.

Appendix D. Intermodel Comparisons of Peak Lumbar Axial Compression Force by Acceleration Direction Quadrants: (a) +X (rear), (b) −X (frontal), (c) +Z (up), (d) −Z (down). Circle Colors Represent Crash Acceleration Directions Indicated by the Color Wheel

Appendix E. Comparison of Shear Force F_x Between Hybrid III, THOR, and GHBMC for all Simulations. Circle Colors Represent Crash Acceleration Directions Indicated by the Color Wheel in Fig. 4

Appendix F. Comparison of Shear Force F_y Between Hybrid III, THOR, and GHBMC for all Simulations. Circle Colors Represent Crash Acceleration Directions Indicated by the Color Wheel in Fig. 4

Appendix G. Comparison of Dynamic Response Index Between Hybrid III, THOR, and GHBMC for all Simulations. Red Lines Indicated Linear Regression fit. Dashed Black Lines Indicated DRI Threshold 18.4 for Nominal Spacecraft Landings. Circle Colors Represent Crash Acceleration Directions Indicated by the Color Wheel in Fig. 4

Appendix I. Comparison of Model Excursion Traces for Simulation 114 (predominantly−X Acceleration Direction) for the GHBMC, THOR, and Hybrid III Models. Excursions Were Tracked at the Pelvis, L1 Spine Load cell Location, and T1 Spine Vertebral Body Center, with the Rigid Seat set as the Reference