A FATIGABLE MUSCULOSKELETAL MODEL FOR PREDICTION OF NECK MANEUVERING LOADINGS ON AVIATORS

Transcription

1 A FATIGABLE MUSCULOSKELETAL MODEL FOR PREDICTION OF NECK MANEUVERING LOADINGS ON AVIATORS X. ZHOU*, P. WHITLEY, and A. PRZEKWAS CFD RESEARCH CORPORATION, 215 Wynn Drive, Huntsville, AL, Abstract In this paper we study cervical musculoskeletal loads and fatigue on military aviators during aerial combat maneuvering (ACM). A whole body articulated multi-body model with detailed neck musculature was utilized to predict the neck loads and muscle fatigue of a fighter pilot during high-g maneuvering. Two flight postures, look-ahead and check-6, were investigated on their effects on neck loadings for a duration of 300 seconds. To account for fatigue and decrease of muscle force capacity, a new dynamic muscle fatigue model based on the fatigue-rest-recovery mechanism was incorporated to predict fatigue of muscles responing to dynamic loading conditions. For both postures, the joint dynamics, muscle forces and fatigue levels, representing the neck biodynamic responses to the applied aircraft acceleration, were obtained and compared. For model calibration and validation purposes, digital, multiaxis in-flight data and measurments are needed in the future. Keywords: Musculoskeletal Model, Muscle Fatigue, High-G Aerial Combat Maneuvering (ACM), Neck Loadings. 1. Introduction Acute and chronic injury and pain in military aviators, such as neck injury and lower back pain attributed to piloting military air vehicles, is a significant health problem which could limit the performance of aviators. For example, high rate of acute or chronic cervical spine injury was observed for fighter pilots (Andersen, 1988; Drew, 2000; Newman, 1997; Vanderbeek, 1988). Repeated exposures to sustained aircraft acceleration are believed to cause muscle fatigue, injuries to neck muscles, ligaments, disc, and cervical spine (N. D. Green, 2003; Harrison et al., 2009). Moreover, seating, task posture, vibration and head supported mass were historically reported as the major contributors to injury and pain (Gallagher & Albery 2008; Green & Brown 2004; Eveland & Pellettiere 2006; Eveland et al. 2008). However, understanding of these injury mechanisms is limited due to lack of data/measurements. For better understanding, indepth investigation is necessary on the musculoskeletal response of the neck structure during Aerial Combat Maneuvering (ACM). Numerical modeling is an effective approach to understand muscle fatigue and neck injury mechanisms for injury prevention and mitigation. In this paper, we aim to study the cervical musculoskeletal loads on military aviators during high-g ACM in order to understand the injury mechanism and help prevent or mitigate the injury or pain level in aviators. 2. Materials and Methods To study neck musculoskeletal loadings during ACM, we utilize an articulated whole-body musculoskeletal with detailed neck musculature to predict joint loads, muscle forces and fatigue. A feedback control algorithm is used to derive joint torques and consequently optimal muscle forces in order to maintain desired postures during high-g maneuvering. The muscle fatigue model is an extension of the classic Hill muscle model with the incorporation of a semi-empirical activationfatigue-recovery mechanism Neck Musculoskeletal Model A whole body articulated multibody model with detailed neck and lumbar musculoskeletal structure was utilized for the current study (Fig. 1). The whole-body model includes a root joint with 3 translational and 3 rotational DOFs (degrees of freedom) placed at the pelvis to express the global *Corresponding author. xxz@cfdrc.com 1

2 position and orientation of the human body. Each leg consisted of 7 DOFs. The hip was modeled as a 3-DOF ball-and-socket joint; the knee was modeled as a 1-DOF joint with hybrid translation and rotation (Delp et al. 1990); the ankle was modeled as a revolute joint (1 DOF); and the foot consisted of 2 revolute joints: the subtalar joint linking the talus and the calcaneus and the metatarsophalangeal (MTP) joint linking the metatarsals and the proximal phalanges. Each arm also consisted of 7 DOFs. The shoulder was modeled as a ball-andsocket joint (3 DOFs), the elbow and forearm rotation were each modeled with a revolute joint (1 DOF) (Holzbaur et al., 2005), and the wrist was modeled as a 2-DOF rotational joint. A highly detailed 24 DOF neck musculoskeletal model with 84 muscle fasicles (Vasavada et al., 2001, 1998) is integrated into the whole-body model. In total, the integrated model has 61 DOFs. On the left of Fig. 1, all the joints and their local coordinate axes are shown; On the right of Fig. 1, the neck muscles are shown. In this study, we look into two common postures of a fighter pilot during high-g ACM: the lookahead posture (seating straight while looking ahead) and the check-6 posture (seating with torso and head tilted as looking for enemy flight targets), as shown in Fig. 2. As seen from the figure, the whole-body model can be manipulated to respective postures accordingly. In addition, a HGU-68/P flight helmet was modeled as a rigid body fixed on the head to simulate the headsupported-mass loading Control Based Posture Maintenance and Muscle Force Prediction A human uses highly sophisticated neural control of the musculoskeletal system to generate right amount of external/contact and muscle forces in order to maintain a posture or achieve desired locomotion. In this section, we will briefly present a simple but effective control framework for maintaining postures or tracking motions (Zhou and Przekwas, 2011). In the control framework, illustrated in Fig. 3, the input is a reference motion in joint space (posture is a specific case of motion) to be tracked by the controller. At any time, based on the human model s current joint position and velocity states as well as the target motion state, a desired acceleration state for the system is computed, which aims to bring closer the current system state and the target motion state. For each controlled joint coordinate q, we compute the desired acceleration using a simply proportional derivative (PD) feedback control rule: Figure 1: The Whole-body Musculoskeletal Model with Detailed Neck Musculature. where is the reference joint coordinate value, velocity and acceleration, respectively, and and are the feedback gains for the velocity errors and position error, respectively. For posture maintenance, the reference joint velocity and acceleration are 0. Figure 3: The Tracking Control Algorithm for Maintaining Postures or Tracking Motion. look ahead check-6 Figure 2: Two Flight Postures Investigated in this Study. Once the desired acceleration is computed, the next step is to compute the needed joint torques ( ), muscle forces ( and additional external forces to produce the desired acceleration, with the consideration of gravity and other known external forces. At last, given the computed torques, muscle forces and all external forces, a forward dynamics simulation is carried out to produce physically valid motion. 2

3 In the simulations performed in this study, the flight acceleration was directly applied to the pelvis body (with 6 global DOFs). And other parts of the body was actuated (controlled) by either joint torques or muscles forces (depending on if there are muscles spanning the joints) to dynamically maintain desired postures. For joints without spanning muscles, e.g. knees, the joint torques are fed to maintain the joint angles. For neck joints with spanning muscles, the muscles forces instead of joint torques are applied. The muscle forces are determined by solving a constrained optimization problem due to the redundancy of the muscles. The objective function of this optimization problem is to minimize the maximum muscle effort and is defined as where is the force of the i-th muscle, and is the maximum attainable isometric force (after fatigue) of the i-th muscle. The constraints of the optimization problem states: for any joint with muscle contributions, the torque contributed from all muscles must equal to the joint torque computed from the desired joint accelerations (via an inverse dynamics algorithm). Once the muscle forces are computed, the activation of each muscle can be derived according to the isometric equilibrium principle. In the case the constraint cannot be satisfied due to muscle fatigue, that is, the muscle cannot generate enough torque to hold the posture of particular joint, we switch to use the joint torque directly (instead of applying the muscle forces). In such a scenario, the muscle forces computed from the optimization will just show how hard the muscle tried to generate the torque but they will not contribute to the forward simulation. By doing so, we can ensure the posture will be maintained closely during the entire simulation and thus proper comparison for different postures can be made later A Semi-empirical Model of Muscle Fatigue To account for fatigue and decrease of muscle force capacity, a dynamic muscle fatigue model is needed. There have been numerous attempts to model muscle force and fatigue mathematically, ranging from simple spring-mass models to comprehensive models using 3D Finite Element Methods (FEM) (Böl et al., 2009) or considering many physiological and metabolic and mechanical factors (such as muscle length, shortening velocity, neural activation, and muscle architecture) (Ding et al., 2000; Lambert et al., 2005; Liu et al., 2002; Ma et al., 2009; Tang et al., 2005). In this work, we developed a new semi-empirical model of muscle fatigue extending the work of (Liu et al., 2002; Xia and Frey Law, 2008). In their models, three muscle-activation states: resting, activated, and fatigued, are used and goverened by simple ordinary differential equations. In the work of (Liu et al., 2002), a parameter called brain effort was used to introduce neuro-stimulation as the input to the model; and in the work of (Xia and Frey Law, 2008), a control mechanism is used instead to bring the activation level closer to the target load level. Their models can predict fatigue for a maximal static exertion (Liu et al., 2002) or submaximal or dynamic conditions (Xia and Frey Law, 2008). The clear biophysical picture and the relatively few parameters make these semiempirical models suitable for the current application. Inspired by their work, we establish a different version of the governing equations neuro-excitation ( ) as the primary input: in which where and are the time constants for activation and deactivation. Here, two empirical parameters are introduced: fatigue factor (F) and recovery factor (R). The value of F dictates how fast the muscle will become fatigued from activate state, and the value of R dictates the speed of recovery from fatigue. The muscle fatigue model is a natural extension of the excitation-activation mechanism of the classic Hill muscle model. Note,, which ensures their summation (equal to 1) is unchanged during the parameter evolution. 3. Results 3.1. Numerical Tests of Fatigue Model First, we study the fatigue model behavior under different constant excitation. In Fig. 4, distribution time history of muscle fibers between the three states ( ) are shown for two constant neural excitations ( ). The horizontal axis is time and the vertical axis is the muscle states (each state has a value between 0 and 1 and their sum equals to 1). As can be seen from the figure, with decreased excitation levels, the muscle becomes fatigued slower and the activation level is kept at the constant level longer. Second, we study the behavior of the model under arbitrary submaximal excitation ( ). In Fig. 5, the model behavior under an intermittent excitation is shown. These results indicate our model is capable of handling arbitrary excitations and thus 3

4 can be used for any muscle load profiles during various human motions. Figure 4: Distribution of Muscle Fibers between Three States (a: active, r: rest, f:fatigue) for Constant Excitations (u= 0.5, 0.25). Here, F=0.05, R = 0.01, Neck Loads during Fighter High-G ACM An idealized fighter ACM acceleration profile (Fig. 6) was generated from the work of Cammarota (Cammarota, 1990a, 1990b) that is representative of acceleration excursion frequency, acceleration level and the duration of the ACM engagement. The maximum G-level is around 7.5G and truncated to 1G as a minimum value. The acceleration profiles represented only the vertical axis and as such excited the whole-body model. Given the two postures, look-ahead and check-6, we performed control based dynamic simulations for posture maintenances for the entire 300 seconds. In both simulations, the postures were dynamically maintained (with minimum variations) by joint torques and muscle forces computed from the feedback law. Fig. 7 and 8 show the predicted joint reaction forces (along the cervical longitudinal direction) and bending moments (along the lateral direction) for the look-ahead and check-6 postures, respectively. The horizontal axis is time (unit: second) and the vertical axis is force (unit: ) or moment (unit: ). Fig. 9 and 10 show the muscle activations of the two postures at the beginning of the simulation ( ) and at the end of the simulation ( ), respectively. In Fig. 11, the muscle fatigue of the two postures at the end of simulation is shown ( ). Note at and, even though the aircraft acceleration is the same, the muscle activation is clearly different due to the fatigue. Intermittent Excitation Figure 6: Fighter ACM Acceleration (G-level). Muscle States Figure 5: The Muscle Fiber Response under an Intermittent Excitation. (F= 0.05, R=0.01, ). 4

5 Figure 9: Muscle Activation at t = 1s for the lookahead posture and the check-6 posture. Figure 7: Forces and Moments for the Look-ahead Posture Figure 10: Muscle Activation at t = 300s for the lookahead posture and the check-6 posture. Figure 8: Forces and Moments for the Check-6 Posture. 5

6 are the same at both times. This suggests that, in reality, the pilot must adjust his posture in order to rest fatigue muscles or change the muscle activation pattern by recruiting non-active or rested muscles during the flight. Figure 11: Muscle Fatigue at t = 300s for the lookahead posture and the check-6 posture. 4. Discussion Comparing the results for the two postures, we found longitudinal joint reaction forces (Fig. 7a and 8a) have similar patterns following the aircraft acceleration but they vary differently among the joints. The forces for the look-ahead posture are close in magnitude while much larger force variation is observed for the check-6 posture. For the check-6 posture, smaller forces are observed on superior cervical joints (e.g. c1, c2). Comparing the cervical joint moments (Fig. 7b and 8b), we can see they have different signs and thus different directions ( look ahead : backward; check-6 : forward). The check-6 posture has much large lateral joint moment requirement, which is around 4 times larger than that of the look-ahead posture. This is clearly due to the movement of the center of gravity of helmet and head to the back of the shoulder. By looking at the muscle activation pattern during the flight (Fig. 9 and 10), significant differences were observed for the two postures. The look ahead posture induces mostly posterior neck muscle activation and fatigue, while the check-6 posture induces mostly anterior neck muscle activation and fatigue. Between these two, the check-6 posture has more significant muscle fatigue. In both cases, we found at the end of simulation ( ), the muscles can no longer generate enough joint torques to maintain the posture due to fatigue. In addition, due to muscle fatigue, the muscle activation pattern at the end of the simulation is different from the start of the simulation even though the aircraft accelerations 5. Conclusion In this paper, we presented a control based simulation framework with a fatigable whole-body musculoskeletal model to predict the neck musculoskeletal loads and fatigue of aviators during high-g flights. Two common postures during the flight, look-ahead and check-6, were investigated in particular. Our results indicate the posture variations during high-g flight significantly affect the cervical musculoskeletal loads (joint forces and moments, muscle activation and fatigue) and the muscle fatigue plays an import role on muscle force capacity and overall activation pattern to generate require joint torque for posture maintenance. For model calibration and validation, digital, multiaxis in-flight subject measurements are needed in the future. The method developed in the paper can be utilized for injury prediction or injury mechanism study during high-g ACM. In addition, it can be used for aviation helmet designs to mitigate fatigue or injury potential during both cruising flight and ACM. Acknowledgement The authors would like to thank Dr. Barry Shender for providing us the idealized fighter ACM acceleration data. The author would also like to thank Dr. Scott Delp of Stanford University and Dr. Anita Vasavada of Washington State University for generously sharing their developed musculoskeletal models which are the bases of the current wholebody model with detailed neck musculature. References Andersen, H.T., Neck injury sustained during exposure to high-g forces in the F16B. Aviation space and environmental medicine. Böl, M., Pipetz, a., Reese, S., Finite element model for the simulation of skeletal muscle fatigue. Materialwissenschaft und Werkstofftechnik 40, Cammarota, J.P., 1990a. Evaluation of full-sortie closed-loop simulated aerial combat maneuvering on the human centrifuge, in: IEEE Conference on Aerospace and Electronics. Cammarota, J.P., 1990b. G-LOC During Closed- Loop Simulated Aerial Combat. NAVAIRDEVCEN Technical Report #N1808-TR

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