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Effect of sub-optimal neuromotor control on the hip joint load during level walking
Journal of Biomechanics 44 (2011) 1716–1721
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Effect of sub-optimal neuromotor control on the hip joint load during level walking Saulo Martelli a,n, Fulvia Taddei a, Angelo Cappello b, Serge van Sint Jan c, Alberto Leardini d, Marco Viceconti a a
Laboratorio di Tecnologia Medica, Istituto Ortopedico Rizzoli, Bologna, Italy Dipartimento di Elettronica, Informatica e Sistemistica, Universita di Bologna, Italy c Department of Anatomy, Universite´ Libre de Bruxelles, Belgium d Movement Analysis Laboratory, Istituto Ortopedico Rizzoli, Bologna, Italy b
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 29 March 2011
Skeletal forces are fundamental information in predicting the risk of bone fracture. The neuromotor control system can drive muscle forces with various task- and health-dependent strategies but current modelling techniques provide a single optimal solution of the muscle load sharing problem. The aim of the present work was to study the variability of the hip load magnitude due to sub-optimal neuromotor control strategies using a subject-specific musculoskeletal model. The model was generated from computed tomography (CT) and dissection data from a single cadaver. Gait kinematics, ground forces and electromyographic (EMG) signals were recorded on a body-matched volunteer. Model results were validated by comparing the traditional optimisation solution with the published hip load measurements and the recorded EMG signals. The solution space of the instantaneous equilibrium problem during the first hip load peak resulted in 105 dynamically equivalent configurations of the neuromotor control. The hip load magnitude was computed and expressed in multiples of the body weight (BW). Sensitivity of the hip load boundaries to the uncertainty on the muscle tetanic stress (TMS) was also addressed. The optimal neuromotor control induced a hip load magnitude of 3.3 BW. Sub-optimal neuromotor controls induced a hip load magnitude up to 8.93 BW. Reducing TMS from the maximum to the minimum the lower boundary of the hip load magnitude varied moderately whereas the upper boundary varied considerably from 4.26 to 8.93 BW. Further studies are necessary to assess how far the neuromotor control can degrade from the optimal activation pattern and to understand which suboptimal controls are clinically plausible. However we can consider the possibility that sub-optimal activations of the muscular system play a role in spontaneous fractures not associated with falls. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Subject-specific musculoskeletal models Sub-optimal neuromotor control Hip loads Muscle force variability Level walking
1. Introduction Load cells and force platforms make possible accurate measurement of the external forces that act on our body during activities of daily living (Sutherland, 2005). However, the determination of the internal forces that the same physical activity induces on our skeleton through the joints, the ligaments, and the muscle insertions remain difficult to quantify. But this information is of vital importance in a number of research and clinical contexts. For example, the risk of fracture that a given subject faces while performing a given motor task depends not only on the specific bone strength, but also on the internal forces.
n Correspondence to: Laboratorio di Tecnologia Medica, Istituto Ortopedico Rizzoli, Via di Barbiano, 1/10, 40136 Bologna, Italy. Tel.: þ39 051 6366554; fax: þ 39 051 6366863. E-mail address: [email protected] (S. Martelli).
0021-9290/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2011.03.039
The problem is affected by a dramatic indeterminacy. Even if we model the skeleton as a mechanism made of idealised joints, represent each major muscle bundle with a single actuator, and impose all the physiological limits to the force expressed by each actuator, the resulting mathematical problem has more unknowns than equations. The best solution, when the kinematics of each segment has been measured experimentally, is to postulate that the neuromotor control activates the muscle fibres ensuring the instantaneous equilibrium while minimising a cost function (Collins, 1995; Menegaldo et al., 2006; Praagman et al., 2006). The assumption that in healthy subjects the neuromotor control works in fairly optimal conditions seems reasonable. Indeed, when applied to volunteers this approach predicts muscle activation patterns in good agreement with electromyography (EMG) recordings (Anderson and Pandy, 2001; Erdemir et al., 2007; Heller et al., 2001). Also, the intensity of the hip load predicted is comparable to that recorded with telemetric instrumented prostheses (Heller et al., 2001; Stansfield et al., 2003).
S. Martelli et al. / Journal of Biomechanics 44 (2011) 1716–1721
This approach presumes that the neuromotor control chooses, among the infinite solutions available, the muscle activation pattern that optimises a certain cost function, always the same one. But this assumption seems unrealistic for the following cases: – A large variability of the internal forces can be observed for a single subject through several repetitions of the same motion task (Bergmann et al., 2001). The ‘‘UnControlled Manifold’’ ¨ theory (Scholz and Schoner, 1999) suggests that the motor control strategy focusses on the goal of the task, and that every trajectory within the manifold of the task-equivalent configuration of the muscle actuators is virtually possible. – While we move, our goal is dependent on a number of factors. Specific activation patterns were found in case of patello-femoral pain (Besier et al., 2009), in unstable conditions (Bergmann et al., 2004), in sudden motion tasks (Yeadon et al., 2010) and different muscles controls were found during the execution of precise and power activities (Anson et al., 2002). – The way we move is also affected by our emotions. Depression has been found a co-factor for the risk of falling in the elders (Skelton and Todd, 2007; Talkowski et al., 2008), whereas somatisation, anxiety and depression were found intrinsic co-factors in non-specific musculoskeletal spinal disorders (Andersson, 1999). – Even if the optimal control assumption is acceptable for normal subjects, does it remain acceptable when used to model specific patients that are known to have neuromotor deficiencies? EMG studies seem to suggest the answer is ‘‘no’’ (Liikavainio et al., 2009; Mahaudens et al., 2009).
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Italy) at the sampling rate of 2000 Hz. Digital band filtering was used to extract the qualitative muscle control pattern (Glitsch and Baumann, 1997). 2.2. The musculoskeletal model The skeletal anatomy was extracted from the CT dataset using dedicated semiautomatic software (Amiras, Mercury Computer System, Inc., USA). The biomechanical model of the musculoskeletal system of the lower-limb was defined as a 7-segment, 10-degree-of-freedom (DOF) articulated system actuated by 82 muscle–tendon units. Each leg was articulated by three ideal joints: a ball and socket at the hip (3 DOF) and a hinge (1 DOF) at both the knee and the ankle (Jonkers et al., 2008). The identification of joint parameters was based on relevant skeletal landmarks identified on the skeletal surface (Taddei et al., 2007). All anatomical landmarks suggested by ISB standards were identified. The local coordinate system was computed for each segment (Wu et al., 2002). The hip centre was defined as the centre of the sphere that best fit the femoral head surface. The hip joint rotations were defined according to ISB standards (Wu et al., 2002). The knee rotation axis was assumed as that connecting the medial and the lateral epicondyles, which is normally considered a good approximation of this axis in surgical procedures (Tanavalee et al., 2001). The ankle flexion axis was assumed as that connecting the medial and the lateral malleoli. An expert anatomist manually registered on the subject-specific skeletal anatomy the muscular model of the lower extremity (Delp et al., 1990) using as reference the muscle line-of-actions digitised during dissection (Fig. 1b). The peak force each muscle can exert was estimated from the physiological cross section area (PCSA), assuming the muscle tetanic stress (TMS) equal to 1 MPa (Glitsch and Baumann, 1997). The muscle mechanical properties were defined accordingly (Daggfeldt and Thorstensson, 2003). Inertial parameters of each segment were derived from CT data (Fig. 1a) assuming homogeneous density properties for both the hard (1.42 g/cm3) and the soft (1.03 g/cm3) tissues (Dumas et al., 2005). Preliminary simulations were run to solve the muscle load sharing problem using a traditional static optimisation approach (Anderson and Pandy, 2001; Collins, 1995; Crowninshield and Brand, 1981) (Fig. 1c). The hip load magnitude was calculated and expressed in multiples of the ground reaction peak (GRp) to account for the inter-subject weight and walking dynamics variability. 2.3. Musculoskeletal model validation
More specifically, in predicting the risk of fracture of an elder who has a history of falls, is it still reasonable to postulate that the muscle activation follows some optimal patterns? This question is very difficult to answer in such general terms; but as a first step a simpler question might be addressed: is the intensity of the loads acting on the skeleton during a given motor task severely affected by neuromotor control strategy? The aim of the present study is to estimate, using a subjectspecific musculoskeletal model, how the intensity of the hip joint reaction acting is affected when the instantaneous equilibrium is achieved in full respect of the physiological constraints, but with sub-optimal activation patterns. Sensitivity of potential suboptimal control strategies to the muscle mechanics parameters was also assessed.
2. Materials and methods 2.1. Data collection A musculoskeletal model of the lower body was developed from a detailed multiscale data collection (Testi et al., 2010). In this project the cadaver of a 81 years old woman, 167 cm height and 63 kg mass with no history of musculoskeletal diseases was examined with a whole body high-resolution computed tomography (CT) protocol. The muscle attachment on bones, the muscle length and their superficial lines of action were digitised during dissection. The volume of each muscle was measured by water immersion. The co-ordinates of the muscle attachments were registered in space through a dedicated software (LhpBuilder, SCS, Italy) into a unique multimodal data collection. A body-matched healthy volunteer (female, 25 years old, 57 kg, 165 cm) was subjected to a detailed gait analysis protocol during level walking (Leardini et al., 2007; Manca et al., 2010), which provided 3D motion (Vicon Motion Capture, Oxford UK) of the lower limb segments (sampling rate 100 Hz) and the ground reaction forces at both feet (sampling rate 2000 Hz). The muscle activity was recorded for the most relevant muscles of the lower limb: gluteus maximus, gluteus medius, rectus femoris, vastus lateralis, vastus medialis, biceps femoris long head, semitendinosus, gastrocnemius medialis, gastrocnemius lateralis, soleus and tibialis anterior. Surface EMG signals were acquired (TelEMGs, BTS,
The predicted hip load under the hypothesis of optimal neuromotor control was compared to those measured in various subjects using telemetric implants (Bergmann et al., 2001). The predicted force patterns exerted by the principal muscles were compared with the corresponding electrical activity (Glitsch and Baumann, 1997) recorded on the body-matched volunteer during the same motion task. The model configuration that produced the first load peak was identified as the subject for the subsequent analysis of sub-optimal neuromotor control conditions.
2.4. Variability of the hip load in sub-optimal motor-control strategies The instantaneous equilibrium at the joints is achieved by every set of muscle forces that satisfies the following equation: B m,n UF n ¼ M m
ð1Þ
where the matrix B m,n contains the muscle lever arm of each of the n muscle action lines acting on each of the m DOFs, F n is a n dimension vector containing the design variables, i.e. the muscle forces, and M m is the m dimension vector that contains the joint net moments necessary to follow the target kinematics. As muscle force we considered only the active component, as the passive forces in the frame of motion here considered are negligible, due to the moderate stretch of the muscle fibre in that position. The active force component depends on a number of factors including the current muscle length, velocity and the activation conditions at the previous frame of motion. These dependencies of the muscle forces are properly described by complex relationships that require a large number of parameters to be identified (e.g. see Thelen et al., 2003) and are often affected by considerable uncertainty. Thus, to include all possible conditions that the neuromotor control system can potentially impose to the musculoskeletal system we constrained the spectrum of possible muscle forces between zero (i.e. completely inactive muscle) and the tetanic muscle forces at their optimal length in isometric conditions (F max ): F n A ½0,F max
ð2Þ
This solution space of the non-homogeneous linear system of equations ensuring the instantaneous equilibrium at the joints (Eq. (1)) is given by the null space of the matrix B m,n plus a particular solution of Eq. (1) (e.g. the optimal neuromotor control solution used in this study). This space is an m–n dimensions hyper-plane in the n-dimensional space of the unknowns (i.e. the muscle forces). In this hyperplane, the domain of the physiologically plausible muscle forces consist in a
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Fig. 1. From CT images and cadaver dissection to the subject-specific musculoskeletal simulation: extracting the skeletal anatomy and the inertial parameters from CT data (a), registering the muscular model by using the dissected fibre path as reference (b), fusing motion data (i.e. kinematics and ground forces) registered on the body-matched volunteer.
bounded portion (the hypersimplex hereinafter) where the boundaries are identified by the constraints (Eq. (2)). Preliminary simulations suggested that the shape of the hypersimplex was acicular; i.e. that the domain width along the direction connecting the two neuromotor control strategies producing the maximum (HRmax) and the minimum (HRmin) hip load was much larger than the width along all the other directions. Therefore, 103 particular solutions of Eq. (1) were obtained by uniformly sampling the vector connecting HRmax and HRmin (the principal force vector hereinafter). For each particular solution 102 perturbations were calculated by adding random combinations of the base vectors of the null space. Thus, the resulting 105 samples of the hypersimplex included the optimal and the sub-optimal neuromotor control conditions. Differences between the hip load magnitude produced by the optimal and the sub-optimal neuromotor controls were calculated and expressed in multiples of the individual body weight (BW) (see Appendix A for details).
2.5. Sensitivity of sub-optimal joint reactions to changes of the tetanic muscle stress (TMS) The peak force a muscle can exert is conventionally estimated through two different parameters: the muscle physiological cross section area (PCSA) and TMS (Daggfeldt and Thorstensson, 2003). But while several methods can be adopted in extracting reliable information on the PCSA (Jolivet et al., 2009), for the TMS estimation the problem is more complex and the literature (Buchanan et al., 2004) reports a very large range (0.35–1.37 MPa). We repeated the estimation of the hip load boundaries spanning the entire TMS range.
3. Results 3.1. Musculoskeletal model validation When the subject-specific model was solved imposing the optimal control condition, the hip load was predicted in reasonably good agreement with reported measurements (Bergmann et al., 2001) (Fig. 2). The major differences were found during stance-to-swing;
Fig. 2. Comparison of the predicted pattern of the hip load (solid black line) with the variability of the hip load magnitude (grey band) measured on 4 subjects through an hip prosthesis instrumented with a telemetric force sensor (Bergmann et al., 2001).
the out-of-bounds and the higher load rate of predictions were probably due to the different healthy conditions of the body-matched volunteer and of the implanted subjects from the reference study (Bergmann et al., 2001). In fact, the walking dynamics of the bodymatched volunteer induced a peak load on the recorded ground reaction of 1.33 BW while this value was always approximately 1 BW on the reference study (Bergmann et al., 2001). The frame corresponding to the first peak of the hip load (2.8 GRp) was selected for the subsequent analysis of the hip load variability in sub-optimal motor-control conditions. This peak was found at 17% of the gait cycle, consistently with earlier studies (Bergmann et al., 2001; Heller et al., 2001). The force patterns predicted for the major muscle groups were found in acceptable agreement with recorded and expected (Nene et al., 2004; Shiavi, 1985) firing patterns, particularly at 17% gait (Fig. 3). A major discrepancy was the near-zero force predicted for the gluteals and the quadriceps muscles close to heel-strike where a consistent electrical activity was recorded. The moderate loads predicted on the vastii during the stance-to-swing phase was
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Fig. 3. For each muscle, on the top the predicted forces and below the recorded electrical activity of the muscle during a complete gait cycle. The shaded region represent the swing phase while the non-shaded region represent the stance phase. The electrical activity is represented by the rectified EMG signal and superimposed, it is visible the EMG envelope (Glitsch and Baumann, 1997). The black bars in the bottom represent the expected firing patterns (Nene et al., 2004; Shiavi, 1985). The dash-line indicate the frame of interest for this study.
neither recorded nor expected (Nene et al., 2004; Shiavi, 1985). Last, a consistent electrical activity was recorded for the tibialis anterior during mid stance when a negligible muscle force was predicted. 3.2. Variability of the hip load in sub-optimal motor-control strategies At 17% of the gait cycle the two extreme sub-optimal neuromotor control strategies on the principal force vector induced the largest variations of the hip load magnitude; the distance between the highest (HRmax ¼7.1 BW) and the lowest (HRmin ¼3.3 BW) hip load value was 3.8 BW. Perturbing intermediate neuromotor control solutions, changes on the hip load magnitude were always below 1 BW. 3.3. Sensitivity of sub-optimal joint reactions to changes of TMS At 17% of the gait cycle the equilibrium at the joints was found for TMS values ranging from 0.57 to 1.37 MPa; when TMS was in the range 0.35–0.57 MPa, the excessive muscle weakness did not guarantee the dynamic balance of the motion. Assuming TMS¼0.57 MPa, the hip load ranged between 3.77 and 4.26 BW
(Fig. 4). This means 13% higher than the lower boundary of the joint load. When TMS was increased to the maximum value (1.37 MPa) by uniform steps of 0.1 MPa the lower boundary of the hip load magnitude initially decreased from 3.77 to 3.3 BW and no significant changes were found as TMS increased from 0.77 to 1.37 MPa. On the contrary, the variation of the upper boundary of the hip load was significant: for the lowest TMS value the maximum hip load magnitude was 4.26 BW while for the highest TMS value it was 8.93 BW, the 275% higher than the corresponding lower boundary of the joint reaction (Fig. 4).
4. Discussion The aim of the present study was to estimate, using a subjectspecific musculoskeletal model, how the intensity of the joint reaction acting on the femur through the hip is affected when the instantaneous equilibrium is achieved in full respect of the physiological constraints, but with sub-optimal activation patterns. When the model was solved imposing the optimal neuromotor control the predicted muscle forces were in an acceptable agreement with the recorded electrical activities. Some discrepancies can
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Fig. 4. Field of possible hip load due to TMS changes (dark grey region). The lowest hip load magnitude was slightly sensitive to TMS changes (3.3–3.77 BW) while the highest hip load magnitude increased from 4.26 to 8.93 BW as TMS increased. The regression lines intersect in a TMS region very close to the lower boundary of the published TMS (0.37 MPa, (Buchanan et al., 2004)) although the numerical optimisation algorithm did not reach convergence for TMS values below 0.57 MPa (light grey region).
be likely attributed to the limits of the optimisation technique. Close to heel strike, the underestimation of the gluteals and the vastii forces were likely due to the tendency of the method to underestimate the muscle co-contractions when rapid changes on the joint net moments occur (Yeadon et al., 2010). The moderate vastii force (o80 N) predicted during stance-to-swing was not expected. However similar force patters were predicted in similar studies (Xiao and Higginson, 2010) suggesting that the complex activation pattern of the quadriceps (Nene et al., 2004) can be roughly described by optimisation techniques. The last major discrepancies can be attributed to cross-talk. The significant activity recorded during early stance and late swing by the EMG sensor of the rectus femoris was probably due to the vastii activity during the same phase of motion (Nene et al., 2004) and, the activity recorded by the tibialis anterior sensor during mid stance was probably due to the high activity of the triceps surae. However a general agreement was found between predicted force patterns and the expected firing patterns, and the major discrepancies were not present at 17% gait, the frame afterwards considered for the evaluation of sub-optimal neuromotor conditions. The predicted hip loads were consistent with published measurements (Bergmann et al., 2001) showing that the total sum of hip muscle forces is reasonable. Thus, in the authors’ opinion, all these limitations should not invalidate the generality of the conclusions. The subsequent analysis explored 105 sub-optimal neuromotor control conditions showed that sub-optimal neuromotor controls can drastically increase the hip load intensity up to approximately 9 BW; this load is of the same order of magnitude of the fracture load of the femoral neck measured in cadaveric studies (Cristofolini et al., 2007). The results seem to support the existence of a principal force axis on the hypersimplex. When TMS was set to 1.37 MPa, sampling the muscle force solutions along the principal force vector we found variations on the hip load up to 5.63 BW while random perturbations of the intermediate solutions induced much smaller variations. Within the hypersimplex the optimal neuromotor control solution was slightly sensitive to TMS changes in agreement with Redl et al. (2007). However, when sub-optimal controls are allowed, the sensitivity of the model predictions to TMS changes is much higher. For instance, the maximum hip load increased from 4.26 to 8.93 BW as TMS increased from 0.57 to 1.37 MPa. To the authors’ knowledge this is the first study that explores the effect of sub-optimal control on the forces acting on the skeleton during motion. Nonetheless the comparison of
intermediate outcomes with published works supports the reliability of our results. Indeed, the gait kinematic and kinetics in our model were consistent with relevant reports (Heller et al., 2001) and, the firing pattern of principal muscles was consistent with expected normal patterns (Shiavi, 1985). The variability of the hip load during level walking in the same subject during repetitions is below 16% (Bergmann et al., 2001). While this value is much smaller than the one reported here, we should not forget that the variability over a repeated task represents the aleatory uncertainty (uncertainty arising because of natural, unpredictable variation in the performance of the system under study) of the neuromotor control. The range we reported in this work represents the epistemic uncertainty (uncertainty due to a lack of knowledge about the behaviour of the system), and in particular to the epistemic uncertainty related to the degradation of the neuromotor control. The large variability of possible sub-optimal control strategies is consistent with the known potential of the neuromotor control system of activating muscles following various strategies (Bergmann et al., 2004; Besier et al., 2009). In epidemiology studies on spontaneous osteoporotic fractures, there is a fraction of the population for which the decrease of bone density appears insufficient to explain the fracture event (Yang et al., 1996). But this observation could be easily explained if we accept that the degradation of the neuromotor control not only increases the risk of falling, but also produces overloads during normal physiological activities. The present study is affected by some limitations. The simulations were run deriving the data from different sources: a cadaveric study and in-vivo recordings on a body-matched volunteer. While this inevitably induces some inaccuracies, the impossibility of collecting all necessary data on living subjects, does balance what we would determine if many of these parameters had to be estimated from the literature. The study was limited to a single instant of the walking cycle. However, it is hard to see how the extension to the entire cycle could produce different conclusions. If the variability of the hip load in a single instant is so big, over the entire cycle it can only be equal or bigger. The method we developed to sample the solution hyperspace does not guarantee that the sampling covers all the hypersimplex. But again, even if the sampling were missing entirely a region of the hypersimplex, this could only produce a variability equal or larger than that reported here.
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Probably the most important limitation of this study is that we have no way to know which of these sub-optimal solutions is clinically plausible. At our current level of understanding there is no way to know how far the neuromotor control can degrade from the optimal activation pattern; the answer to this question requires further studies. Nevertheless the results presented here seem relevant for biomechanics research. The great variability of the intensity of the hip load observed for sub-optimal solutions suggests that the determination of the internal forces transmitted to the skeleton by postulating some optimal control is probably in many cases too optimistic. It seems more reasonable to imagine probabilistic approaches to this problem, where the probability associated to each sub-optimal solution is estimated from quantifications of neuromotor condition of the patient. The present study suggests that the deviation of the optimal neuromotor control could drive the intensity of the internal forces acting on the skeleton to considerably higher levels that those predicted in optimal conditions. If this is true, we can consider the possibility that spontaneous fractures might be due to skeletal overloading produced by the sub-optimal control of the muscles’ activation.
Conflict of interest statement There is no potential conflict of interests related to this study. None of the authors received nor will receive direct or indirect benefits from third parties for the performance of this study.
Acknowledgments Data were produced during the EU-funded project LHDL (IST2004-026932) and freely available at www.physiomespace.com
Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jbiomech.2011.03.039.
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Effect of sub-optimal neuromotor control on the hip joint load during level walking Saulo Martelli a,n, Fulvia Taddei a, Angelo Cappello b, Serge van Sint Jan c, Alberto Leardini d, Marco Viceconti a a
Laboratorio di Tecnologia Medica, Istituto Ortopedico Rizzoli, Bologna, Italy Dipartimento di Elettronica, Informatica e Sistemistica, Universita di Bologna, Italy c Department of Anatomy, Universite´ Libre de Bruxelles, Belgium d Movement Analysis Laboratory, Istituto Ortopedico Rizzoli, Bologna, Italy b
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 29 March 2011
Skeletal forces are fundamental information in predicting the risk of bone fracture. The neuromotor control system can drive muscle forces with various task- and health-dependent strategies but current modelling techniques provide a single optimal solution of the muscle load sharing problem. The aim of the present work was to study the variability of the hip load magnitude due to sub-optimal neuromotor control strategies using a subject-specific musculoskeletal model. The model was generated from computed tomography (CT) and dissection data from a single cadaver. Gait kinematics, ground forces and electromyographic (EMG) signals were recorded on a body-matched volunteer. Model results were validated by comparing the traditional optimisation solution with the published hip load measurements and the recorded EMG signals. The solution space of the instantaneous equilibrium problem during the first hip load peak resulted in 105 dynamically equivalent configurations of the neuromotor control. The hip load magnitude was computed and expressed in multiples of the body weight (BW). Sensitivity of the hip load boundaries to the uncertainty on the muscle tetanic stress (TMS) was also addressed. The optimal neuromotor control induced a hip load magnitude of 3.3 BW. Sub-optimal neuromotor controls induced a hip load magnitude up to 8.93 BW. Reducing TMS from the maximum to the minimum the lower boundary of the hip load magnitude varied moderately whereas the upper boundary varied considerably from 4.26 to 8.93 BW. Further studies are necessary to assess how far the neuromotor control can degrade from the optimal activation pattern and to understand which suboptimal controls are clinically plausible. However we can consider the possibility that sub-optimal activations of the muscular system play a role in spontaneous fractures not associated with falls. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Subject-specific musculoskeletal models Sub-optimal neuromotor control Hip loads Muscle force variability Level walking
1. Introduction Load cells and force platforms make possible accurate measurement of the external forces that act on our body during activities of daily living (Sutherland, 2005). However, the determination of the internal forces that the same physical activity induces on our skeleton through the joints, the ligaments, and the muscle insertions remain difficult to quantify. But this information is of vital importance in a number of research and clinical contexts. For example, the risk of fracture that a given subject faces while performing a given motor task depends not only on the specific bone strength, but also on the internal forces.
n Correspondence to: Laboratorio di Tecnologia Medica, Istituto Ortopedico Rizzoli, Via di Barbiano, 1/10, 40136 Bologna, Italy. Tel.: þ39 051 6366554; fax: þ 39 051 6366863. E-mail address: [email protected] (S. Martelli).
0021-9290/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jbiomech.2011.03.039
The problem is affected by a dramatic indeterminacy. Even if we model the skeleton as a mechanism made of idealised joints, represent each major muscle bundle with a single actuator, and impose all the physiological limits to the force expressed by each actuator, the resulting mathematical problem has more unknowns than equations. The best solution, when the kinematics of each segment has been measured experimentally, is to postulate that the neuromotor control activates the muscle fibres ensuring the instantaneous equilibrium while minimising a cost function (Collins, 1995; Menegaldo et al., 2006; Praagman et al., 2006). The assumption that in healthy subjects the neuromotor control works in fairly optimal conditions seems reasonable. Indeed, when applied to volunteers this approach predicts muscle activation patterns in good agreement with electromyography (EMG) recordings (Anderson and Pandy, 2001; Erdemir et al., 2007; Heller et al., 2001). Also, the intensity of the hip load predicted is comparable to that recorded with telemetric instrumented prostheses (Heller et al., 2001; Stansfield et al., 2003).
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This approach presumes that the neuromotor control chooses, among the infinite solutions available, the muscle activation pattern that optimises a certain cost function, always the same one. But this assumption seems unrealistic for the following cases: – A large variability of the internal forces can be observed for a single subject through several repetitions of the same motion task (Bergmann et al., 2001). The ‘‘UnControlled Manifold’’ ¨ theory (Scholz and Schoner, 1999) suggests that the motor control strategy focusses on the goal of the task, and that every trajectory within the manifold of the task-equivalent configuration of the muscle actuators is virtually possible. – While we move, our goal is dependent on a number of factors. Specific activation patterns were found in case of patello-femoral pain (Besier et al., 2009), in unstable conditions (Bergmann et al., 2004), in sudden motion tasks (Yeadon et al., 2010) and different muscles controls were found during the execution of precise and power activities (Anson et al., 2002). – The way we move is also affected by our emotions. Depression has been found a co-factor for the risk of falling in the elders (Skelton and Todd, 2007; Talkowski et al., 2008), whereas somatisation, anxiety and depression were found intrinsic co-factors in non-specific musculoskeletal spinal disorders (Andersson, 1999). – Even if the optimal control assumption is acceptable for normal subjects, does it remain acceptable when used to model specific patients that are known to have neuromotor deficiencies? EMG studies seem to suggest the answer is ‘‘no’’ (Liikavainio et al., 2009; Mahaudens et al., 2009).
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Italy) at the sampling rate of 2000 Hz. Digital band filtering was used to extract the qualitative muscle control pattern (Glitsch and Baumann, 1997). 2.2. The musculoskeletal model The skeletal anatomy was extracted from the CT dataset using dedicated semiautomatic software (Amiras, Mercury Computer System, Inc., USA). The biomechanical model of the musculoskeletal system of the lower-limb was defined as a 7-segment, 10-degree-of-freedom (DOF) articulated system actuated by 82 muscle–tendon units. Each leg was articulated by three ideal joints: a ball and socket at the hip (3 DOF) and a hinge (1 DOF) at both the knee and the ankle (Jonkers et al., 2008). The identification of joint parameters was based on relevant skeletal landmarks identified on the skeletal surface (Taddei et al., 2007). All anatomical landmarks suggested by ISB standards were identified. The local coordinate system was computed for each segment (Wu et al., 2002). The hip centre was defined as the centre of the sphere that best fit the femoral head surface. The hip joint rotations were defined according to ISB standards (Wu et al., 2002). The knee rotation axis was assumed as that connecting the medial and the lateral epicondyles, which is normally considered a good approximation of this axis in surgical procedures (Tanavalee et al., 2001). The ankle flexion axis was assumed as that connecting the medial and the lateral malleoli. An expert anatomist manually registered on the subject-specific skeletal anatomy the muscular model of the lower extremity (Delp et al., 1990) using as reference the muscle line-of-actions digitised during dissection (Fig. 1b). The peak force each muscle can exert was estimated from the physiological cross section area (PCSA), assuming the muscle tetanic stress (TMS) equal to 1 MPa (Glitsch and Baumann, 1997). The muscle mechanical properties were defined accordingly (Daggfeldt and Thorstensson, 2003). Inertial parameters of each segment were derived from CT data (Fig. 1a) assuming homogeneous density properties for both the hard (1.42 g/cm3) and the soft (1.03 g/cm3) tissues (Dumas et al., 2005). Preliminary simulations were run to solve the muscle load sharing problem using a traditional static optimisation approach (Anderson and Pandy, 2001; Collins, 1995; Crowninshield and Brand, 1981) (Fig. 1c). The hip load magnitude was calculated and expressed in multiples of the ground reaction peak (GRp) to account for the inter-subject weight and walking dynamics variability. 2.3. Musculoskeletal model validation
More specifically, in predicting the risk of fracture of an elder who has a history of falls, is it still reasonable to postulate that the muscle activation follows some optimal patterns? This question is very difficult to answer in such general terms; but as a first step a simpler question might be addressed: is the intensity of the loads acting on the skeleton during a given motor task severely affected by neuromotor control strategy? The aim of the present study is to estimate, using a subjectspecific musculoskeletal model, how the intensity of the hip joint reaction acting is affected when the instantaneous equilibrium is achieved in full respect of the physiological constraints, but with sub-optimal activation patterns. Sensitivity of potential suboptimal control strategies to the muscle mechanics parameters was also assessed.
2. Materials and methods 2.1. Data collection A musculoskeletal model of the lower body was developed from a detailed multiscale data collection (Testi et al., 2010). In this project the cadaver of a 81 years old woman, 167 cm height and 63 kg mass with no history of musculoskeletal diseases was examined with a whole body high-resolution computed tomography (CT) protocol. The muscle attachment on bones, the muscle length and their superficial lines of action were digitised during dissection. The volume of each muscle was measured by water immersion. The co-ordinates of the muscle attachments were registered in space through a dedicated software (LhpBuilder, SCS, Italy) into a unique multimodal data collection. A body-matched healthy volunteer (female, 25 years old, 57 kg, 165 cm) was subjected to a detailed gait analysis protocol during level walking (Leardini et al., 2007; Manca et al., 2010), which provided 3D motion (Vicon Motion Capture, Oxford UK) of the lower limb segments (sampling rate 100 Hz) and the ground reaction forces at both feet (sampling rate 2000 Hz). The muscle activity was recorded for the most relevant muscles of the lower limb: gluteus maximus, gluteus medius, rectus femoris, vastus lateralis, vastus medialis, biceps femoris long head, semitendinosus, gastrocnemius medialis, gastrocnemius lateralis, soleus and tibialis anterior. Surface EMG signals were acquired (TelEMGs, BTS,
The predicted hip load under the hypothesis of optimal neuromotor control was compared to those measured in various subjects using telemetric implants (Bergmann et al., 2001). The predicted force patterns exerted by the principal muscles were compared with the corresponding electrical activity (Glitsch and Baumann, 1997) recorded on the body-matched volunteer during the same motion task. The model configuration that produced the first load peak was identified as the subject for the subsequent analysis of sub-optimal neuromotor control conditions.
2.4. Variability of the hip load in sub-optimal motor-control strategies The instantaneous equilibrium at the joints is achieved by every set of muscle forces that satisfies the following equation: B m,n UF n ¼ M m
ð1Þ
where the matrix B m,n contains the muscle lever arm of each of the n muscle action lines acting on each of the m DOFs, F n is a n dimension vector containing the design variables, i.e. the muscle forces, and M m is the m dimension vector that contains the joint net moments necessary to follow the target kinematics. As muscle force we considered only the active component, as the passive forces in the frame of motion here considered are negligible, due to the moderate stretch of the muscle fibre in that position. The active force component depends on a number of factors including the current muscle length, velocity and the activation conditions at the previous frame of motion. These dependencies of the muscle forces are properly described by complex relationships that require a large number of parameters to be identified (e.g. see Thelen et al., 2003) and are often affected by considerable uncertainty. Thus, to include all possible conditions that the neuromotor control system can potentially impose to the musculoskeletal system we constrained the spectrum of possible muscle forces between zero (i.e. completely inactive muscle) and the tetanic muscle forces at their optimal length in isometric conditions (F max ): F n A ½0,F max
ð2Þ
This solution space of the non-homogeneous linear system of equations ensuring the instantaneous equilibrium at the joints (Eq. (1)) is given by the null space of the matrix B m,n plus a particular solution of Eq. (1) (e.g. the optimal neuromotor control solution used in this study). This space is an m–n dimensions hyper-plane in the n-dimensional space of the unknowns (i.e. the muscle forces). In this hyperplane, the domain of the physiologically plausible muscle forces consist in a
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Fig. 1. From CT images and cadaver dissection to the subject-specific musculoskeletal simulation: extracting the skeletal anatomy and the inertial parameters from CT data (a), registering the muscular model by using the dissected fibre path as reference (b), fusing motion data (i.e. kinematics and ground forces) registered on the body-matched volunteer.
bounded portion (the hypersimplex hereinafter) where the boundaries are identified by the constraints (Eq. (2)). Preliminary simulations suggested that the shape of the hypersimplex was acicular; i.e. that the domain width along the direction connecting the two neuromotor control strategies producing the maximum (HRmax) and the minimum (HRmin) hip load was much larger than the width along all the other directions. Therefore, 103 particular solutions of Eq. (1) were obtained by uniformly sampling the vector connecting HRmax and HRmin (the principal force vector hereinafter). For each particular solution 102 perturbations were calculated by adding random combinations of the base vectors of the null space. Thus, the resulting 105 samples of the hypersimplex included the optimal and the sub-optimal neuromotor control conditions. Differences between the hip load magnitude produced by the optimal and the sub-optimal neuromotor controls were calculated and expressed in multiples of the individual body weight (BW) (see Appendix A for details).
2.5. Sensitivity of sub-optimal joint reactions to changes of the tetanic muscle stress (TMS) The peak force a muscle can exert is conventionally estimated through two different parameters: the muscle physiological cross section area (PCSA) and TMS (Daggfeldt and Thorstensson, 2003). But while several methods can be adopted in extracting reliable information on the PCSA (Jolivet et al., 2009), for the TMS estimation the problem is more complex and the literature (Buchanan et al., 2004) reports a very large range (0.35–1.37 MPa). We repeated the estimation of the hip load boundaries spanning the entire TMS range.
3. Results 3.1. Musculoskeletal model validation When the subject-specific model was solved imposing the optimal control condition, the hip load was predicted in reasonably good agreement with reported measurements (Bergmann et al., 2001) (Fig. 2). The major differences were found during stance-to-swing;
Fig. 2. Comparison of the predicted pattern of the hip load (solid black line) with the variability of the hip load magnitude (grey band) measured on 4 subjects through an hip prosthesis instrumented with a telemetric force sensor (Bergmann et al., 2001).
the out-of-bounds and the higher load rate of predictions were probably due to the different healthy conditions of the body-matched volunteer and of the implanted subjects from the reference study (Bergmann et al., 2001). In fact, the walking dynamics of the bodymatched volunteer induced a peak load on the recorded ground reaction of 1.33 BW while this value was always approximately 1 BW on the reference study (Bergmann et al., 2001). The frame corresponding to the first peak of the hip load (2.8 GRp) was selected for the subsequent analysis of the hip load variability in sub-optimal motor-control conditions. This peak was found at 17% of the gait cycle, consistently with earlier studies (Bergmann et al., 2001; Heller et al., 2001). The force patterns predicted for the major muscle groups were found in acceptable agreement with recorded and expected (Nene et al., 2004; Shiavi, 1985) firing patterns, particularly at 17% gait (Fig. 3). A major discrepancy was the near-zero force predicted for the gluteals and the quadriceps muscles close to heel-strike where a consistent electrical activity was recorded. The moderate loads predicted on the vastii during the stance-to-swing phase was
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Fig. 3. For each muscle, on the top the predicted forces and below the recorded electrical activity of the muscle during a complete gait cycle. The shaded region represent the swing phase while the non-shaded region represent the stance phase. The electrical activity is represented by the rectified EMG signal and superimposed, it is visible the EMG envelope (Glitsch and Baumann, 1997). The black bars in the bottom represent the expected firing patterns (Nene et al., 2004; Shiavi, 1985). The dash-line indicate the frame of interest for this study.
neither recorded nor expected (Nene et al., 2004; Shiavi, 1985). Last, a consistent electrical activity was recorded for the tibialis anterior during mid stance when a negligible muscle force was predicted. 3.2. Variability of the hip load in sub-optimal motor-control strategies At 17% of the gait cycle the two extreme sub-optimal neuromotor control strategies on the principal force vector induced the largest variations of the hip load magnitude; the distance between the highest (HRmax ¼7.1 BW) and the lowest (HRmin ¼3.3 BW) hip load value was 3.8 BW. Perturbing intermediate neuromotor control solutions, changes on the hip load magnitude were always below 1 BW. 3.3. Sensitivity of sub-optimal joint reactions to changes of TMS At 17% of the gait cycle the equilibrium at the joints was found for TMS values ranging from 0.57 to 1.37 MPa; when TMS was in the range 0.35–0.57 MPa, the excessive muscle weakness did not guarantee the dynamic balance of the motion. Assuming TMS¼0.57 MPa, the hip load ranged between 3.77 and 4.26 BW
(Fig. 4). This means 13% higher than the lower boundary of the joint load. When TMS was increased to the maximum value (1.37 MPa) by uniform steps of 0.1 MPa the lower boundary of the hip load magnitude initially decreased from 3.77 to 3.3 BW and no significant changes were found as TMS increased from 0.77 to 1.37 MPa. On the contrary, the variation of the upper boundary of the hip load was significant: for the lowest TMS value the maximum hip load magnitude was 4.26 BW while for the highest TMS value it was 8.93 BW, the 275% higher than the corresponding lower boundary of the joint reaction (Fig. 4).
4. Discussion The aim of the present study was to estimate, using a subjectspecific musculoskeletal model, how the intensity of the joint reaction acting on the femur through the hip is affected when the instantaneous equilibrium is achieved in full respect of the physiological constraints, but with sub-optimal activation patterns. When the model was solved imposing the optimal neuromotor control the predicted muscle forces were in an acceptable agreement with the recorded electrical activities. Some discrepancies can
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Fig. 4. Field of possible hip load due to TMS changes (dark grey region). The lowest hip load magnitude was slightly sensitive to TMS changes (3.3–3.77 BW) while the highest hip load magnitude increased from 4.26 to 8.93 BW as TMS increased. The regression lines intersect in a TMS region very close to the lower boundary of the published TMS (0.37 MPa, (Buchanan et al., 2004)) although the numerical optimisation algorithm did not reach convergence for TMS values below 0.57 MPa (light grey region).
be likely attributed to the limits of the optimisation technique. Close to heel strike, the underestimation of the gluteals and the vastii forces were likely due to the tendency of the method to underestimate the muscle co-contractions when rapid changes on the joint net moments occur (Yeadon et al., 2010). The moderate vastii force (o80 N) predicted during stance-to-swing was not expected. However similar force patters were predicted in similar studies (Xiao and Higginson, 2010) suggesting that the complex activation pattern of the quadriceps (Nene et al., 2004) can be roughly described by optimisation techniques. The last major discrepancies can be attributed to cross-talk. The significant activity recorded during early stance and late swing by the EMG sensor of the rectus femoris was probably due to the vastii activity during the same phase of motion (Nene et al., 2004) and, the activity recorded by the tibialis anterior sensor during mid stance was probably due to the high activity of the triceps surae. However a general agreement was found between predicted force patterns and the expected firing patterns, and the major discrepancies were not present at 17% gait, the frame afterwards considered for the evaluation of sub-optimal neuromotor conditions. The predicted hip loads were consistent with published measurements (Bergmann et al., 2001) showing that the total sum of hip muscle forces is reasonable. Thus, in the authors’ opinion, all these limitations should not invalidate the generality of the conclusions. The subsequent analysis explored 105 sub-optimal neuromotor control conditions showed that sub-optimal neuromotor controls can drastically increase the hip load intensity up to approximately 9 BW; this load is of the same order of magnitude of the fracture load of the femoral neck measured in cadaveric studies (Cristofolini et al., 2007). The results seem to support the existence of a principal force axis on the hypersimplex. When TMS was set to 1.37 MPa, sampling the muscle force solutions along the principal force vector we found variations on the hip load up to 5.63 BW while random perturbations of the intermediate solutions induced much smaller variations. Within the hypersimplex the optimal neuromotor control solution was slightly sensitive to TMS changes in agreement with Redl et al. (2007). However, when sub-optimal controls are allowed, the sensitivity of the model predictions to TMS changes is much higher. For instance, the maximum hip load increased from 4.26 to 8.93 BW as TMS increased from 0.57 to 1.37 MPa. To the authors’ knowledge this is the first study that explores the effect of sub-optimal control on the forces acting on the skeleton during motion. Nonetheless the comparison of
intermediate outcomes with published works supports the reliability of our results. Indeed, the gait kinematic and kinetics in our model were consistent with relevant reports (Heller et al., 2001) and, the firing pattern of principal muscles was consistent with expected normal patterns (Shiavi, 1985). The variability of the hip load during level walking in the same subject during repetitions is below 16% (Bergmann et al., 2001). While this value is much smaller than the one reported here, we should not forget that the variability over a repeated task represents the aleatory uncertainty (uncertainty arising because of natural, unpredictable variation in the performance of the system under study) of the neuromotor control. The range we reported in this work represents the epistemic uncertainty (uncertainty due to a lack of knowledge about the behaviour of the system), and in particular to the epistemic uncertainty related to the degradation of the neuromotor control. The large variability of possible sub-optimal control strategies is consistent with the known potential of the neuromotor control system of activating muscles following various strategies (Bergmann et al., 2004; Besier et al., 2009). In epidemiology studies on spontaneous osteoporotic fractures, there is a fraction of the population for which the decrease of bone density appears insufficient to explain the fracture event (Yang et al., 1996). But this observation could be easily explained if we accept that the degradation of the neuromotor control not only increases the risk of falling, but also produces overloads during normal physiological activities. The present study is affected by some limitations. The simulations were run deriving the data from different sources: a cadaveric study and in-vivo recordings on a body-matched volunteer. While this inevitably induces some inaccuracies, the impossibility of collecting all necessary data on living subjects, does balance what we would determine if many of these parameters had to be estimated from the literature. The study was limited to a single instant of the walking cycle. However, it is hard to see how the extension to the entire cycle could produce different conclusions. If the variability of the hip load in a single instant is so big, over the entire cycle it can only be equal or bigger. The method we developed to sample the solution hyperspace does not guarantee that the sampling covers all the hypersimplex. But again, even if the sampling were missing entirely a region of the hypersimplex, this could only produce a variability equal or larger than that reported here.
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Probably the most important limitation of this study is that we have no way to know which of these sub-optimal solutions is clinically plausible. At our current level of understanding there is no way to know how far the neuromotor control can degrade from the optimal activation pattern; the answer to this question requires further studies. Nevertheless the results presented here seem relevant for biomechanics research. The great variability of the intensity of the hip load observed for sub-optimal solutions suggests that the determination of the internal forces transmitted to the skeleton by postulating some optimal control is probably in many cases too optimistic. It seems more reasonable to imagine probabilistic approaches to this problem, where the probability associated to each sub-optimal solution is estimated from quantifications of neuromotor condition of the patient. The present study suggests that the deviation of the optimal neuromotor control could drive the intensity of the internal forces acting on the skeleton to considerably higher levels that those predicted in optimal conditions. If this is true, we can consider the possibility that spontaneous fractures might be due to skeletal overloading produced by the sub-optimal control of the muscles’ activation.
Conflict of interest statement There is no potential conflict of interests related to this study. None of the authors received nor will receive direct or indirect benefits from third parties for the performance of this study.
Acknowledgments Data were produced during the EU-funded project LHDL (IST2004-026932) and freely available at www.physiomespace.com
Appendix A. Supplementary data Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jbiomech.2011.03.039.
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