Effect of muscle wrapping on model estimates of neck muscle strength

Of the computational models of the cervical spine reported in the literature, not one takes into account the changes in muscle paths due to the underlying vertebrae. Instead, all model the individual muscle paths as straight-line segments. The major aim of this study was to quantify the changes in muscle moment arm, muscle force and joint moment due to muscle wrapping in the cervical spine. Five muscles in a straight-line model of the cervical spine were wrapped around underlying vertebrae, and the results obtained from this model were compared against the original. The two models were then validated against experimental and computational data. Results show that muscle wrapping has a significant effect on muscle moment arms and therefore joint moments and should not be neglected.     

Three-dimensional temporomandibular joint muscle attachment morphometry and its impacts on musculoskeletal modeling

In musculoskeletal models of the human temporomandibular joint (TMJ), muscles are typically represented by force vectors that connect approximate muscle origin and insertion centroids (centroid-to-centroid force vectors). This simplification assumes equivalent moment arms and muscle lengths for all fibers within a muscle even with complex geometry and may result in inaccurate estimations of muscle force and joint loading. The objectives of this study were to quantify the three-dimensional (3D) human TMJ muscle attachment morphometry and examine its impact on TMJ mechanics. 3D muscle attachment surfaces of temporalis, masseter, lateral pterygoid, and medial pterygoid muscles of human cadaveric heads were generated by co-registering measured attachment boundaries with underlying skull models created from cone-beam computerized tomography (CBCT) images. A bounding box technique was used to quantify 3D muscle attachment size, shape, location, and orientation. Musculoskeletal models of the mandible were then developed and validated to assess the impact of 3D muscle attachment morphometry on joint loading during jaw maximal open-close. The 3D morphometry revealed that muscle lengths and moment arms of temporalis and masseter muscles varied substantially among muscle fibers. The values calculated from the centroid-to-centroid model were significantly different from those calculated using the ‘Distributed model’, which considered crucial 3D muscle attachment morphometry. Consequently, joint loading was underestimated by more than 50% in the centroid-to-centroid model. Therefore, it is necessary to consider 3D muscle attachment morphometry, especially for muscles with broad attachments, in TMJ musculoskeletal models to precisely quantify the joint mechanical environment critical for understanding TMJ function and mechanobiology.     

A parametric model of muscle moment arm as a function of joint angle: Application to the dorsiflexor muscle group in mice

A parametric model was developed to describe the relationship between muscle moment arm and joint angle. The model was applied to the dorsiflexor muscle group in mice, for which the moment arm was determined as a function of ankle angle. The moment arm was calculated from the torque measured about the ankle upon application of a known force along the line of action of the dorsiflexor muscle group. The dependence of the dorsiflexor moment arm on ankle angle was modeled as r=R sin(a+Δ), where r is the moment arm calculated from the measured torque and a is the joint angle. A least-squares curve fit yielded values for R, the maximum moment arm, and Δ, the angle at which the maximum moment arm occurs as offset from 90°. Parametric models were developed for two strains of mice, and no differences were found between the moment arms determined for each strain. Values for the maximum moment arm, R, for the two different strains were 0.99 and 1.14 mm, in agreement with the limited data available from the literature. While in some cases moment arm data may be better fitted by a polynomial, use of the parametric model provides a moment arm relationship with meaningful anatomical constants, allowing for the direct comparison of moment arm characteristics between different strains and species.     

Muscle wrapping on arbitrary meshes with the heat method

Muscle paths play an important role in musculoskeletal simulations by determining a muscle’s length and how its force is distributed to joints. Most previous approaches estimate the way in which muscles ‘wrap’ around bones and other structures with smooth analytical wrapping surfaces. In this paper, we employ Newton’s method with discrete differential geometry to permit muscle wrapping over arbitrary polygonal mesh surfaces that represent underlying bones and structures. Precomputing distance fields allows us to speed up computations for the common situation where many paths cross the same wrapping surfaces. We found positive results for the accuracy, robustness, and efficiency of the method. However the method did not exhibit continuous changes in path length for dynamic simulations. Nonetheless this approach provides a valuable step toward fast muscle wrapping on arbitrary meshes.     

Exploring novel objective functions for simulating muscle coactivation in the neck

Musculoskeletal modeling allows for analysis of individual muscles in various situations. However, current techniques to realistically simulate muscle response when significant amounts of intentional coactivation is required are inadequate. This would include stiffening the neck or spine through muscle coactivation in preparation for perturbations or impacts. Muscle coactivation has been modeled previously in the neck and spine using optimization techniques that seek to maximize the joint stiffness by maximizing total muscle activation or muscle force. These approaches have not sought to replicate human response, but rather to explore the possible effects of active muscle. Coactivation remains a challenging feature to include in musculoskeletal models, and may be improved by extracting optimization objective functions from experimental data. However, the components of such an objective function must be known before fitting to experimental data. This study explores the effect of components in several objective functions, in order to recommend components to be used for fitting to experimental data. Four novel approaches to modeling coactivation through optimization techniques are presented, two of which produce greater levels of stiffness than previous techniques. Simulations were performed using OpenSim and MATLAB cooperatively. Results show that maximizing the moment generated by a particular muscle appears analogous to maximizing joint stiffness. The approach of optimizing for maximum moment generated by individual muscles may be a good candidate for developing objective functions that accurately simulate muscle coactivation in complex joints. This new approach will be the focus of future studies with human subjects.     

Physically correlated muscle activation for a human head and neck computational model

A computational 50th percentile male head and neck complex model was correlated to physical experimental data. The computational model utilizes 15 muscle pairs represented by the Hill Muscle Model with the complete head/neck system modeled using MADYMO?. The model was used for analysis and optimization of activation and deactivation of muscle activity in flexion and extension. Sensitivity analysis performed using the model shows that, of the multiple parameters within the Hill Model, activation level and timing prove to have the greatest effect on the system kinematics. In addition, the rate by which an activation level is changed becomes an important factor in the simulation. With the use of numerical optimization techniques, a pattern was determined for the applied activation/deactivation rates and timing of flexors and extensors during flexion and extension of the head. The numerical optimization result correlated to within 9% of measured value during the initial flexion of the head. The optimized activation model reflected an activation onset 90 ms after the start of the impulse load, which agrees with published reaction times of muscles. Activation and deactivation rates for the extensors were found to be 1.7 and 0.29%, respectively. While the onset of activation of the flexor muscles occurred before rebound, it was found that muscles, at near the mid-plane, were triggered by the optimized model to abate the flexion. Rates of activation and deactivation of the flexors were found to be 0.9 and 0.3%, respectively. Both the extensors as well as the flexors were found to activate only up to 70% before deactivating. Therefore, it was evident from this study that using the Hill Muscle Model with the activation parameter modeled as binary, 0 or 100%, may lead to inaccurate simulation results.     

Evaluation of a method to scale muscle strength for gait simulations of children with cerebral palsy

Cerebral palsy (CP) is a neurological disorder that results in life-long mobility impairments. Musculoskeletal models used to investigate mobility deficits for children with CP often lack subject-specific characteristics such as altered muscle strength, despite a high prevalence of muscle weakness in this population. We hypothesized that incorporating subject-specific strength scaling within musculoskeletal models of children with CP would improve accuracy of muscle excitation predictions in walking simulations. Ten children (13.5 ± 3.3 years; GMFCS level II) with spastic CP participated in a gait analysis session where lower-limb kinematics, ground reaction forces, and bilateral electromyography (EMG) of five lower-limb muscles were collected. Isometric strength was measured for each child using handheld dynamometry. Three musculoskeletal models were generated for each child including a ‘Default’ model with the generic musculoskeletal model’s muscle strength, a ‘Uniform’ model with muscle strength scaled allometrically, and a ‘Custom’ model with muscle strength scaled based on handheld dynamometry strength measures. Muscle-driven gait simulations were generated using each model for each child. Simulation accuracy was evaluated by comparing predicted muscle excitations and measured EMG signals, both in the duration of muscle activity and the root-mean-square difference (RMSD) between signals. Improved agreement with EMG were found in both the ‘Custom’ and ‘Uniform’ models compared to the ‘Default’ model indicated by improvement in RMSD summed across all muscles, as well as RMSD and duration of activity for individual muscles. Incorporating strength scaling into musculoskeletal models can improve the accuracy of walking simulations for children with CP.     

Specificity of resistance training responses in neck muscle size and strength

This study examined hypertrophy after head extension resistance training to assess which muscles of the complicated cervical neuromuscular system were used in this activity. We also determined if conventional resistance exercises, which are likely to evoke isometric action of the neck, induce generalized hypertrophy of the cervical muscle. Twenty-two active college students were studied. [mean (SE) age, weight and height: 21 (1) years, 71 (4) kg and 173 (3) cm, respectively]. Subjects were assigned to one of three groups: RESX (head extension exercise and other resistance exercises), RES (resistance exercises without specific neck exercise), or CON (no training). Groups RESX (n = 8) and RES (n = 6) trained 3 days/week for 12 weeks with large-muscle mass exercises (squat, deadlift, push press, bent row and mid-thigh pull). Group RESX also performed three sets of ten repetitions of a head extension exercise 3 days/week with a load equal to the 3 × 10 repetition maximum (RM). Group CON (n = 8) was a control group. The cross-sectional area (CSA) of nine individual muscles or muscle groups was determined by magnetic resonance imaging (MRI) of the cervical region. The CSA data were averaged over four contiguous transaxial slices in which all muscles of interest were visible. The 3 × 10 RM for the head extension exercise increased for RESX after training [from 17.9 (1.0) to 23.9 (1.4) kg, P < 0.05] but not for RES [from 17.6 (1.4) to 17.7 (1.9)␣kg] or CON [from 10.1 (2.2) to 10.3 (2.1) kg]. RESX showed an increase in total neck muscle CSA after training [from 19.5 (3.0) to 22.0 (3.6) cm², P < 0.05], but RES and CON did not [from 19.6 (2.9) to 19.7 (2.9)␣cm² and 17.0 (2.5) to 17.0 (2.4) cm², respectively]. This hypertrophy for RESX was due mainly to increases in CSA of 23.9 (3.2), 24.0 (5.8), and 24.9 (5.3)% for the splenius capitis, and semispinalis capitis and cervicis muscles, respectively. The lack of generalized neck muscle hypertrophy in RES was not due to insufficient training. For example, the CSA of their quadriceps femoris muscle group, as assessed by MRI, increased by 7 (1)% after this short-term training (P < 0.05). The results suggest that: (1) the splenius capitis, and semispinalis capitis and cervicis muscles are mainly responsible for head extension; (2) short-term resistance training does not provide a sufficient stimulus to evoke neck muscle hypertrophy unless specific neck exercises are performed; and (3) the postural role of head extensors provides modest loading in bipeds. Accepted: 15 October 1996     

Influence of ground reaction force perturbations on anterior cruciate ligament loading during sidestep cutting

Anterior cruciate ligament (ACL) injury risk is likely increased under unexpected loading conditions. Such situations may arise from mid-air contact with another athlete, or misjudgments in landing height, stride length or surface compliance resulting in an unbalanced landing and unexpected changes in the ground reaction forces (GRFs). The purpose this study was to identify how GRF perturbations influence ACL loading during sidestep cutting. Muscle-actuated simulations of sidestep cutting were generated and analyzed for 20 subjects. Perturbations of 20, 40 and 60% of the nominal value were applied to the posterior, vertical, and medial GRF. Open-loop, forward dynamics simulations were run with no feedback or correction mechanism which allowed deviations from the experimentally measured kinematics as a result of the GRF perturbations. Posterior and vertical GRF perturbations significantly increased ACL loading, although the change was more pronounced with posterior perturbations. These changes were primarily due to the sagittal plane component of ACL loading regardless of perturbation direction. Peak ACL loading occurred almost immediately after initial ground contact, and was thus predicated on initial joint configuration. The results of this study give merit to including knee flexion angle at initial ground contact in the evolving neuromuscular training modalities aimed at preventing non-contact ACL injury.     

The interaction of muscle moment arm,knee laxity,and torque in a multi-scale musculoskeletal model of the lower limb

IntroductionMusculoskeletal modeling allows insight into the interaction of muscle force and knee joint kinematics that cannot be measured in the laboratory. However, musculoskeletal models of the lower extremity commonly use simplified representations of the knee that may limit analyses of the interaction between muscle forces and joint kinematics. The goal of this research was to demonstrate how muscle forces alter knee kinematics and consequently muscle moment arms and joint torque in a musculoskeletal model of the lower limb that includes a deformable representation of the knee.MethodsTwo musculoskeletal models of the lower limb including specimen-specific articular geometries and ligament deformability at the knee were built in a finite element framework and calibrated to match mean isometric torque data collected from 12 healthy subjects. Muscle moment arms were compared between simulations of passive knee flexion and maximum isometric knee extension and flexion. In addition, isometric torque results were compared with predictions using simplified knee models in which the deformability of the knee was removed and the kinematics at the joint were prescribed for all degrees of freedom.ResultsPeak isometric torque estimated with a deformable knee representation occurred between 45° and 60° in extension, and 45° in flexion. The maximum isometric flexion torques generated by the models with deformable ligaments were 14.6% and 17.9% larger than those generated by the models with prescribed kinematics; by contrast, the maximum isometric extension torques generated by the models were similar. The change in hamstrings moment arms during isometric flexion was greater than that of the quadriceps during isometric extension (a mean RMS difference of 9.8 mm compared to 2.9 mm, respectively).DiscussionThe large changes in the moment arms of the hamstrings, when activated in a model with deformable ligaments, resulted in changes to flexion torque. When simulating human motion, the inclusion of a deformable joint in a multi-scale musculoskeletal finite element model of the lower limb may preserve the realistic interaction of muscle force with knee kinematics and torque.     

A computationally efficient strategy to estimate muscle forces in a finite element musculoskeletal model of the lower limb

Concurrent multiscale simulation strategies are required in computational biomechanics to study the interdependence between body scales. However, detailed finite element models rarely include muscle recruitment due to the computational burden of both the finite element method and the optimization strategies widely used to estimate muscle forces. The aim of this study was twofold: first, to develop a computationally efficient muscle force prediction strategy based on proportional-integral-derivative (PID) controllers to track gait and chair rise experimental joint motion with a finite element musculoskeletal model of the lower limb, including a deformable knee representation with 12 degrees of freedom; and, second, to demonstrate that the inclusion of joint-level deformability affects muscle force estimation by using two different knee models and comparing muscle forces between the two solutions. The PID control strategy tracked experimental hip, knee, and ankle flexion/extension with root mean square errors below 1°, and estimated muscle, contact and ligament forces in good agreement with previous results and electromyography signals. Differences up to 11% and 20% in the vasti and biceps femoris forces, respectively, were observed between the two knee models, which might be attributed to a combination of differing joint contact geometry, ligament behavior, joint kinematics, and muscle moment arms. The tracking strategy developed in this study addressed the inevitable tradeoff between computational cost and model detail in musculoskeletal simulations and can be used with finite element musculoskeletal models to efficiently estimate the interdependence between muscle forces and tissue deformation.     

Effects of training and creatine supplement on muscle strength and body mass

The purpose of this study was to test the effect of creatine supplement on the size of the extra- and intracellular compartments and on the increase of isokinetic force during a strength training-program. Twenty-five healthy male subjects (age 22.0+/-2.9 years) participated in this experiment. Seven subjects formed the control-group. They did not complete any training and did not have any dietary supplement. The eighteen other subjects were randomly divided into a creatine- (n = 8) and a placebo-group (n = 10). They were submitted to a controlled strength-training program for 42 days followed by a detraining period of 21 days. Creatine and placebo were given over a period of 9 weeks. The size of the body water compartments was assessed by bioimpedance spectroscopy and the isokinetic force was determined during a single squat by means of an isokinetic dynamometer. These measurements were completed beforehand, at the end of the training period, and after the determining period. Both placebo- and creatine-group increased the isokinetic force by about 6% after the training period, showing that creatine ingestion does not induce a higher increase of the force measured during a single movement. No change in body mass was observed in the control- and placebo-groups during the entire experiment period while the body mass of the creatine-group was increased by 2 kg (P < 0.001). This change can be attributed partially to an increase (P = 0.039) in the body water content (+1.11), and more specifically, to an increase (P < 0.001) in the volume of the inter-cellular compartment (+0.61). Nevertheless, the relative volumes of the body water compartments remained constant and therefore the gain in body mass cannot be attributed to water retention, but probably to dry matter growth accompanied with a normal water volume.     

Discrete wavelet transform analysis of surface electromyography for the fatigue assessment of neck and shoulder muscles

Assessment of neuromuscular fatigue is essential for early detection and prevention of risks associated with work-related musculoskeletal disorders. In recent years, discrete wavelet transform (DWT) of surface electromyography (SEMG) has been used to evaluate muscle fatigue, especially during dynamic contractions when the SEMG signal is non-stationary. However, its application to the assessment of work-related neck and shoulder muscle fatigue is not well established. Therefore, the purpose of this study was to establish DWT analysis as a suitable method to conduct quantitative assessment of neck and shoulder muscle fatigue under dynamic repetitive conditions. Ten human participants performed 40 min of fatiguing repetitive arm and neck exertions while SEMG data from the upper trapezius and sternocleidomastoid muscles were recorded. The ten of the most commonly used wavelet functions were used to conduct the DWT analysis. Spectral changes estimated using power of wavelet coefficients in the 12–23 Hz frequency band showed the highest sensitivity to fatigue induced by the dynamic repetitive exertions. Although most of the wavelet functions tested in this study reasonably demonstrated the expected power trend with fatigue development and recovery, the overall performance of the “Rbio3.1” wavelet in terms of power estimation and statistical significance was better than the remaining nine wavelets.     

The effect of leg dominance and landing height on ACL loading among female athletes

Female athletes are more prone to anterior cruciate ligament (ACL) injury. A neuromuscular imbalance called leg dominance may provide a biomechanical explanation. Therefore, the purpose of this study was to compare the side-to-side lower limb differences in movement patterns, muscle forces and ACL forces during a single-leg drop-landing task from two different heights. We hypothesized that there will be significant differences in lower limb movement patterns (kinematics), muscle forces and ACL loading between the dominant and non-dominant limbs. Further, we hypothesized that significant differences between limbs will be present when participants land from a greater drop-landing height. Eight recreational female participants performed dominant and non-dominant single-leg drop landings from 30 to 60 cm. OpenSim software was used to develop participant-specific musculoskeletal models and to calculate muscle forces. We also predicted ACL loading using our previously established method. There were no significant differences between dominant and non-dominant leg landing except in ankle dorsiflexion and GMED muscle forces at peak GRF. Landing from a greater height resulted in significant differences among most kinetics and kinematics variables and ACL forces. Minimal differences in lower-limb muscle forces and ACL loading between the dominant and non-dominant legs during single-leg landing may suggest similar risk of injury across limbs in this cohort. Further research is required to confirm whether limb dominance may play an important role in the higher incidence of ACL injury in female athletes with larger and sport-specific cohorts.     

Incorporating the length-dependent passive-force generating muscle properties of the extrinsic finger muscles into a wrist and finger biomechanical musculoskeletal model

Dynamic movement trajectories of low mass systems have been shown to be predominantly influenced by passive viscoelastic joint forces and torques compared to momentum and inertia. The hand is comprised of 27 small mass segments. Because of the influence of the extrinsic finger muscles, the passive torques about each finger joint become a complex function dependent on the posture of multiple joints of the distal upper limb. However, biomechanical models implemented for the dynamic simulation of hand movements generally don’t extend proximally to include the wrist and distal upper limb. Thus, they cannot accurately represent these complex passive torques. The purpose of this short communication is to both describe a method to incorporate the length-dependent passive properties of the extrinsic index finger muscles into a biomechanical model of the upper limb and to demonstrate their influence on combined movement of the wrist and fingers. Leveraging a unique set of experimental data, that describes the net passive torque contributed by the extrinsic finger muscles about the metacarpophalangeal joint of the index finger as a function of both metacarpophalangeal and wrist postures, we simulated the length-dependent passive properties of the extrinsic finger muscles. Dynamic forward simulations demonstrate that a model including these properties passively exhibits coordinated movement between the wrist and finger joints, mimicking tenodesis, a behavior that is absent when the length-dependent properties are removed. This work emphasizes the importance of incorporating the length-dependent properties of the extrinsic finger muscles into biomechanical models to study healthy and impaired hand movements.     

Cervical and axioscapular muscle stiffness measured with shear wave elastography: A comparison between different levels of work-related neck disability

Assessing muscle mechanical properties in terms of stiffness may provide important insights into mechanisms underlying work-related neck pain. This study compared stiffness of cervical and axioscapular muscles between 92 participants (sonographers) with no (n = 31), mild (n = 43) or moderate/severe (n = 18) neck disability. It was hypothesized that participants with more severe neck pain and disability would present with altered distribution of stiffness in cervical and axioscapular muscles than those with no disability. Using shear wave elastography, the shear modulus (kPa) of five cervical and six axioscapular muscles or muscle segments were measured in a relaxed seated upright or side-lying position. Muscle activity was measured simultaneously using surface electromyography during the elastography measurements and scapular depression was measured using a measurement tape and inclinometer before the elastography measurements to evaluate their potential confounding influences on shear modulus. Increased shear modulus was found in deeper than superficial cervical muscles and more cranial than caudal axioscapular muscles. However, no differences in shear modulus of the cervical or axioscapular muscles were found between sonographers with varying levels of disability. This study suggests no alterations in stiffness of cervical and axioscapular muscles were associated with work-related neck pain and disability.     

The effect of forearm support on children’s head, neck and upper limb posture and muscle activity during computer use

Use of computers by children has increased rapidly, however few studies have addressed factors which may reduce musculoskeletal stress during computer use by children. This study quantified the postural and muscle activity effects of providing forearm support when children used computers. Twelve male and 12 female children (10–12 years) who regularly used computers were recruited. Activities were completed using a computer with two workstation configurations, one of which provided for forearm support on the desk surface. 3D posture was analysed using an infra-red motion analysis system. Surface EMG was collected from five muscle groups in the neck/shoulder region and right upper limb. Providing a support surface resulted in more elevated and flexed upper limbs. The use of forearm or wrist support was associated with reduced muscle activity for most muscle groups. Muscle activity reductions with support were of sufficient magnitude to be clinically meaningful. The provision of a supporting surface for the arm is therefore likely to be useful for reducing musculoskeletal stresses associated with computing tasks for children.     

Biomechanical consequences of running with deep core muscle weakness

The deep core muscles are often neglected or improperly trained in athletes. Improper function of this musculature may lead to abnormal spinal loading, muscle strain, or injury to spinal structures, all of which have been associated with increased low back pain (LBP) risk. The purpose of this study was to identify potential strategies used to compensate for weakness of the deep core musculature during running and to identify accompanying changes in compressive and shear spinal loads. Kinematically-driven simulations of overground running were created for eight healthy young adults in OpenSim at increasing levels of deep core muscle weakness. The deep core muscles (multifidus, quadratus lumborum, psoas, and deep fascicles of the erector spinae) were weakened individually and together. The superficial longissimus thoracis was a significant compensator for 4 out of 5 weakness conditions (p < 0.05). The deep erector spinae required the largest compensations when weakened individually (up to a 45 ± 10% increase in compensating muscle force production, p = 0.004), revealing it may contribute most to controlling running kinematics. With complete deep core muscle weakness, peak anterior shear loading increased on all lumbar vertebrae (up to 19%, p = 0.001). Additionally, compressive spinal loading increased on the upper lumbar vertebrae (up to 15%, p = 0.007) and decreased on the lower lumbar vertebrae (up to 8%, p = 0.008). Muscular compensations may increase risk of muscular fatigue or injury and increased spinal loading over numerous gait cycles may result in damage to spinal structures. Therefore, insufficient strength of the deep core musculature may increase a runner’s risk of developing LBP.     

The effect of strength training on estimates of mitochondrial density and distribution throughout muscle fibres

The purpose of this study was to investigate the effect of strength training (12 weeks, 3 days/week, four lower-body exercises) of young individuals (mean age 23.6 years) on estimates of mitochondrial distribution throughout muscle fibres. A control group (mean age 21. 7 years) was followed simultaneously. Skeletal muscle biopsy samples were obtained from the vastus lateralis, pre- and post-training. The regional distribution of subsarcolemmal and intermyofibrillar mitochondrial populations was determined using quantitative histochemical staining of succinate dehydrogenase (SDH) in type I and II muscle fibres. Strength training resulted in significant increases of 26% and 28% in the cross-sectional area of type I and II fibres, respectively (P < 0.05). Overall SDH activity decreased by 13% with strength training (P < 0.05). The decrease in SDH activity with strength training between fibre types and between subsarcolemmal and intermyofibrillar regions of muscle fibres was not different. Fibre area and SDH activity was unchanged in the control group. We conclude that the muscle hypertrophy associated with strength training results in reduced density of regionally distributed mitochondria, as indicated by the reduction in the activity of SDH.