The co-contraction index of the upper limb for young and old adult cyclists.

Bicycling is a popular and convenient means of transportation amongst the elderly in the Netherlands. However, the uptake of the electric bicycle resulted in an increase of single-sided bicycle accidents amongst the elderly (Veiligheid, 2010). Since elderly are prone to severe injuries, bicycle stability is currently a popular research topic. Three main balance strategies have been proposed in former studies: steering as the primary balance strategy and trunk -and lateral knee movement as secondary balance strategies (Moore et al., 2011; Cain, 2013). Since steering is the primary strategy for bicycle stability, the stiffness of the arms plays an important role in active stability during cycling. It has been shown that the arm stiffness of a passive rider is an important factor on the stability of a bicycle (Doria and Tognazzo, 2014). In the study presented here, the co-contraction index (CCI) of the upper limb for young and old adult cyclist is studied. Data is collected during experiments based on the setup described in (Kiewiet et al., 2014), wherein contact forces, muscle activities and motions of the rider and bicycle are measured for 15 young adult (mean±sd: 25.3±2.8 yrs) and 15 old adult (mean±sd: 58.1±2.1 yrs) subjects during unperturbed and perturbed cycling. The arm stiffness is defined as a co-contraction ratio between muscle activity of the m. Biceps Brachii and m. Triceps Lateralis. Results suggest that older adult cyclists use more co-contraction of their arm muscles during cycling, compared to young cyclists. The inter-subject variability of the found CCI was higher for the old adult subject group, compared to the young group. The results support the initial hypothesis that the increase in co-contraction of the upper limb for older cyclists is higher during perturbed cycling compared to unperturbed cycling than for younger cyclists. The findings might give direction towards solutions for increasing the safety and stability for elderly cyclists.

The influence of a user-adaptive prosthetic knee across varying walking speeds: A randomized cross-over trial.

Previously conducted trials comparing the gait pattern of individuals with a transfemoral amputation using a user-adaptive and a non-microprocessor-controlled prosthetic knee (NMPK) found mixed and conflicting results. Few trials, however, have compared user-adaptive to non-adaptive prosthetic knees across different walking speeds. Because of the ability of variable damping, the effect of user-adaptive knees might be more pronounced at lower or higher walking speeds. Our aim was to compare the Rheo Knee II (a microprocessor-controlled prosthetic knee) with NMPKs across varying walking speeds. In addition, we studied compensatory mechanisms associated with non-optimal prosthetic knee kinematics, such as intact ankle vaulting and vertical acceleration of the pelvis. Nine persons with a transfemoral amputation or knee disarticulation were included and measured with their own NMPK and with the Rheo Knee II. Measurements were performed at three walking speeds: preferred walking speed, 70% preferred walking speed and 115% preferred walking speed. No differences on peak prosthetic knee flexion during swing were found between prosthetic knee conditions. In addition, prosthetic knee flexion increased significantly with walking speed for both prosthetic knee conditions. At 70% preferred walking speed we found that vaulting of the intact ankle was significantly decreased while walking with the Rheo Knee II compared to the NMPK condition (P=0.028). We did not find differences in peak vertical acceleration of the pelvis during initial and mid-swing of the prosthetic leg. In conclusion, comparison of walking with the Rheo Knee II to walking with a NMPK across different walking speeds showed limited differences in gait parameters.

Sensitivity of subject-specific models to Hill muscle-tendon model parameters in simulations of gait.

Subject-specific musculoskeletal (MS) models of the lower extremity are essential for applications such as predicting the effects of orthopedic surgery. We performed an extensive sensitivity analysis to assess the effects of potential errors in Hill muscle-tendon (MT) model parameters for each of the 56 MT parts contained in a state-of-the-art MS model. We used two metrics, namely a Local Sensitivity Index (LSI) and an Overall Sensitivity Index (OSI), to distinguish the effect of the perturbation on the predicted force produced by the perturbed MT parts and by all the remaining MT parts, respectively, during a simulated gait cycle. Results indicated that sensitivity of the model depended on the specific role of each MT part during gait, and not merely on its size and length. Tendon slack length was the most sensitive parameter, followed by maximal isometric muscle force and optimal muscle fiber length, while nominal pennation angle showed very low sensitivity. The highest sensitivity values were found for the MT parts that act as prime movers of gait (Soleus: average OSI=5.27%, Rectus Femoris: average OSI=4.47%, Gastrocnemius: average OSI=3.77%, Vastus Lateralis: average OSI=1.36%, Biceps Femoris Caput Longum: average OSI=1.06%) and hip stabilizers (Gluteus Medius: average OSI=3.10%, Obturator Internus: average OSI=1.96%, Gluteus Minimus: average OSI=1.40%, Piriformis: average OSI=0.98%), followed by the Peroneal muscles (average OSI=2.20%) and Tibialis Anterior (average OSI=1.78%) some of which were not included in previous sensitivity studies. Finally, the proposed priority list provides quantitative information to indicate which MT parts and which MT parameters should be estimated most accurately to create detailed and reliable subject-specific MS models.

TLEM 2.0 - a comprehensive musculoskeletal geometry dataset for subject-specific modeling of lower extremity.

When analyzing complex biomechanical problems such as predicting the effects of orthopedic surgery, subject-specific musculoskeletal models are essential to achieve reliable predictions. The aim of this paper is to present the Twente Lower Extremity Model 2.0, a new comprehensive dataset of the musculoskeletal geometry of the lower extremity, which is based on medical imaging data and dissection performed on the right lower extremity of a fresh male cadaver. Bone, muscle and subcutaneous fat (including skin) volumes were segmented from computed tomography and magnetic resonance images scans. Inertial parameters were estimated from the image-based segmented volumes. A complete cadaver dissection was performed, in which bony landmarks, attachments sites and lines-of-action of 55 muscle actuators and 12 ligaments, bony wrapping surfaces, and joint geometry were measured. The obtained musculoskeletal geometry dataset was finally implemented in the AnyBody Modeling System (AnyBody Technology A/S, Aalborg, Denmark), resulting in a model consisting of 12 segments, 11 joints and 21 degrees of freedom, and including 166 muscle-tendon elements for each leg. The new TLEM 2.0 dataset was purposely built to be easily combined with novel image-based scaling techniques, such as bone surface morphing, muscle volume registration and muscle-tendon path identification, in order to obtain subject-specific musculoskeletal models in a quick and accurate way. The complete dataset, including CT and MRI scans and segmented volume and surfaces, is made available at http://www.utwente.nl/ctw/bw/research/projects/TLEMsafe for the biomechanical community, in order to accelerate the development and adoption of subject-specific models on large scale. TLEM 2.0 is freely shared for non-commercial use only, under acceptance of the TLEMsafe Research License Agreement.

Recovery response latencies to tripping perturbations during gait decrease with practice.

There are several control mechanisms that contribute to keep gait stability under the presence of perturbations. For larger perturbations, responses with longer latencies produce adequate reactions to the perturbation. Latencies might be shorter, and the risk for falling might decrease provided that the reaction is adequate. It is possible that training the recovery responses through a sequence of perturbations induce some changes in the reactions. The goal of this paper is to test if the recovery response mechanisms might change during a training session with multiple perturbations. Differences in the recovery reactions executed at the beginning and at the end of a sequence of perturbations were analyzed. The latency of the burst in the Rectus Femoris (RF), measured with surface EMG (sEMG), showed a significant reduction during the course of the experimental session. When trials are repeated, subjects are able to generate a more appropriate response to the perturbations.

Prediction of ground reaction forces and moments during various activities of daily living.

Inverse dynamics based simulations on musculoskeletal models is a commonly used method for the analysis of human movement. Due to inaccuracies in the kinematic and force plate data, and a mismatch between the model and the subject, the equations of motion are violated when solving the inverse dynamics problem. As a result, dynamic inconsistency will exist and lead to residual forces and moments. In this study, we present and evaluate a computational method to perform inverse dynamics-based simulations without force plates, which both improves the dynamic consistency as well as removes the model׳s dependency on measured external forces. Using the equations of motion and a scaled musculoskeletal model, the ground reaction forces and moments (GRF&Ms) are derived from three-dimensional full-body motion. The method entails a dynamic contact model and optimization techniques to solve the indeterminacy problem during a double contact phase and, in contrast to previously proposed techniques, does not require training or empirical data. The method was applied to nine healthy subjects performing several Activities of Daily Living (ADLs) and evaluated with simultaneously measured force plate data. Except for the transverse ground reaction moment, no significant differences (P>0.05) were found between the mean predicted and measured GRF&Ms for almost all ADLs. The mean residual forces and moments, however, were significantly reduced (P>0.05) in almost all ADLs using our method compared to conventional inverse dynamic simulations. Hence, the proposed method may be used instead of raw force plate data in human movement analysis using inverse dynamics.

Evaluation of a morphing based method to estimate muscle attachment sites of the lower extremity.

To generate subject-specific musculoskeletal models for clinical use, the location of muscle attachment sites needs to be estimated with accurate, fast and preferably automated tools. For this purpose, an automatic method was used to estimate the muscle attachment sites of the lower extremity, based on the assumption of a relation between the bone geometry and the location of muscle attachment sites. The aim of this study was to evaluate the accuracy of this morphing based method. Two cadaver dissections were performed to measure the contours of 72 muscle attachment sites on the pelvis, femur, tibia and calcaneus. The geometry of the bones including the muscle attachment sites was morphed from one cadaver to the other and vice versa. For 69% of the muscle attachment sites, the mean distance between the measured and morphed muscle attachment sites was smaller than 15 mm. Furthermore, the muscle attachment sites that had relatively large distances had shown low sensitivity to these deviations. Therefore, this morphing based method is a promising tool for estimating subject-specific muscle attachment sites in the lower extremity in a fast and automated manner.

Modeling of WalkMECH: a fully-passive energy-efficient transfemoral prosthesis prototype.

In this paper we present the port-based model of WalkMECH, a fully-passive transfemoral prosthesis prototype that has been designed and realized for normal walking. The model has been implemented in a simulation environment so to analyze the performance of the prosthetic leg in walking experiments and so to enhance the mechanics of the system. The accuracy of the model has been validated by experimental tests with a unilateral amputee participant.

Variable stiffness actuated prosthetic knee to restore knee buckling during stance: a modeling study.

Most modern intelligent knee prosthesis use dampers to modulate dynamic behavior and prevent excessive knee flexion, but they dissipate energy and do not assist in knee extension. Energy efficient variable stiffness control (VSA) can reduce the energy consumption yet effectively modulate the dynamic behavior and use stored energy during flexion to assist in subsequent extension. A principle design of energy efficient VSA in a prosthetic knee is proposed and analyzed for the specific case of rejection of a disturbed stance phase. The concept is based on the principle that the output stiffness of a spring can be changed without changing the energy stored in the elastic elements of the spring. The usability of this concept to control a prosthetic knee is evaluated using a model. Part of the stance phase of the human leg was modeled by a double pendulum. Specifically the rejection of a common disturbance of transfemoral prosthetic gait, an unlocked knee at heel strike, was evaluated. The ranges of spring stiffnesses were determined such that the angular characteristics of a normal stance phase were preserved, but disturbances could also be rejected. The simulations predicted that energy efficient VSA can be useful for the control of prosthetic knees.

A simple controller for the prediction of three-dimensional gait.

The objective of this study is to investigate the potential of forward dynamic modeling in predicting the functional outcome of complicated orthopedic procedures involving relocation or removal of muscles or correction osteotomies in the lower extremities. For this purpose, we developed a torque actuated forward dynamics based three-dimensional model of gait, that extends the previous reported work of Van der Kooij et al. (2003). The mechanical properties are scaled to the subject and lateral stability is provided by an 'offset plus proportional' controller (Hof, 2008). Kinematic constraints are formulated based on three independent gait descriptors and implemented in an optimization algorithm. The computational effort is small (1min per gait cycle on a 1GHz processor) and the control scheme generates symmetric and cyclic gait based on the desired gait descriptors. An interface with the inverse dynamics based AnyBody Modeling System, a musculoskeletal modeling tool, provides insight in muscle activities. The proposed control scheme is robust against mediolateral perturbations. The predictive capacity of the model is evaluated by simulating pathological gait by means of weakening the hip abductors, and the model is able to predict some of the trends of compensatory strategies in such a perturbed mechanical system.

Sensitivity of subject-specific models to errors in musculo-skeletal geometry.

Subject-specific musculo-skeletal models of the lower extremity are an important tool for investigating various biomechanical problems, for instance the results of surgery such as joint replacements and tendon transfers. The aim of this study was to assess the potential effects of errors in musculo-skeletal geometry on subject-specific model results. We performed an extensive sensitivity analysis to quantify the effect of the perturbation of origin, insertion and via points of each of the 56 musculo-tendon parts contained in the model. We used two metrics, namely a Local Sensitivity Index (LSI) and an Overall Sensitivity Index (OSI), to distinguish the effect of the perturbation on the predicted force produced by only the perturbed musculo-tendon parts and by all the remaining musculo-tendon parts, respectively, during a simulated gait cycle. Results indicated that, for each musculo-tendon part, only two points show a significant sensitivity: its origin, or pseudo-origin, point and its insertion, or pseudo-insertion, point. The most sensitive points belong to those musculo-tendon parts that act as prime movers in the walking movement (insertion point of the Achilles Tendon: LSI=15.56%, OSI=7.17%; origin points of the Rectus Femoris: LSI=13.89%, OSI=2.44%) and as hip stabilizers (insertion points of the Gluteus Medius Anterior: LSI=17.92%, OSI=2.79%; insertion point of the Gluteus Minimus: LSI=21.71%, OSI=2.41%). The proposed priority list provides quantitative information to improve the predictive accuracy of subject-specific musculo-skeletal models.

Design of a fully-passive transfemoral prosthesis prototype.

In this study, we present the mechanical design of a prototype of a fully-passive transfemoral prosthesis for normal walking. The conceptual working principle at the basis of the design is inspired by the power flow in human gait, with the main purpose of realizing an energy efficient device. The mechanism is based on three elements, which are responsible of the energetic coupling between the knee and ankle joints. The design parameters of the prototype are determined according to the human body and the natural gait characteristics, in order to mimic the dynamic behavior of a healthy leg. Hereby, we present the construction details of the prototype, which realizes the working principle of the conceptual mechanism.

Energy efficient walking with central pattern generators: from passive dynamic walking to biologically inspired control.

Like human walking, passive dynamic walking-i.e. walking down a slope with no actuation except gravity-is energy efficient by exploiting the natural dynamics. In the animal world, neural oscillators termed central pattern generators (CPGs) provide the basic rhythm for muscular activity in locomotion. We present a CPG model, which automatically tunes into the resonance frequency of the passive dynamics of a bipedal walker, i.e. the CPG model exhibits resonance tuning behavior. Each leg is coupled to its own CPG, controlling the hip moment of force. Resonance tuning above the endogenous frequency of the CPG-i.e. the CPG's eigenfrequency-is achieved by feedback of both limb angles to their corresponding CPG, while integration of the limb angles provides resonance tuning at and below the endogenous frequency of the CPG. Feedback of the angular velocity of both limbs to their corresponding CPG compensates for the time delay in the loop coupling each limb to its CPG. The resonance tuning behavior of the CPG model allows the gait velocity to be controlled by a single parameter, while retaining the energy efficiency of passive dynamic walking.

Ambulatory assessment of ankle and foot dynamics.

Ground reaction force (GRF) measurement is important in the analysis of human body movements. The main drawback of the existing measurement systems is the restriction to a laboratory environment. This paper proposes an ambulatory system for assessing the dynamics of ankle and foot, which integrates the measurement of the GRF with the measurement of human body movement. The GRF and the center of pressure (CoP) are measured using two six-degrees-of-freedom force sensors mounted beneath the shoe. The movement of foot and lower leg is measured using three miniature inertial sensors, two rigidly attached to the shoe and one on the lower leg. The proposed system is validated using a force plate and an optical position measurement system as a reference. The results show good correspondence between both measurement systems, except for the ankle power estimation. The root mean square (RMS) difference of the magnitude of the GRF over 10 evaluated trials was (0.012 +/- 0.001) N/N (mean +/- standard deviation), being (1.1 +/- 0.1)% of the maximal GRF magnitude. It should be noted that the forces, moments, and powers are normalized with respect to body weight. The CoP estimation using both methods shows good correspondence, as indicated by the RMS difference of (5.1 +/- 0.7) mm, corresponding to (1.7 +/- 0.3)% of the length of the shoe. The RMS difference between the magnitudes of the heel position estimates was calculated as (18 +/- 6) mm, being (1.4 +/- 0.5)% of the maximal magnitude. The ankle moment RMS difference was (0.004 +/- 0.001) Nm/N, being (2.3 +/- 0.5)% of the maximal magnitude. Finally, the RMS difference of the estimated power at the ankle was (0.02 +/- 0.005) W/N, being (14 +/- 5)% of the maximal power. This power difference is caused by an inaccurate estimation of the angular velocities using the optical reference measurement system, which is due to considering the foot as a single segment. The ambulatory system considers separate heel and forefoot segments, thus allowing an additional foot moment and power to be estimated. Based on the results of this research, it is concluded that the combination of the instrumented shoe and inertial sensing is a promising tool for the assessment of the dynamics of foot and ankle in an ambulatory setting.

Resonance tuning in a neuro-musculo-skeletal model of the forearm.

In rhythmic movements, humans activate their muscles in a robust and energy efficient way. These activation patterns are oscillatory and seem to originate from neural networks in the spinal cord, called central pattern generators (CPGs). Evidence for the existence of CPGs was found for instance in lampreys, cats and rats. There are indications that CPGs exist in humans as well, but this is not proven yet. Energy efficiency is achieved by resonance tuning: the central nervous system is able to tune into the resonance frequency of the limb, which is determined by the local reflex gains. The goal of this study is to investigate if the existence of a CPG in the human spine can explain the resonance tuning behavior, observed in human rhythmic limb movement. A neuro-musculo-skeletal model of the forearm is proposed, in which a CPG is organized in parallel to the local reflexloop. The afferent and efferent connections to the CPG are based on clues about the organization of the CPG, found in literature. The model is kept as simple as possible (i.e., lumped muscle models, groups of neurons are lumped into half-centers, simple reflex model), but incorporates enough of the essential dynamics to explain behavior-such as resonance tuning-in a qualitative way. Resonance tuning is achieved above, at and below the endogenous frequency of the CPG in a highly non-linear neuro- musculo-skeletal model. Afferent feedback of muscle lengthening to the CPG is necessary to accomplish resonance tuning above the endogenous frequency of the CPG, while feedback of muscle velocity is necessary to compensate for the phase lag, caused by the time delay in the loop coupling the limb to the CPG. This afferent feedback of muscle lengthening and velocity represents the Ia and II fibers, which-according to literature-is the input to the CPG. An internal process of the CPG, which integrates the delayed muscle lengthening and feeds it to the half-center model, provides resonance tuning below the endogenous frequency. Increased co-contraction makes higher movement frequencies possible. This agrees with studies of rhythmic forearm movements, which have shown that co-contraction increases with movement frequency. Robustness against force perturbations originates mainly from the CPG and the local reflex loop. The CPG delivers an increasing part of the necessary muscle activation for increasing perturbation size. As far as we know, the proposed neuro-musculo-skeletal model is the first that explains the observed resonance tuning in human rhythmic limb movement.

Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity.

BACKGROUND: To assist in the treatment of gait disorders, an inverse and forward 3D musculoskeletal model of the lower extremity will be useful that allows to evaluate if-then scenarios. Currently available anatomical datasets do not comprise sufficiently accurate and complete information to construct such a model. The aim of this paper is to present a complete and consistent anatomical dataset, containing the orientations of joints (hip, knee, ankle and subtalar joints), muscle parameters (optimum length, physiological cross sectional area), and geometrical parameters (attachment sites, 'via' points). METHODS: One lower extremity, taken from a male embalmed specimen, was studied. Position and geometry were measured with a 3D-digitizer. Optotrak was used for measurement of rotation axes of joints. Sarcomere length was measured by laser diffraction. FINDINGS: A total of 38 muscles were measured. Each muscle was divided in different muscle lines of action based on muscle morphology. 14 Ligaments of the hip, knee and ankle were included. INTERPRETATION: The presented anatomical dataset embraces all necessary data for state of the art musculoskeletal modelling of the lower extremity. Implementation of these data into an (existing) model is likely to significantly improve the estimation of muscle forces and will thus make the use of the model as a clinical tool more feasible.

Energy efficient and robust rhythmic limb movement by central pattern generators.

Humans show great energy efficiency and robustness in rhythmic tasks, such as walking and arm swinging. In this study a mathematical model of rhythmic limb movement is presented, which shows that tight local coupling of Central Pattern Generators (CPGs) to limbs could explain part of this behavior. Afferent feedback to flexor and extensor centers of the CPG is crucial in providing energy efficiency by means of resonance tuning. Feedback of positional information provides resonance tuning above the endogenous frequency of the CPG. Integral feedback provides resonance tuning at and below the endogenous frequency. Feedback of velocity information is necessary to compensate for the time delay in the loop, coupling limb to CPG; without velocity feedback bi-stability occurs and resonance tuning is not possible at high movement frequencies. The concepts of energy efficient and robust control of rhythmic limb movements are also applicable to robotics. It is the first CPG model, which provides resonance tuning at natural limb frequencies above and below its endogenous frequency.

Bifurcation and stability analysis in musculoskeletal systems: a study in human stance.

Reflexes are important in the control of such daily activities as standing and walking. The goal of this study is to establish how reflexive feedback of muscle length, velocity, and force can lead to stable equilibria (i.e., posture) and limit cycles (e.g., ankle clonus and gait). The influence of stretch reflexes on the behavior and stability of musculoskeletal systems was examined using a model of human stance. We computed branches of fold and Hopf bifurcations by numerical bifurcation analysis of the model. These fold and Hopf branches divide the parameter space, constructed by the reflexive feedback gains, into regions of different behavior: unstable posture, stable posture, and stable limit cycles. These limit cycles correspond to a neural deficiency, termed ankle clonus. We also linked bifurcation analysis to known biomechanical concepts by linearizing the model: the fold branch corresponds to zero ankle stiffness and defines the minimal muscle length feedback necessary for stable posture; the Hopf branch is related to unstable reflex loops. Crossing the Hopf branch can lead to the above-mentioned stable limit cycles. The Hopf branch reduces with increasing time delays, making the subject's posture more susceptible to unstable reflex loops. This might be one of the reasons why elderly people, or those with injuries to the central nervous system, often have trouble with standing and other posture tasks. The influence of cocontraction and force feedback on the behavior of the posture model was also investigated. An increase in cocontraction leads to an increase in ankle stiffness (i.e., intrinsic muscle stiffness) and a decrease in the effective reflex loop gain. On the one hand, positive force feedback increases the ankle stiffness (i.e., intrinsic and reflexive muscle stiffness); on the other hand it makes the posture more susceptible to unstable reflex loops. For negative force feedback, the opposite is true. Finally, we calculated areas of reflex gains for perturbed stance and quiet stance in healthy subjects by fitting the model to data from the literature. The overlap of these areas of reflex gains could indicate that stretch reflexes are the major control mechanisms in both quiet and perturbed stance. In conclusion, this study has successfully combined bifurcation analysis with the more common biomechanical concepts and tools to determine the influence of reflexes on the stability and quality of stance. In the future, we will develop this line of research to look at rhythmic tasks, such as walking.

Multiple-step strategies to recover from stumbling perturbations.

This study has analysed the recovery from an induced stumble whilst walking on a treadmill. Four stumbling conditions were tested; at early swing with short and long durations and at mid and late swing with short duration. The experiment set-up, including the possibility of being stumbled, did not alter the normal gait patterns and the recovery strategies depended on the perturbation conditions. For the early swing perturbation, delayed lowering and elevating strategies were performed using the perturbed leg. A lowering strategy was seen for mid and late swing perturbations. An elevating strategy consisted of an elevation of the swing limb while a lowering one consisted of bringing the foot quickly to the ground. There were two groups of reactions to the experimental perturbation of gait. In the first, there was an effort to complete the disturbed step as normally as possible, so the following steps were less constrained to maintain treadmill speed. In the second group of reactions, the perturbed step was aborted and the recovery effort transferred to the contralateral limb. In many cases, several steps were needed to regain normal gait pattern. The study of recovery reactions from gait perturbations should include at least three steps after the perturbed one.

Revised planimetric model of unipennate skeletal muscle: a mechanical approach.

OBJECTIVE: Planimetric models which are simple, in the sense that small numerical effort is needed, are used to study functional consequences of skeletal muscle architecture. This paper argues with the approach to derive force of a unipennate muscle based on only equilibrium of the aponeurosis (tendon-sheet). In such an approach intramuscular pressure gradients are neglected and no suitable aponeurosis force can be determined. METHOD: The approach presented in this paper is based on mechanical equilibrium of whole muscle. A volume-related force is introduced to keep muscle volume constant. Mechanical equilibrium of whole muscle yields a different relation between fiber and muscle force as well as length changes as a consequence of pennation, compared with relations derived when only equilibrium of aponeurosis is considered. RESULTS: The newly derived relation improved prediction of the rat gastrocnemius medialis muscle force-length characteristics. CONCLUSION: The prediction of muscle geometry and the prediction of force-length characteristics are very good with a simple model such as a planimetric model. This conclusion suggests that the influence of properties neglected in such a simple model are either small or are internally compensated for in the net effects.