Skeletal muscle models composed of motor units: A review.

The mathematical muscle models should include several aspects of muscle structure and physiology. First, muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties and play different roles in generating muscle force. Second, whole muscle activity is an effect of net excitatory inputs to a pool of motoneurons innervating the muscle, which have different excitability, influencing MU recruitment. In this review, we compare various methods for modeling MU twitch and tetanic forces and then discuss muscle models composed of different MU types and number. We first present four different analytical functions used for twitch modeling and show limitations related to the number of twitch describing parameters. We also show that a nonlinear summation of twitches should be considered in modeling tetanic contractions. We then compare different muscle models, most of which are variations of Fuglevand's model, adopting a common drive hypothesis and the size principle. We pay attention to integrating previously developed models into a consensus model based on physiological data from in vivo experiments on the rat medial gastrocnemius muscle and its respective motoneurons. Finally, we discuss the shortcomings of existing models and potential applications for studying MU synchronization, potentiation, and fatigue.

Estimation of contractile parameters of successive twitches in unfused tetanic contractions of single motor units - A proof-of-concept study using ultrafast ultrasound imaging in vivo.

During a voluntary contraction, motor units (MUs) fire a train of action potentials, causing summation of the twitch forces, resulting in fused or unfused tetanus. Twitches have been important in studying whole-muscle contractile properties and differentiation between MU types. However, there are still knowledge gaps concerning the voluntary force generation mechanisms. Current methods rely on the spike-triggered averaging technique, which cannot track changes in successive twitches' properties in response to individual neural firings. This study proposes a method that estimates successive twitches contractile parameters of single MUs during low force voluntary isometric contractions in human biceps brachii. We used a previously developed ultrafast ultrasound imaging method to estimate unfused tetanic activity signals of single MUs. A twitch decomposition model was used to decompose unfused tetanic activity signals into individual twitches. This study found that the contractile parameters varied within and across MUs. There was an association between the inter-spike interval and the contraction time (r = 0.49,p < 0.001) and the half-relaxation time (r = 0.58,p < 0.001), respectively. The method shows the proof-of-concept to study MU contractile properties of individual twitches in vivo, which can provide further insights into the force generation mechanisms of voluntary contractions and response to individual neural discharges.

Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle.

The synchronized firings of active motor units (MUs) increase the oscillations of muscle force, observed as physiological tremor. This study aimed to investigate the effects of synchronizing the firings within three types of MUs (slow-S, fast resistant to fatigue-FR, and fast fatigable-FF) on the muscle force production using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including 8 S, 23 FR, and 26 FF) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions.

Biomechanical conditioning of the motor unit transitory force decrease following a reduction in stimulation rate.

BACKGROUND: The biomechanical background of the transitory force decrease following a sudden reduction in the stimulation frequency under selected experimental conditions was studied on fast resistant motor units (MUs) of rat medial gastrocnemius in order to better understand the mechanisms of changes in force transmission. METHODS: Firstly, MUs were stimulated with three-phase trains of stimuli (low-high-low frequency pattern) to identify patterns when the strongest force decrease (3-36.5%) following the middle high frequency stimulation was observed. Then, in the second part of experiments, the MUs which presented the largest force decrease in the last low-frequency phase were alternatively tested under one of five conditions to analyse the influence of biomechanical factors of the force decrease: (1) determine the influence of muscle stretch on amplitude of the force decrease, (2) determine the numbers of interpulse intervals necessary to evoke the studied phenomenon, (3) study the influence of coactivation of other MUs on the studied force decrease, (4) test the presence of the transitory force decrease at progressive changes in stimulation frequency, (5) and perform mathematical analysis of changes in twitch-shape responses to individual stimuli within a tetanus phase with the studied force decrease. RESULTS: Results indicated that (1) the force decrease was highest when the muscle passive stretch was optimal for the MU twitch (100 mN); (2) the middle high-frequency burst of stimuli composed of at least several pulses was able to evoke the force decrease; (3) the force decrease was eliminated by a coactivation of 10% or more MUs in the examined muscle; (4) the transitory force decrease occured also at the progressive decrease in stimulation frequency; and (5) a mathematical decomposition of contractions with the transitory force decrease into twitch-shape responses to individual stimuli revealed that the force decrease in question results from the decrease of twitch forces and a shortening in contraction time whereas further force restitution is related to the prolongation of relaxation. CONCLUSIONS: High sensitivity to biomechanical conditioning indicates that the transitory force decrease is dependent on disturbances in the force transmission predominantly by collagen surrounding active muscle fibres.

Separation of electrocardiographic from electromyographic signals using dynamic filtration.

Trunk muscle electromyographic (EMG) signals are often contaminated by the electrical activity of the heart. During low or moderate muscle force, these electrocardiographic (ECG) signals disturb the estimation of muscle activity. Butterworth high-pass filters with cut-off frequency of up to 60 Hz are often used to suppress the ECG signal. Such filters disturb the EMG signal in both frequency and time domain. A new method based on the dynamic application of Savitzky-Golay filter is proposed. EMG signals of three left trunk muscles and pure ECG signal were recorded during different motor tasks. The efficiency of the method was tested and verified both with the experimental EMG signals and with modeled signals obtained by summing the pure ECG signal with EMG signals at different levels of signal-to-noise ratio. The results were compared with those obtained by application of high-pass, 4th order Butterworth filter with cut-off frequency of 30 Hz. The suggested method is separating the EMG signal from the ECG signal without EMG signal distortion across its entire frequency range regardless of amplitudes. Butterworth filter suppresses the signals in the 0-30 Hz range thus preventing the low-frequency analysis of the EMG signal. An additional disadvantage is that it passes high-frequency ECG signal components which is apparent at equal and higher amplitudes of the ECG signal as compared to the EMG signal. The new method was also successfully verified with abnormal ECG signals.

Power frequency spectrum analysis of surface EMG signals of upper limb muscles during elbow flexion - A comparison between healthy subjects and stroke survivors.

After a stroke, motor units stop working properly and large, fast-twitch units are more frequently affected. Their impaired functions can be investigated during dynamic tasks using electromyographic (EMG) signal analysis. The aim of this paper is to investigate changes in the parameters of the power/frequency function during elbow flexion between affected, non-affected, and healthy muscles. Fifteen healthy subjects and ten stroke survivors participated in the experiments. Electromyographic data from 6 muscles of the upper limbs during elbow flexion were filtered and normalized to the amplitudes of EMG signals during maximal isometric tasks. The moments when motion started and when the flexion angle reached its maximal value were found. Equal intervals of 0.3407 s were defined between these two moments and one additional interval before the start of the flexion (first one) was supplemented. For each of these intervals the power/frequency function of EMG signals was calculated. The mean (MNF) and median frequencies (MDF), the maximal power (MPw) and the area under the power function (APw) were calculated. MNF was always higher than MDF. A significant decrease in these frequencies was found in only three post-stroke survivors. The frequencies in the first time interval were nearly always the highest among all intervals. The maximal power was nearly zero during first time interval and increased during the next ones. The largest values of MPw and APw were found for the flexor muscles and they increased for the muscles of the affected arm compared to the non-affected one of stroke survivors.

A General Mathematical Algorithm for Predicting the Course of Unfused Tetanic Contractions of Motor Units in Rat Muscle.

An unfused tetanus of a motor unit (MU) evoked by a train of pulses at variable interpulse intervals is the sum of non-equal twitch-like responses to these stimuli. A tool for a precise prediction of these successive contractions for MUs of different physiological types with different contractile properties is crucial for modeling the whole muscle behavior during various types of activity. The aim of this paper is to develop such a general mathematical algorithm for the MUs of the medial gastrocnemius muscle of rats. For this purpose, tetanic curves recorded for 30 MUs (10 slow, 10 fast fatigue-resistant and 10 fast fatigable) were mathematically decomposed into twitch-like contractions. Each contraction was modeled by the previously proposed 6-parameter analytical function, and the analysis of these six parameters allowed us to develop a prediction algorithm based on the following input data: parameters of the initial twitch, the maximum force of a MU and the series of pulses. Linear relationship was found between the normalized amplitudes of the successive contractions and the remainder between the actual force levels at which the contraction started and the maximum tetanic force. The normalization was made according to the amplitude of the first decomposed twitch. However, the respective approximation lines had different specific angles with respect to the ordinate. These angles had different and non-overlapping ranges for slow and fast MUs. A sensitivity analysis concerning this slope was performed and the dependence between the angles and the maximal fused tetanic force normalized to the amplitude of the first contraction was approximated by a power function. The normalized MU contraction and half-relaxation times were approximated by linear functions depending on the normalized actual force levels at which each contraction starts. The normalization was made according to the contraction time of the first contraction. The actual force levels were calculated initially from the recorded tetanic curves and subsequently from the modeled curves obtained from the summation of all models of the preceding contractions (the so called "full prediction"). The preciseness of the prediction was verified by two coefficients estimating the error between the modeled and the experimentally recorded curves. The proposed approach was tested for 30 MUs from the database and for three additional MUs, not included in the initial set. It was concluded that this general algorithm can be successfully used for modeling of a unfused tetanus course of a single MU of fast and slow type.

Prolonged activity evokes potentiation and the "sag" phenomenon in slow motor units of rat soleus.

Slow motor units (MUs) have no sag in their unfused tetani. This study in anesthetized rats shows that the sag can be observed in slow soleus MUs after prolonged activity. Twitches and unfused tetanic contractions were recorded from male (n=35) and female (n=39) MUs before and after the four minutes of the fatigue test (trains of 13 pulses at 40 Hz repeated every second). After this activity twitch contractions potentiated and a shift in the steep part of the force-frequency curve towards lower frequencies was observed in both sexes. Initially no sag was visible in unfused tetani, but after the fatigue test the phenomenon was observed in 77% of male, while in 13% of female MUs, the result consistent with the previously reported higher content of IIa myosin and faster contraction of MUs in male soleus. The decomposition of tetani with sag into trains of twitch-shape responses to consecutive stimuli revealed higher forces of initial decomposed twitches than later. The revealed alterations the force development due to long-lasting activation of slow MUs were sex-related and more pronounced in male soleus.

Estimation of the error between experimental tetanic force curves of MUs of rat medial gastrocnemius muscle and their models by summation of equal successive contractions.

More accurate muscle models require appropriate modelling of individual twitches of motor units (MUs) and their unfused tetanic contractions. It was shown in our previous papers, using a few MUs, that modelling of unfused tetanic force curves by summation of equal twitches is not accurate, especially for slow MUs. The aim of this study was to evaluate this inaccuracy using a statistical number of MUs of the rat medial gastrocnemius muscle (15 of slow, 15 of fast resistant and 15 of fast fatigable type). Tetanic contractions were evoked by trains of 41 stimuli at random interpulse intervals and different mean frequencies, resembling discharge patterns observed during natural muscle activity. The tetanic curves were calculated by the summation of equal twitches according to the respective experimental patterns. The previously described 6-parameter analytical function for twitch modelling was used. Comparisons between the experimental and the modelled curves were made using two coefficients: the fit coefficient and the area coefficient. The errors between modelled and experimental tetanic forces were substantially different between the three MU types. The error was the most significant for slow MUs, which develop much higher forces in real contractions than could be predicted based on the summation of equal twitches, while the smallest error was observed for FF MUs--their recorded tetanic forces were similar to those predicted by modelling. The obtained results indicate the importance of the inclusion of the type-specific non-linearity in the summation of successive twitch-like contractions of MUs in order to increase the reliability of modelling skeletal muscle force.

Decomposition of motor unit tetanic contractions of rat soleus muscle: Differences between males and females.

Mathematical decomposition of tetanic contractions of slow motor units (MUs) of the rat heterogeneous medial gastrocnemius muscle revealed immense variability of twitch-shape responses to successive pulses, contrary to results obtained for fast MUs. The aim of this study in rat soleus muscle, almost exclusively composed of slow MUs, was to reveal whether such variability of twitch-shape decomposed components was a common property of slow MUs in the two studied muscles, and whether ranges of the force amplitude or time parameters of these decomposed twitches showed sex differences. Unfused tetanic contractions evoked by stimulation at variable interpulse intervals were analyzed for 10 MUs of males and 10 MUs of females. Significantly higher variability between parameters of the decomposed responses was observed for male soleus MUs, as the mean ratio of forces of the strongest decomposed twitch and the first (the weakest) decomposed twitch amounted to 3.8 for males and 2.8 for females. The ratios of the contraction times of the longest decomposed to the first twitch were much more similar between male and female MUs, 2.6 and 2.9, respectively. Consequently, the mean ratio of the force-time area for the strongest decomposed to the first twitch was much bigger in male than female MUs (7.35 vs. 5.07, respectively). Our observations indicate that high variability of responses to successive stimuli is a general property of slow MUs in different rat muscles, but the mechanisms of summation of individual twitches into tetanic contractions of MUs are not identical for male and female rats.

Physiological consequences of doublet discharges on motoneuronal firing and motor unit force.

The double discharges are observed at the onset of contractions of mammalian motor units (MUs), especially during their recruitment to strong or fast movements. Doublets lead to MU force increase and improve ability of muscles to maintain high force during prolonged contractions. In this review we discuss an ability to produce doublets by fast and slow motoneurons (MNs), their influence on the course of action potential afterhyperpolarization (AHP) as well as its role in modulation of the initial stage of the firing pattern of MNs. In conclusion, a generation of doublets is an important strategy of motor control, responsible for fitting the motoneuronal firing rate to the optimal for MUs at the start of their contraction, necessary for increment of muscle force.

Dynamic changes of twitchlike responses to successive stimuli studied by decomposition of motor unit tetanic contractions in rat medial gastrocnemius.

Unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals (IPIs) were recorded for 10 fast fatigable (FF), 10 fast resistant (FR), and 10 slow (S) motor units (MUs) and subsequently decomposed with a mathematical algorithm into trains of twitch-shape responses to successive stimuli. The mean stimulation frequencies were matched for each MU to evoke tetani of similar fusion degrees, whereas the variability range of IPIs was in each case 50-150% of the mean IPI. Force and time parameters of decomposed twitches were analyzed and related to the first response. Considerable variability of the analyzed twitch parameters was observed in each MU, although the largest range of variability occurred in slow MUs. In general, the decomposed twitch responses had longer duration and higher force than single-twitch contractions, although for nine FF and six FR MUs some of the decomposed responses were slightly weaker (but not faster) than the first twitches of these MUs. Comparison of the strongest decomposed twitch to the first decomposed twitch revealed ratios of forces up to 2.35, 3.33, and 6.89 for FF, FR, and S MUs and ratios of force-time areas up to 3.54, 4.67, and 14.26 for FF, FR, and S MUs, whereas for the contraction times the ratios of the longest decomposed twitch to the first twitch amounted to 2.46, 2.07, and 3.52 for FF, FR, and S MUs, respectively. The results indicate that contractile responses to successive action potentials are considerably variable, especially for slow MUs.

An approach for simulation of the muscle force modeling it by summation of motor unit contraction forces.

Muscle force is due to the cumulative effect of repetitively contracting motor units (MUs). To simulate the contribution of each MU to whole muscle force, an approach implemented in a novel computer program is proposed. The individual contraction of an MU (the twitch) is modeled by a 6-parameter analytical function previously proposed; the force of one MU is a sum of its contractions due to an applied stimulation pattern, and the muscle force is the sum of the active MUs. The number of MUs, the number of slow, fast-fatigue-resistant, and fast-fatigable MUs, and their six parameters as well as a file with stimulation patterns for each MU are inputs for the developed software. Different muscles and different firing patterns can be simulated changing the input data. The functionality of the program is illustrated with a model consisting of 30 MUs of rat medial gastrocnemius muscle. The twitches of these MUs were experimentally measured and modeled. The forces of the MUs and of the whole muscle were simulated using different stimulation patterns that included different regular, irregular, synchronous, and asynchronous firing patterns of MUs. The size principle of MUs for recruitment and derecruitment was also demonstrated using different stimulation paradigms.

Variability of the twitch parameters of the rat medial gastrocnemius motor units--experimental and modeling study.

In the present study a previously proposed model of a twitch based on an analytical function with four-parameters (lead, contraction and half-relaxation times and maximum force of the twitch) was validated on 115 motor units (MUs), divided into slow (S), fast-fatigue resistant (FR) and fast fatigable (FF) types. The original records were collected from electrophysiological experiments performed on MUs from the medial gastrocnemius muscle of five rats. Besides the easy calculation of the twitch parameters and their variability, the usefulness of the model was confirmed by eliminating artifacts and noise in the original twitch records, as well as by calculations of the velocity of force increase and decrease, the area under force records, and by normalization of all twitches with respect to the maximal force and contraction time. It was concluded that: (1) the four-parameter twitch model describes precisely the individual contractions of various MUs; (2) all physiological twitch parameters are distributed continuously and located within overlapping intervals for different MU types; this distribution is not linear, but exponential; (3) S MUs can be distinguished from fast ones on the basis of some twitch parameters (contraction and half-relaxation times, velocity of contraction), but the same cannot be applied for FF and FR MUs; (4) the analysis of the normalized twitches reveals the differences in shapes for different types of MUs, which shows that twitches of different MUs cannot be obtained from one standard pattern scaled in time and force. These results may have functional implications for studying effectiveness of twitch summation during tetanic contractions and the work performed by various types of MUs.

Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units.

Repeated stimulation of motor units (MUs) causes an increase of the force output that cannot be explained by linear summation of equal twitches evoked by the same stimulation pattern. To explain this phenomenon, an algorithm for reconstructing the individual twitches, that summate into an unfused tetanus is described in the paper. The algorithm is based on an analytical function for the twitch course modeling. The input parameters of this twitch model are lead time, contraction and half-relaxation times and maximal force. The measured individual twitches and unfused tetani at 10, 20, 30 and 40 Hz stimulation frequency of three rat motor units (slow, fast resistant to fatigue and fast fatigable) are processed. It is concluded that: (1) the analytical function describes precisely the course of individual twitches; (2) the summation of equal twitches does not follow the results from the experimentally measured unfused tetani, the differences depend on the type of the MU and are bigger for higher values of stimulation frequency and fusion index; (3) the reconstruction of individual twitches from experimental tetanic records can be successful if the tetanus is feebly fused (fusion index up to 0.7); (4) both the maximal forces and time parameters of individual twitches subtracted from unfused tetani change and influence the course of each tetanus. A discrepancy with respect to the relaxation phase was observed between experimental results and model prediction for tetani with fusion index exceeding 0.7. This phase was predicted longer than the experimental one for better fused tetani. Therefore, a separate series of physiological experiments and then, more complex model are necessary for explanation of this distinction.

Experimental and modelling investigation of learning a fast elbow flexion in the horizontal plane.

Changes in the kinematic and electromyographic characteristics that occur while learning to move as fast as possible have been studied experimentally. Experimental investigation of what happens to the individual motor units (MUs) is more difficult. Access to each MU is impossible, and the recruitment and force developing properties of all individual MUs cannot be known. Thus, what is currently known about MU firing is based on experiments that have recorded relatively few MUs compared to what exists in the entire muscle. A recently developed muscle model (Raikova and Aladjov, 2002, J. Biomechanics, 35, 1123-1135) composed of MUs with different properties can be used for such investigation. The process of learning fast elbow flexion in the horizontal plane was simulated and the results were compared with experimentally measured data. Comparing the simulation results of the very first trial of a particular subject with those of the last trail (at the end of the learning process), it can be concluded that the speed of limb motion and muscle forces increase initially as a result of the more synchronous MUs activation and the increase of firing rate of active MUs. Further improvement necessitated an appreciable reduction in the motor task requirements (i.e. less muscle force and less MUs' activity) set in the computational algorithm by optimization criteria. This forced the next process-inclusion of additional MUs.

The influence of the way the muscle force is modeled on the predicted results obtained by solving indeterminate problems for a fast elbow flexion.

A critical point in models of the human limbs when the aim is to investigate the motor control is the muscle model. More often the mechanical output of a muscle is considered as one musculotendon force that is a design variable in optimization tasks solved predominantly by static optimization. For dynamic conditions, the relationship between the developed force, the length and the contraction velocity of a muscle becomes important and rheological muscle models can be incorporated in the optimization tasks. Here the muscle activation can be a design variable as well. Recently a new muscle model was proposed. A muscle is considered as a mixture of motor units (MUs) with different peculiarities and the muscle force is calculated as a sum of the MUs twitches. The aim of the paper is to compare these three ways for presenting the muscle force. Fast elbow flexion is investigated using a planar model with five muscles. It is concluded that the rheological models are suitable for calculation of the current maximal muscle forces that can be used as weight factors in the objective functions. The model based on MUs has many advantages for precise investigations of motor control. Such muscle presentation can explain the muscle co-contraction and the role of the fast and the slow MUs. The relationship between the MUs activation and the mechanical output is more clear and closer to the reality.

Hierarchical genetic algorithm versus static optimization-investigation of elbow flexion and extension movements.

The applicability of static optimization (and, respectively, frequently used objective functions) for prediction of individual muscle forces for dynamic conditions has often been discussed. Some of the problems are whether time-independent objective functions are suitable, and how to incorporate muscle physiology in models. The present paper deals with a twofold task: (1) implementation of hierarchical genetic algorithm (HGA) based on the properties of the motor units (MUs) twitches, and using multi-objective, time-dependent optimization functions; and (2) comparison of the results of the HGA application with those obtained through static optimization with a criterion "minimum of a weighted sum of the muscle forces raised to the power of n". HGA and its software implementation are presented. The moments of neural stimulation of all MUs are design variables coding the problem in the terms of HGA. The main idea is in using genetic operations to find these moments, so that the sum of MUs twitches satisfies the imposed goals (required joint moments, minimal sum of muscle forces, etc.). Elbow flexion and extension movements with different velocities are considered as proper illustration. It is supposed that they are performed by two extensor muscles and three flexor muscles. The results show that HGA is a suitable means for precise investigation of motor control. Many experimentally observed phenomena (such as antagonistic co-contraction, three-phasic behavior of the muscles during fast movements) can find their explanation by the properties of the MUs twitches. Static optimization is also able to predict three-phasic behavior and could be used as practicable and computationally inexpensive method for total estimation of the muscle forces.

Prediction of Individual Muscle Forces Using Lagrange Multipliers Method - A Model of the Upper Human Limb in the Sagittal Plane: I. Theoretical Considerations.

Analytical solutions of indeterminate problems formulated for biomechanical models with more than one degree of freedom (DOF) are rarely found. This paper is an extension of the investigations of a 1 DOF model (Raikova, 1996, J. Biomechanics, 763-772) for a more complex 3 DOF model. The proposed model of the human upper limb is in the sagittal plane and includes ten muscle elements, four of them being two-joint ones. The formulated optimization task is solved analytically using the method of Lagrange multipliers. It is supposed that the optimization function is complex but can be approximated by a weighted sum of the squared muscle forces, where the nature of the weight factors of the muscles are unknown. The proposed computational algorithm for determination of the unknown individual muscle forces and joint reactions is easily implemented and may be extended without difficulties for more DOF and muscles. The aim is to establish a means of investigation of the possible weight coefficients for different modelled situations, which will help in searching for their physiological interpretation and analytical description.

Prediction of Individual Muscle Forces Using Lagrange Multipliers Method - A Model of the Upper Human Limb in the Sagittal Plane: II. Numerical Experiments and Sensitivity Analysis.

Using the method of Lagrange multipliers an analytical solution of the optimization problem formulated for a two-dimensional, 3DOF model of the human upper limb has been described in Part I of this investigation. The objective criterion used is the following: [formula: see text], where F(i) -s are the muscle forces modelled and c(i) -s are unknown weight factors. This study is devoted to the numerical experiments performed in order to investigate which sets of the weight factors may predict physiologically reasonable muscle forces and joint reactions. A sensitivity analysis is also presented. The influence of: the gravity forces, different external loads applied to the hand, changes of the weight factors and of joint angle on the optimal solution is studied. A general conclusion may be drawn: using the above mentioned objective criterion, practically all motor tasks performed by the human upper limb may be described if the c(i) -s are properly chosen. These weight factors generally depend on the joint moments and must be different (their magnitudes as well as their signs) for agonistic muscles and for their antagonists.