Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.     

Postfatigue potentiation of the paralyzed soleus muscle: evidence for adaptation with long-term electrical stimulation training.

Understanding the torque output behavior of paralyzed muscle has important implications for the use of functional neuromuscular electrical stimulation systems. Postfatigue potentiation is an augmentation of peak muscle torque during repetitive activation after a fatigue protocol. The purposes of this study were 1) to quantify postfatigue potentiation in the acutely and chronically paralyzed soleus and 2) to determine the effect of long-term soleus electrical stimulation training on the potentiation characteristics of recently paralyzed soleus muscle. Five subjects with chronic paralysis (>2 yr) demonstrated significant postfatigue potentiation during a repetitive soleus activation protocol that induced low-frequency fatigue. Ten subjects with acute paralysis (<6 mo) demonstrated no torque potentiation in response to repetitive stimulation. Seven of these acute subjects completed 2 yr of home-based isometric soleus electrical stimulation training of one limb (compliance = 83%; 8,300 contractions/wk). With the early implementation of electrically stimulated training, potentiation characteristics of trained soleus muscles were preserved as in the acute postinjury state. In contrast, untrained limbs showed marked postfatigue potentiation at 2 yr after spinal cord injury (SCI). A single acute SCI subject who was followed longitudinally developed potentiation characteristics very similar to the untrained limbs of the training subjects. The results of the present investigation support that postfatigue potentiation is a characteristic of fast-fatigable muscle and can be prevented by timely neuromuscular electrical stimulation training. Potentiation is an important consideration in the design of functional electrical stimulation control systems for people with SCI.     

Doublet stimulation protocol to minimize musculoskeletal stress during paralyzed quadriceps muscle testing.

With long-term electrical stimulation training, paralyzed muscle can serve as an effective load delivery agent for the skeletal system. Muscle adaptations to training, however, will almost certainly outstrip bone adaptations, exposing participants in training protocols to an elevated risk for fracture. Assessing the physiological properties of the chronically paralyzed quadriceps may transmit unacceptably high shear forces to the osteoporotic distal femur. We devised a two-pulse doublet strategy to measure quadriceps physiological properties while minimizing the peak muscle force. The purposes of the study were 1) to determine the repeatability of the doublet stimulation protocol, and 2) to compare this protocol among individuals with and without spinal cord injury (SCI). Eight individuals with SCI and four individuals without SCI underwent testing. The doublet force-frequency relationship shifted to the left after SCI, likely reflecting enhancements in the twitch-to-tetanus ratio known to exist in paralyzed muscle. Posttetanic potentiation occurred to a greater degree in subjects with SCI (20%) than in non-SCI subjects (7%). Potentiation of contractile rate occurred in both subject groups (14% and 23% for SCI and non-SCI, respectively). Normalized contractile speed (rate of force rise, rate of force fall) reflected well-known adaptations of paralyzed muscle toward a fast fatigable muscle. The doublet stimulation strategy provided repeatable and sensitive measurements of muscle force and speed properties that revealed meaningful differences between subjects with and without SCI. Doublet stimulation may offer a unique way to test muscle physiological parameters of the quadriceps in subjects with uncertain musculoskeletal integrity.     

Endurance exercise training reduces lactate production

In situ muscle stimulation in trained and untrained rats was used to reevaluate whether adaptations induced by endurance exercise training result in decreased lactate production by contracting muscles. The gastrocnemius-plantaris-soleus muscle group was stimulated to perform isotonic contractions. After 3 min of stimulation with 100-ms trains at 50 Hz at 60/min, the increases in lactate concentration in the plantaris, soleus, and fast-twitch red muscle (deep portion of lateral head of gastrocnemius) were only approximately 50% as great in trained as in sedentary rats. In the predominantly fast-twitch white superficial portion of the medial head of the gastrocnemius the increase in lactate concentration was 28% less in the trained than in the sedentary group. The decreases in muscle glycogen concentration seen after 3 min of stimulation at 60 trains/min were smaller in the trained than in the untrained group. The reduction in lactate accumulation that occurred in the different muscles in response to training was roughly proportional to the degree of glycogen sparing. These results show that endurance training induces adaptations that result in a slower production of lactate by muscle during contractile activity.     

Fatigue and non-fatigue mathematical muscle models during functional electrical stimulation of paralyzed muscle

Electrical muscle stimulation demonstrates potential for preventing muscle atrophy and restoring functional movement after spinal cord injury (SCI). Control systems used to optimize delivery of electrical stimulation protocols depend upon the algorithms generated using computational models of paralyzed muscle force output. The Hill–Huxley-type model, while being highly accurate, is also very complex, making it difficult for real-time implementation. In this paper, we propose a Wiener–Hammerstein system to model the paralyzed skeletal muscle under electrical stimulus conditions. The proposed model has substantial advantages in identification algorithm analysis and implementation including computational complexity and convergence, which enable it to be used in real-time model implementation. Experimental data sets from the soleus muscles of 14 subjects with SCI were collected and tested. The simulation results show that the proposed model outperforms the Hill–Huxley-type model not only in peak force prediction, but also in fitting performance for force output of each individual stimulation train.     

Asymmetric bone adaptations to soleus mechanical loading after spinal cord injury

The purpose of this report is to examine longitudinal bone mineral density (BMD) changes in individuals with spinal cord injury (SCI) who began unilateral soleus electrical stimulation early after injury. Twelve men with SCI and seven without SCI underwent peripheral quantitative computed tomography assessment of distal tibia BMD. After 4.5 to 6 years of training, average trained limb BMD was 27.5% higher than untrained limb BMD. The training effect was more pronounced in the central core of the tibia cross-section (40.5% between-limb difference). No between-limb difference emerged in the anterior half of the tibia (19.2 mg/cm(3) difference, p>0.05). A robust between-limb difference emerged in the posterior half of the tibia (76.1 mg/cm(3) difference, p=0.0439). The posterior tibia BMD of one subject remained within the range of non-SCI values for 3.8 years post-SCI. The results support that the constrained orientation of soleus mechanical loads, administered over several years, elicited bone-sparing effects in the posterior tibia. This study provides a demonstration of the bone-protective potential of a carefully controlled dose of mechanical load. The specific orientation of applied mechanical loads may strongly influence the manifestation of BMD adaptations in humans with SCI.     

Mechanical properties of fast and slow skeletal muscle with special reference to collagen and endurance training

The mechanical properties of the slow soleus and the fast rectus femoris muscle under passive stretching were studied in endurance trained, untrained and lathyritic rats, aged 3 months. The soleus muscle with more abundant and cross-linked collagen had higher ultimate tensile strength and tangent modulus compared to the fast rectus femoris muscle which, on the other hand, had higher maximum strain. The inhibition of collagen cross-linking by lathyrism resulted in decreased tensile strength and stiffness, especially in the soleus muscle, whereas endurance training showed the opposite effects. It is supposed that the properties of collagen partly explain the capacity of slow muscles to maintain posture and to perform prolonged dynamic work. The effects of training on the tensile properties further indicate the close relationship between intramuscular collagen and the endurance capacity of muscles.     

Twitch contractile properties of plantar flexor muscles in power and endurance trained athletes

This study compared twitch contractile properties of plantar flexor muscles among three groups of 12 subjects each: endurance and power trained athletes and untrained subjects. The posterior tibial nerve was stimulated by supramaximal square wave pulses of 1-ms duration. Power trained athletes had higher twitch maximal force, maximal rates of force development and relaxation and also maximal voluntary contraction (MVC) force. The trained subjects had a smaller twitch maximal force: MVC force ratio and shorter twitch contraction and half-relaxation times than the untrained subjects with no significant differences between the two groups. Thus, the short time for evoked twitches in the athletes compared to the untrained subjects would seem unrelated to the type of training. It is concluded that power training induces a more evident increase of muscle force-generating capacity and speed of contraction and relaxation than endurance training. Accepted: 24 April 1999     

Adaptations in rat skeletal muscle following long-term resistance exercise training

The purpose of this investigation was to determine whether long-term, heavy resistance training would cause adaptations in rat skeletal muscle structure and function. Ten male Wistar rats (3 weeks old) were trained to climb a 40-cm vertical ladder (4 days/week) while carrying progressively heavier loads secured to their tails. After 26 weeks of training the rats were capable of lifting up to 800 g or 140% of their individual body mass for four sets of 12–15 repetitions per session. No difference in body mass was observed between the trained rats and age-matched sedentary control rats. Absolute and relative heart mass were greater in trained rats than control rats. When expressed relative to body mass, the mass of the extensor digitorum longus (EDL) and soleus muscles was greater in trained rats than control rats. No difference in absolute muscle mass or maximum force-producing capacity was evident in either the EDL or soleus muscles after training, although both muscles exhibited an increased resistance to fatigue. Individual fibre hypertrophy was evident in all four skeletal muscles investigated, i.e. EDL, soleus, plantaris and rectus femoris muscles of trained rats, but muscle fibre type proportions within each of the muscles tested remained unchanged. Despite an increased ability of the rats to lift progressively heavier loads, this heavy resistance training model did not induce gross muscle hypertrophy nor did it increase the force-producing capacity of the EDL or soleus muscles. Accepted: 17 September 1997     

Glucose transporters and maximal transport are increased in endurance-trained rat soleus.

Voluntary wheel running induces an increase in the concentration of the regulatable glucose transporter (GLUT4) in rat plantaris muscle but not in soleus muscle (K. J. Rodnick, J. O. Holloszy, C. E. Mondon, and D. E. James. Diabetes 39: 1425-1429, 1990). Wheel running also causes hypertrophy of the soleus in rats. This study was undertaken to ascertain whether endurance training that induces enzymatic adaptations but no hypertrophy results in an increase in the concentration of GLUT4 protein in rat soleus (slow-twitch red) muscle and, if it does, to determine whether there is a concomitant increase in maximal glucose transport activity. Female rats were trained by treadmill running at 25 m/min up a 15% grade, 90 min/day, 6 days/wk for 3 wk. This training program induced increases of 52% in citrate synthase activity, 66% in hexokinase activity, and 47% in immunoreactive GLUT4 protein concentration in soleus muscles without causing hypertrophy. Glucose transport activity stimulated maximally with insulin plus contractile activity was increased to roughly the same extent (44%) as GLUT4 protein content in soleus muscle by the treadmill exercise training. In a second set of experiments, we examined whether a swim-training program increases glucose transport activity in the soleus in the presence of a maximally effective concentration of insulin. The swimming program induced a 44% increase in immunoreactive GLUT4 protein concentration. Glucose transport activity maximally stimulated with insulin was 62% greater in soleus muscle of the swimmers than in untrained controls. Training did not alter the basal rate of 2-deoxyglucose uptake.(ABSTRACT TRUNCATED AT 250 WORDS)     

Training decreases muscle glycogen turnover during exercise

The present study was undertaken to determine the effects of endurance training on glycogen kinetics during exercise. A new model describing glycogen kinetics was applied to quantitate the rates of synthesis and degradation of glycogen. Trained and untrained rats were infused with a 25% glucose solution with 6-³H-glucose and U-¹⁴C-lactate at 1.5 and 0.5 μCi · min⁻¹ (where 1 Ci = 3.7 × 10¹⁰ Bq), respectively, during rest (30 min) and exercise (60 min). Blood samples were taken at 10-min intervals starting just prior to isotopic infusion, until the cessation of exercise. Tissues harvested after the cessation of exercise were muscle (soleus, deep, and superficial vastus lateralis, gastrocnemius), liver, and heart. Tissue glycogen was quantitated and analyzed for incorporation of ³H and ¹⁴C via liquid scintillation counting. There were no net decreases in muscle glycogen concentration from trained rats, whereas muscle glycogen concentration decreased to as much as 64% (P < 0.05) in soleus in muscles from untrained rats after exercise. Liver glycogen decreased in both trained (30%) and untrained (40%) rats. Glycogen specific activity increased in all tissues after exercise indicating isotope incorporation and, thus, glycogen synthesis during exercise. There were no differences in muscle glycogen synthesis rates between trained and untrained rats after exercise. However, training decreased muscle glycogen degradation rates in total muscle (i.e., the sum of the degradation rates of all of the muscles sampled) tenfold (P < 0.05). We have applied a model to describe glycogen kinetics in relation to glucose and lactate metabolism during exercise in trained and untrained rats. Training significantly decreases muscle glycogen degradation rates during exercise. Accepted: 22 May 1998     

Exercise adaptation attenuates VEGF gene expression in human skeletal muscle

Angiogenesis is a component of the multifactoral adaptation to exercise training, and vascular endothelial growth factor (VEGF) is involved in extracellular matrix changes and endothelial cell proliferation. However, there is limited evidence supporting the role of VEGF in the exercise training response. Thus we studied mRNA levels of VEGF, using quantitative Northern analysis, in untrained and trained human skeletal muscle at rest and after a single bout of exercise. Single leg knee-extension provided the acute exercise stimulus and the training modality. Four biopsies were collected from the vastus lateralis muscle at rest in the untrained and trained conditions before and after exercise. Training resulted in a 35% increase in muscle oxygen consumption and an 18% increase in number of capillaries per muscle fiber. At rest, VEGF/18S mRNA levels were similar before (0.38 +/- 0.04) and after (1.2 +/- 0.4) training. When muscle was untrained, acute exercise greatly elevated VEGF/18S mRNA levels (16.9 +/- 6.7). The VEGF/18S mRNA response to acute exercise in the trained state was markedly attenuated (5.4 +/- 1.3). These data support the concept that VEGF is involved in exercise-induced skeletal muscle angiogenesis and appears to be subject to a negative feedback mechanism as exercise adaptations occur.     

Effect of contractile activity on rat skeletal muscle beta-adrenoceptor properties

The effect of fiber type and endurance exercise training on skeletal muscle beta-adrenoceptor properties were assessed using a direct radioligand binding technique. Six separate muscles, composed of a variety of different fiber types, were examined in treadmill trained and sedentary rats. In trained animals, sarcolemmal preparations from heart and slow twitch soleus muscle exhibited a significantly greater receptor concentration than membranes from white fast twitch glycolytic fibers of the vastus lateralis. No significant changes were observed between trained and sedentary rat muscle beta-adrenoceptor density (beta max, fmole/mg protein) or affinity (Kd, nM) within each muscle type, despite significantly increased myocardial/body weight ratios and skeletal muscle enzyme adaptations associated with the exercise program. These results suggest that muscle beta-adrenoceptor properties may be influenced in part by the motor nerve innervation to that muscle, and are further discussed with respect to a possible relationship between exercise intensity and receptor regulation.     

Hypertrophic response to unilateral concentric isokinetic resistance training.

The purposes of this study were to 1) determine the effect of concentric isokinetic training on strength and cross-sectional area (CSA) of selected extensor and flexor muscles of the forearm and leg, 2) examine the potential for preferential hypertrophy of individual muscles within a muscle group, 3) identify the location (proximal, middle, or distal level) of hypertrophy within an individual muscle, and 4) determine the effect of unilateral concentric isokinetic training on strength and hypertrophy of the contralateral limbs. Thirteen untrained male college students [mean age 25.1 +/- 6.1 (SD) yr] volunteered to perform six sets of 10 repetitions of extension and flexion of the nondominant limbs three times per week for 8 wk, using a Cybex II isokinetic dynamometer. Pretraining and posttraining peak torque and muscle CSA measurements for both the dominant and nondominant limbs were determined utilizing a Cybex II isokinetic dynamometer and magnetic resonance imaging scanner, respectively. The results indicated significant (P less than 0.0008) hypertrophy in all trained muscle groups as well as preferential hypertrophy of individual muscles and at specific levels. None of the muscles of the contralateral limbs increased significantly in CSA. In addition, significant (P less than 0.0008) increases in peak torque occurred for trained forearm extension and flexion as well as trained leg flexion. There were no significant increases in peak torque, however, for trained leg extension or for any movement in the contralateral limbs. These data suggest that concentric isokinetic training results in significant strength and hypertrophic responses in the trained limbs.     

Effects of stimulation frequency versus pulse duration modulation on muscle fatigue.

During functional electrical stimulation (FES), both the frequency and intensity can be increased to increase muscle force output and counteract the effects of muscle fatigue. Most current FES systems, however, deliver a constant frequency and only vary the stimulation intensity to control muscle force. This study compared muscle performance and fatigue produced during repetitive electrical stimulation using three different strategies: (1) constant pulse-duration and stepwise increases in frequency (frequency-modulation); (2) constant frequency and stepwise increases in pulse-duration (pulse-duration-modulation); and (3) constant frequency and pulse-duration (no-modulation). Surface electrical stimulation was delivered to the quadriceps femoris muscles of 12 healthy individuals and isometric forces were recorded. Muscle performance was assessed by measuring the percent changes in the peak forces and force-time integrals between the first and the last fatiguing trains. Muscle fatigue was assessed by measuring percent declines in peak force between the 60Hz pre- and post-fatigue testing trains. The results showed that frequency-modulation showed better performance for both peak forces and force-time integrals in response to the fatiguing trains than pulse-duration-modulation, while producing similar levels of muscle fatigue. Although frequency-modulation is not commonly used during FES, clinicians should consider this strategy to improve muscle performance.     

Contractile properties of old rat muscles: effect of increased use

To examine how different kinds of activity affect the composition and contractile properties of aging skeletal muscle, old male rats were strength and swim trained. The mass of weights lifted during the strength training increased by 85 +/- 9% (P less than 0.05), which was accompanied by an increase by 32 +/- 5% (P less than 0.05) of the estimated force developed. The wet muscle weight of the soleus and the plantaris decreased significantly with age. The phenomenon was counteracted but not neutralized by the strength training. Twitch and tetanic tension also decreased significantly with age in both the soleus and plantaris muscle. This was avoided by the strength training. This training also significantly decreased time to peak tension and half-relaxation time of both muscles. The swim training increased the heart-to-body weight ratio by 21 +/- 5% (P less than 0.05) and the endurance of the soleus muscle. Time to peak tension and triosephosphate dehydrogenase activity of the plantaris muscle were strongly correlated (P less than 0.001) with myosin adenosinetriphosphatase activity. The results show that the composition and contractile properties of old skeletal muscle are considerably affected by strength training repeated during a substantial period of old age, whereas swim training only affects the endurance of the skeletal muscle.     

A musculo-skeletal model of rat ankle motion and its experimental test on rat

A biomechanical musculo-skeletal model of functional electrical stimulation (FES)-induced rat ankle motion was implemented and tested in rat experiments. The muscle model is a new Hill-based model which includes established physiological relations of force-velocity and force-length-frequency. However, the series-elastic component and the activation component of previous Hill-based models are replaced by a new component which accounts for dynamic time delays and recruitment that occur in real muscle force generation during limb movements. The skeletal model includes gravity and dynamic forces that occur in real rat ankle motions. In computer simulations, various FES patterns were applied to the tibialis anterior (TA) and soleus (SO) model muscles to produce walk-like ankle motions. In lab experiments, the same stimulation patterns were applied by epimysial electrodes implanted in the TA and SO muscles of live rats cordotomized at level T7. The resulting rat motions were recorded by video camera. Video data was converted to ankle angle-vs-time files for comparison with corresponding model angle-vs-time files. Over a physiologically significant range of ankle motions, model parameters were adjustable to yield model motions that agreed with rat motions to within 2 degrees (root mean square differences of rat and model ankle angles). This is shown in plots of model and rat motions presented here for representative cases of FES. The accuracy of our model in reproducing real ankle motions supports the hypothesis that our new muscle model generates correct muscle forces over a useful range of limb motions. It suggests that the model may be useful in the design of FES neural prostheses.     

Supplementation with α-Lipoic Acid,CoQ10, and Vitamin E Augments Running Performance and Mitochondrial Function in Female Mice

Antioxidant supplements are widely consumed by the general public; however, their effects of on exercise performance are controversial. The aim of this study was to examine the effects of an antioxidant cocktail (α-lipoic acid, vitamin E and coenzyme Q10) on exercise performance, muscle function and training adaptations in mice. C57Bl/J6 mice were placed on antioxidant supplement or placebo-control diets (n = 36/group) and divided into trained (8 wks treadmill running) (n = 12/group) and untrained groups (n = 24/group). Antioxidant supplementation had no effect on the running performance of trained mice nor did it affect training adaptations; however, untrained female mice that received antioxidants performed significantly better than placebo-control mice (p ≤ 0.05). Furthermore, antioxidant-supplemented females (untrained) showed elevated respiratory capacity in freshly excised muscle fibers (quadriceps femoris) (p ≤ 0.05), reduced oxidative damage to muscle proteins (p ≤ 0.05), and increased expression of mitochondrial proteins (p ≤ 0.05) compared to placebo-controls. These changes were attributed to increased expression of proliferator-activated receptor gamma coactivator 1α (PGC-1α) (p ≤ 0.05) via activation of AMP-activated protein kinase (AMPK) (p ≤ 0.05) by antioxidant supplementation. Overall, these results indicate that this antioxidant supplement exerts gender specific effects; augmenting performance and mitochondrial function in untrained females, but does not attenuate training adaptations.     

Transfer effects in endurance exercise. Adaptations in trained and untrained muscles

The effects of 8 weeks of bicycle endurance training (5 X /week for 30 min) on maximal oxygen uptake capacity (VO2max) during arm and leg ergometry, and on the ultrastructure of an untrained arm muscle (m. deltoideus), and a trained leg muscle (m. vastus lateralis) were studied. With the training, leg-VO2max for bicycling increased by +13%, while the capillary per fiber ratio and the volume density of mitochondria in m. vastus lateralis increased by +15% and +40%, respectively. In contrast, the untrained m. deltoideus showed an unchanged capillary per fiber ratio and a decreased mitochondrial volume density (-17%). Despite this decrease of mitochondrial volume arm-VO2max increased by +9%. It seems unlikely that the observed discrepancy can be explained by cardiovascular adaptations, since arm cranking did not fully tax the cardiovascular system (arm-VO2max/leg-VO2max: 0.74 and 0.71 before and after training, respectively). Thus neither cardiovascular adaptations nor local structural changes in the untrained muscles could explain the increased arm-VO2max. However, the enhanced capacity for lactate clearance after endurance training could be sufficient to account for the larger VO2max during arm cranking. We propose that an increased net oxidation of lactate might be responsible for the increased arm-VO2max found after bicycle endurance training.     

Age- and training-related changes in the collagen metabolism of rat skeletal muscle

The effects of ageing and life-long endurance training on the collagen metabolism of skeletal muscle were evaluated in a longitudinal study. Wistar rats performed treadmill running 5 days a week for 2 years. The activities of collagen biosynthesis enzymes, prolyl-4-hydroxylase and galactosylhydroxylysyl glucosyltransferase, were highest in the muscles of the youngest animals, decreased up to the age of 2 months and from then on remained virtually unchanged. The enzyme activity in young animals was higher in the slow collagenous soleus muscle than in the rectus femoris muscle. The enzyme activity in the soleus muscle was higher for older trained rats than older untrained rats. The relative proportion of type I collagen increased and that of type III collagen decreased with age, suggesting a more marked contribution by type I collagen to the age-related accumulation of total muscular collagen. The results show that collagen biosynthesis decreases with maturation and that life-long endurance training maintains a higher level of biosynthesis in slow muscles.