Mathematical modelling of the contribution of mechanical inhomogeneity in the myocardium to contractile function

Earlier we developed a mathematical model of the cardiac muscle that allowed for inactivation through the effects of cooperativity of contractile proteins. In the present work we used the model to analyze the mechanical function of an inhomogeneous myocardium. To simulate the latter we chose, as the simplest sytstem, a duplex in which muscles with different mechanical properties were connected in series and in parallel. Numerical experiments showed that the basic effect due to the inhomogeneity consists in the non-additivity of the mechanical characteristics of the muscle, e.g., of the relationship between end-systolic length and end-systolic force (Les - Pes). As a rule, non-additivity consists in a negative inotropic effect. The analysis showed that the cause of non-additivity is redistribution of loads between muscles (in a parallel duplex), redistribution of lengths (in a serial duplex), changes in the rate of contraction of each muscle compared to contraction that when working separately, shifts in time to Les. Also, the model predicts that additional inactivation of contractile proteins in a muscle within a duplex against isolation is the substantial mechanism of enhanced non-additivity. Among the factors of inhomogeneity studied the basic determinants are difference in amplitudes between isometric tensions developed by each muscle in isolation and the asynchronism in the development of these tensions.     

Co-contraction of lumbar muscles during the development of time-varying triaxial moments

The recruitment and co-contraction of lumbar muscles were investigated during the voluntary development of slowly and rapidly varying trunk flexion and extension, lateral bending, and axial twisting moments. Myoelectric signals were recorded from 14 lumbar muscles in nine young men during maximum voluntary exertions and cyclic isometric exertions. System identification techniques were used to calibrate dynamic models of the relationship between myoelectric signals and force. To assess co-contraction, the predicted muscle forces were subdivided into a task-moment set of muscle forces that minimally satisfied moment equilibrium and a co-contraction set of muscle forces that produced zero net moment. The sum of co-contraction muscle forces was used to quantify the degree of co-contraction present. Co-contraction was largely dependent on the direction of exertion and relatively less dependent on the subject or the rate of exertion. Co-contractions were estimated to contribute approximately 16-19% to the sum of muscle forces at a lumbar cross section during attempted extension of the trunk. Estimated co-contractions during attempted lateral bending and axial twisting were two to three times greater, which demonstrates that co-contraction is a major determinant of spinal loading in these tasks. This analysis suggests that substantial contractions of lumbar muscles, especially during asymmetric exertions, are used for reasons other than equilibrating moments at the L3-L4 level.     

Isometric and isotonic contractions in airway smooth muscle

Canine tracheal smooth muscle was used as an in vitro model of smooth muscle in intrapulmonary airways to determine whether active tension curves derived from isometric and isotonic muscles are similar, and thus resemble striated muscle in this respect. Isometric, isotonic after-loaded, and isotonic free-loaded contractions elicited at different lengths and loads, were analysed. The data demonstrate that length-tension (L-T) diagrams were different in these various types of contractions for electrically and carbachol driven tracheal smooth muscles strips. In general, at any given length active tension is less in isotonic and free-loaded modes of contraction as compared with isometric. We conclude that the ability to actively develop tension at a given length in airway smooth muscle depends on the mode of contraction.     

Simultaneous stiffness and force measurements reveal subtle injury to rabbit soleus muscles

The time course of force generation and the time course of muscle stiffness were measured in rabbit soleus muscles during eccentric contraction to understand the underlying basis for the force loss in these muscles. Muscles were activated for 600 msec every 10 sec for 30 min. Soleus muscles contracting isometrically maintained constant tension throughout the treatment period, while muscles subjected to eccentric contraction rapidly dropped tension generation by 75% within the first few minutes and then an additional 10% by the end of 30 min. This indicated a dramatic loss in force-generating ability throughout the 30 min treatment period. To estimate the relative number of cross-bridges attached during the isometric force generation phase immediately preceding each eccentric contraction, stiffness was measured during a small stretch of a magnitude equal to 1.5% of the fiber length. Initially, muscle stiffness exceeded 1300 g/mm and, as eccentric treatment progressed, stiffness decreased to about 900 g/mm. Thus, while muscle stiffness decreased by only 30% over the 30 min treatment period, isometric force decreased by 85%. In isometrically activated muscles, stiffness remained constant throughout the treatment period. These data indicate that, while soleus muscles decreased their force generating capability significantly, there were a number of cross-bridges still attached that were not generating force. In summary, the loss of force generating capacity in the rabbit soleus muscle appears to be related to a fundamental change in myosin cross-bridge properties without the more dramatic morphological changes observed in other eccentric contraction models. These results are compared and contrasted with the observations made on muscles composed primarily of fast fibers.     

Effects of hip center location on the moment-generating capacity of the muscles

We have developed a three-dimensional biomechanical model of the human lower extremity to study how the location of the hip center affects the moment-generating capacity of four muscle groups: the hip abductors, adductors, flexors, and extensors. The model computes the maximum isometric force and the resulting joint moments that each of 25 muscle-tendon complexes develops at any body position. Abduction, adduction, flexion, and extension moments calculated with the model correspond closely with isometric joint moments measured during maximum voluntary contractions. We used the model to determine (1) the hip center locations that maximize and minimize the moment-generating capacity of each muscle group and (2) the effects of superior-inferior, anterior-posterior, and medial-lateral displacement of the hip center on the moment arms, maximum isometric muscle forces, and maximum isometric moments generated by each muscle group. We found that superior-inferior displacement of the hip center has the greatest effect on the force- and moment-generating capacity of the muscles. A 2 cm superior displacement decreases abduction force (44%), moment arm (12%), and moment (49%), while a 2 cm inferior displacement increases abduction force (20%), moment arm (7%) and moment (26%). Similarly, a 2 cm superior displacement decreases flexion force (27%), moment arm (6%), and moment (22%), while inferior displacement increases all three variables. Anterior-posterior displacement alters the moment-generating capacity of the flexors and extensors considerably, primarily due to moment arm changes. Medial-lateral displacement has a large effect on the moment-generating capacity of the adductors only. A 2 cm medial displacement decreases adduction moment arm (20%), force (26%) and moment (40%). These results demonstrate that the force- and moment-generating capacities of the muscles are sensitive to the location of the hip center.     

Harvesting of peripheral blood progenitor cells with different programmes of discontinuous flow systems

PURPOSE: To investigate whether a rapid and practical determination of the temporal frequency characteristic (TFC) of the visual system can be obtained by using the visually evoked potentials (VEPs) elicited by pseudorandom binary sequence (PRBS) stimulation. METHODS: VEPs were recorded from eight volunteers. For the conventional steady state VEPs (S-VEP), the eye was stimulated with five stimulus frequencies. To acquire the PRBS-VEPs, the eye was stimulated with a PRBS stimulus for 40 seconds. The TFC for the S-VEP was calculated from the root mean squared amplitude for each frequency using Fourier transform. For the PRBS stimulus, a cross-correlation function between PRBS (x[t]) and PRBS-VEP (y[t]) was calculated to obtain the TFC. RESULTS: The TFCs obtained by the PRBS and S-VEP methods were highly correlated (P < 0.05), and the TFC curves resembled those in the literature. Most important, the data necessary to determine the TFCs using the PRBS stimulus could be obtained in 4 minutes, whereas that for the S-VEP required 60 minutes for the two eyes. CONCLUSIONS: The high correlation between the TFCs obtained by the two methods indicated that the PRBS technique gives a good measure of the TFC of the human visual system. The significantly shorter time required for this method demonstrated that it is a practical method for determining the linear (and nonlinear) property of the visual system and that it may be useful in clinical applications.     

Large index-fingertip forces are produced by subject-independent patterns of muscle excitation

Are fingertip forces produced by subject-independent patterns of muscle excitation? If so, understanding the mechanical basis underlying these muscle coordination strategies would greatly assist surgeons in evaluating options for restoring grasping. With the finger in neutral ad- abduction and flexed 45 degrees at the MCP and PIP, and 10 degrees at DIP joints, eight subjects attempted to produce maximal voluntary forces in four orthogonal directions perpendicular to the distal phalanx (palmar, dorsal, lateral and medial) and in one direction collinear with it (distal). Forces were directed within 4.7 +/- 2.2 degrees (mean +/- S.D.) of target and their magnitudes clustered into three distinct levels (p < 0.05; post hoc pairwise RMANOVA). Palmar (27.9 +/- 4.1 N), distal (24.3 +/- 8.3 N) and medial (22.9 +/- 7.8 N) forces were highest, lateral (14.7 +/- 4.8 N) was intermediate, and dorsal (7.5 +/- 1.5 N) was lowest. Normalized fine-wire EMGs from all seven muscles revealed distinct muscle excitation groups for palmar, dorsal and distal forces (p < 0.05; post hoc pairwise RMANOVA). Palmar force used flexors, extensors and dorsal interosseous; dorsal force used all muscles; distal force used all muscles except for extensors; medial and lateral forces used all muscles including significant co-excitation of interossei. The excitation strategies predicted to achieve maximal force by a 3-D computer model (four pinjoints, inextensible tendons, extensor mechanism and isometric force models for all seven muscles) reproduced the observed use of extensors and absence of palmar interosseous to produce palmar force (to regulate net joint flexion torques), the absence of extensors for distal force, and the use of intrinsics (strong MCP flexors) for dorsal force. The model could not predict the interossei co-excitation seen for medial and lateral forces, which may be a strategy to prevent MCP joint damage. The model predicts distal force to be most sensitive to dorsal interosseous strength, and palmar and distal forces to be very sensitive to MCP and PIP flexor moment arms, and dorsal force to be sensitive to the moment arm of and the tension allocation to the PIP extensor tendon of the extensor mechanism.     

Activation of the rotator cuff in generating isometric shoulder rotation torque

This study compared and quantified electromyographic muscle activation of the rotator cuff with the isometric torque generated by performing shoulder rotation in various positions. Twenty healthy volunteers were tested in 29 shoulder positions. Using a Cybex II dynamometer synchronously with electromyography, surface electrodes were placed over the pectoralis major muscle and three parts of the deltoid muscle. Intramuscular wire electrodes were inserted into the four rotator cuff muscles. We found that the greatest external rotation isometric force is generated in the frontal and scapular planes in the neutral or full internal rotation positions. The sagittal, dependent, and the scapular plane with 45 degrees of elevation in rotational positions of either full or half external rotation generated the greatest torques for internal rotation isometric force. The rotator cuff muscles generated greatest electromyographic activity in neutral to midrotational positions. The scapular plane with 90 degrees of shoulder elevation in neutral rotation best isolated the subscapularis muscle. The infraspinatus-teres minor muscles were isolated in the sagittal plane with 90 degrees of shoulder elevation in a half externally rotated position. We were unable to isolate the supraspinatus muscle in any of these tested positions. These positions are recommended for manual muscle testing and for strengthening these muscles.     

Effects of lactic acid accumulation and ATP decrease on muscle tension and relaxation

The present study was undertaken to evaluate the effect of lactic acid accumulation on peak tension and relaxation rate of the isometric twitch. Isolated extensor digitorum longus muscle from rat was stimulated electrically at a frequency of 2/s under anaerobic conditions. Comparison was made with muscles in which glycolysis was blocked with iodoacetic acid (IAA). Stimulation of unpoisoned muscles for 3 min decreased tension to 50% and increased relaxation time to 250% of the initial value. Lactate increased 15-fold, and muscle pH decreased from 7.10 to 6.76. Stimulation of IAA-poisoned muscles for 1 min decreased tension to 50% but did not increase the relaxation time. Stimulation of IAA-poisoned muscle resulted in a pronounced decrease (about 50%) of the ATP and total adenine nucleotide content in muscle, whereas only a small decrease (10-15%) occurred in unpoisoned muscle. The main findings in the present study were that tension decline in unpoisoned muscle is closely related to decrease in muscle pH and increase in ADP but not to ATP content per se and that slowing of relaxation rate is closely related to decrease in muscle pH but not to muscle content of ATP or creatine phosphate.     

Ultrasonographic cross-sectional characteristics of muscles of the head and neck

OBJECTIVE: Computed tomography and magnetic resonance imaging are the common techniques for evaluating cross-sectional areas and volumes of human jaw muscles. Because computed tomography has the disadvantage of showing cumulative biological effects and because MRI poses a problem in terms of clinical availability and cost, the purpose of this study was to determine whether ultrasonography could be used to measure local linear cross-sectional dimensions of muscles of the head and neck. STUDY DESIGN: In 46 patients with signs and symptoms of temporomandibular disorders, the anterior temporalis, anterior masseter, deep masseter, anterior digastric, posterior digastric, and sternocleidomastoid muscles were measured bilaterally by ultrasonography to assess linear local cross-sectional dimensions. Measurements were made in 2 sessions with a time interval of at least 5 minutes. Data were analyzed for reliability and variability through use of the intraclass correlation coefficient (ICC) and the repeatability coefficient (RC). To assess local muscle asymmetry patterns, the absolute asymmetry index was used, with the mean maximum muscle diameters of the respective right and left sides calculated from 3 consecutive measurements. RESULTS: Satisfactory visualization of muscles was obtained in 93.8% of 1104 imaging procedures. For the ultrasound measurements there was a significant difference in local cross-sectional dimensions between the first and second sessions for the anterior temporalis muscle only (P < .01). Acceptable intrarater reliabilities were obtained for the deep masseter (ICC = 0.92), anterior digastric (ICC = 0.91), and sternocleidomastoid (ICC = 0.86) muscles, whereas evaluation of the posterior digastric (ICC = 0.74), anterior masseter (ICC = 0.72), and anterior temporalis (ICC = 0.70) muscles was associated with moderate reliability. Variability of repeated measurements was found to be acceptable for the anterior temporalis (RC = 0.32 mm) and posterior digastric (RC = 0.48 mm) muscles. Analysis of muscle site-related local cross-sectional dimensions showed a significant difference between the right and left sides for the deep masseter muscle only (P < .05). The study population investigated revealed mean asymmetry indices ranging from 5.3% for the anterior digastric muscle to 8.7% for the deep masseter muscle. CONCLUSIONS: Ultrasonography may prove to be a reliable diagnostic technique for the evaluation of cross-sectional dimensions and areas of muscles of the head and neck.     

Changes in torque and electromyographic activity of the quadriceps femoris muscles following isometric training

BACKGROUND AND PURPOSE: The purpose of this study was to examine the effect of isometric training of the quadriceps femoris muscles, at different joint angles, on torque production and electromyographic (EMG) activity. SUBJECTS: One hundred seven women were randomly assigned to one of four groups. Three groups trained with isometric contractions three times per week at a knee flexion angle of 30, 60, or 90 degrees. The fourth group, which served as a control, did not exercise. METHODS: Isometric torque was measured using a dynamometer, and EMG activity was measured using a multichannel EMG system. Measurements were obtained during maximal isometric contraction of the quadriceps femoris muscles at 15-degree increments from 15 to 105 degrees of knee flexion. Measurements were taken before and after 8 weeks of training. RESULTS: Following isometric exercise, increased torque and EMG activity occurred not only at the angle at which subjects exercised, but also at angles in the range of motion at which exercise did occur. Further analyses indicated that exercising in the lengthened position for the quadriceps femoris muscles (90 degrees of knee flexion) produced increased torque across all angles measured and appeared to be the more effective position for transferring strength and EMG activity to adjacent angles following isometric training as compared with the shorter positions of the muscle (30 degrees and 60 degrees of knee flexion). CONCLUSION AND DISCUSSION: These findings suggest that an efficient method for increasing isometric knee extension torque and EMG activity throughout the entire range of motion is to exercise with the quadriceps femoris muscles in the lengthened position.     

Biomechanical characteristics of unconditioned and conditioned latissimus dorsi muscles used for cardiocirculatory assistance

An understanding of the biomechanical characteristics of striated skeletal muscles involved in cardiocirculatory assistance is a prerequisite to assess their efficacy and to evaluate their haemodynamic benefits. Six goats had their latissimus dorsi muscles evaluated by isometric strain gauge testing. Total tension, and both active and passive force development at different preloads were measured. The relationship between muscle impedance and starting length was also studied. Four additional muscles were submitted to isometric and isotonic strain gauge testing after 3 months of chronic electrical stimulation (Broussais Hospital protocol) with the contralateral muscle serving as a control. In isometric testing, both conditioned and unconditioned goat latissimus dorsi displayed a Frank-Starling length-tension curve, and a linear relationship between muscle impedance and starting length was found. Chronic stimulation preserved muscle mass and isometric force. Transformed muscles showed a mean 59% reduction of maximal shortening velocity; means (s.d.) residual shortening velocity at maximal work and power output was 0.17(0.07) m/s. The work and power output were both reduced 65% after stimulation, and the residual maximal power at optimal preload varied from approximately 7.7 and 9.6 W/kg. It is concluded that, following the Broussais protocol, the goat latissimus dorsi muscle retained mass and most of its isometric force-generating capacity, but lost significant work and power potential. The residual power output did not, however, preclude the possibility of a significant cardiocirculatory contribution, providing that the conditions for optimal energy transduction are adequately delineated.     

Intratumoral administration of neocarzinostatin conjugated to monoclonal antibody A7 in a model of pancreatic cancer

PURPOSE: To evaluate the effects of age on mechanical performance of rat myocardium. METHODS: Left ventricular papillary muscles were isolated from male Wistar rats at 1, 3, 6 and 12 months of age. Muscles were studied isometrically and isotonically, stimulated at 0.2 Hz, perfused with Krebs-Henseleit solution having an external calcium concentration of 2.52 mM, and maintained at 28 degrees C. RESULTS: Peak isometric developed tension was significantly higher in 1 month than 3, 6 and 12 months. Peak rate of isometric tension rise decreased substantially between 1, 3 and 12 months. Time to peak isometric developed tension showed a significant increase of both 3 and 12 months of age. Time to half relaxation increased significantly from 3 to 6 and from 3 to 12 months. Maximum rate of tension decline decreased from 3 to 6 and from 3 to 12 months. No difference in resting tension was noted among any group. Isotonically, peak shortening and time to peak shortening increased from 1 to 3 months of age. Time to half re-lengthening increased from 3 to 6 and from 3 to 12 months of age. No difference in peak shortening velocity, peak relaxation velocity and relative change in muscle length was noted among any groups. CONCLUSION: The maturation affects the mechanical performance of cardiac muscle.     

A mathematical model for analysis of pharmacologically induced changes in the kinetics of cardiac muscle

A mathematical model of the isometric contraction of cardiac muscle is developed and utilized to characterize the inotropic and lusitropic effects of cardioactive compounds in isolated guinea pig left atria. In contrast to metrics that are based on minima and maxima of an isometric twitch and its derivative function, the entire time course of the twitch is used to quantify the kinetics of the contraction-relaxation cycle. The model relates observed tension to a time-dependent activation function that describes generation of internal force and a coupling function that determines mechanical response to the activation function. The model is structured so that it is suitable for nonlinear curve fitting to observed data. Results obtained using the model for fitting experimental data from tissues treated with different classes of cardioactive compounds agree with more qualitative results presented by other authors. Experiments using the model to fit data over an extended (90 min) time course revealed differences in the kinetic profiles of milrinone and forskolin. Computer simulations that demonstrate the effect of each model parameter on twitch kinetics are presented, and the relationships between the model and other theoretical and empirical models of cardiac muscle are discussed. The mathematical model is useful to enable a more quantitative understanding of the kinetics of cardiac muscle contraction and relaxation and identify compounds that may be selective for inotropic or lusitropic effects.     

Inhibition of Ca2+ release in rat atrophied gastrocnemius muscle

Contractile parameters of a twitch contraction and changes in these parameters during repetitive stimulation are modified by muscle atrophy induced by tetrodotoxin (TTX). These altered parameters included developed tension (DT), contraction time (tC), half-relaxation time (tR, 1/2), average rate of force development (DT tC-1) and peak rate of relaxation (DTdtmin-1). These modifications may be related to different Ca2+ concentration transients in the myoplasm during muscle stimulation. We have used dantrolene sodium (DS) in TTX-treated rat gastrocnemius muscle to test this hypothesis. In situ isometric contractile responses of rat gastrocnemius muscle during repetitive stimulation at 10 Hz were analysed before and after administration of DS. After DS administration, twitch amplitude, tC, tR, 1/2 and DT tC-1 decreased and DTdtmin-1 relative to DT increased in atrophied muscle. During repetitive stimulation, a progressive enhancement developed tension (staircase) was absent in atrophied muscle, but DT increased to 171 +/- 4%, presenting a staircase response after DS treatment. This potentiation was accompanied by an increase in DT tC-1 to 175.6 +/- 7%. Inhibition of Ca2+ release in atrophied muscle resulted in twitch contractile parameters and contractile responses to 10 Hz stimulation that were similar, in many respects, to those responses in control (non-atrophied) muscles.     

Surgery for aortic dissection associated with congenital bicuspid aortic valve

The Distribution Moment (DM) model has simulated experimental data on skeletal muscle, but it has not been used previously to study the mechanics of active contraction in cardiac muscle. In contrast to previous models of striated muscle contraction, all parameters have physical meaning and assumptions concerning biophysical events within the cell are consistent with available data. In order to simulate cardiac muscle deactivation using the DM model it was necessary to make the cross-bridge detachment rates large for large displacements from the neutral equilibrium position of a cross-bridge. To examine the effect of cooperativity on cardiac muscle contraction, we used the DM model's tight coupling scheme with binding of one or two calcium sites regulating contraction. As observed experimentally, our model predicted a reduction of isometric tension development following rapid shortening lengthening transients when contraction is regulated by either one or two calcium binding sites. The predicted deactivating effect increased if the transient was applied late in the twitch when contraction is regulated by two calcium binding sites, but not when it is regulated by one site. This is the first study in which deactivation has been simulated without making any provisions for length-dependent calcium trononin dissociation.     

Time course study of the isometric contractile properties of mdx mouse striated muscles

The isometric twitch and tetanic contractions of three hindlimb muscles (soleus, plantaris, extensor digitorum longus) were recorded in situ in groups of mdx and C57BL/10 control mice at young, adult and old ages (3, 4, 6, 8, 13, 26, 39 and 52 weeks). Based on a two-way analysis of variance (age/phenotype) the mdx phenotype did not modify the absolute tension but was associated with a significant decrease in the tetanic tension normalized to muscle weight in all the muscles which became heavier. These results suggest that the contractile material in mdx is not so powerful as in controls. Moreover, significantly faster time to peak and half-relaxation time were observed in mdx soleus and plantaris. Comparison between these contraction characteristics and those of other experimental models suggests that the high percentage of regenerated fibres in mdx muscles could play a role in modifying contractile properties.     

Effects of load and tone on the mechanics of isolated human bronchial smooth muscle

Isotonic and isometric properties of nine human bronchial smooth muscles were studied under various loading and tone conditions. Freshly dissected bronchial strips were electrically stimulated successively at baseline, after precontraction with 10(-7) M methacholine (MCh), and after relaxation with 10(-5) M albuterol (Alb). Resting tension, i.e., preload determining optimal initial length (Lo) at baseline, was held constant. Compared with baseline, MCh decreased muscle length to 93 +/- 1% Lo (P < 0.001) before any electrical stimulation, whereas Alb increased it to 111 +/- 3% Lo (P < 0.01). MCh significantly decreased maximum unloaded shortening velocity (0.045 +/- 0.007 vs. 0.059 +/- 0.007 Lo/s), maximal extent of muscle shortening (8.4 +/- 1.2 vs. 13.9 +/- 2.4% Lo), and peak isometric tension (6.1 +/- 0.8 vs. 7.2 +/- 1.0 mN/mm2). Alb restored all these contractile indexes to baseline values. These findings suggest that MCh reversibly increased the number of active actomyosin cross bridges under resting conditions, limiting further muscle shortening and active tension development. After the electrically induced contraction, muscles showed a transient phase of decrease in tension below preload. This decrease in tension was unaffected by afterload levels but was significantly increased by MCh and reduced by Alb. These findings suggest that the cross bridges activated before, but not during, the electrically elicited contraction may modulate the phase of decrease in tension below preload, reflecting the active part of resting tension.