Mechanical analysis of extrapulmonary volume displacements in the thorax and abdomen

Currently, the effect of intrathoracoabdominal, extrapulmonary volume displacements (Vep) are not well understood. Various clinical conditions can lead to volume displacements caused by gas or liquid accumulations. To analyze the pressure and volume changes that occur by Vep, we used a mathematical model of chest wall and lung mechanics that accounts for static changes associated with rib cage, diaphragm, abdomen, and lungs. By solving the model equations, we obtained simulations of the pleural and abdominal displacements that clearly differentiate the mechanisms involved. When abdominal displacement occurs, the reduction in lung volume is less than that caused by an equal displacement in pleural space. Abdominal displacement produces an increased pressure that expands the rib cage significantly, whereas pleural displacement does not produce a comparable action. Furthermore, our model predicts the conditions under which the work of inspiration is expected to increase as a consequence of these displacements. Finally, an important distinction is predicted between abdominal displacements caused by gas or liquid accumulation. Although an abdominal gas displacement tends to decrease the resting lung volume, the weight effect of a liquid displacement tends to increase the resting lung volume by pulling down the diaphragm.     

Action of the diaphragm on the rib cage inferred from a force-balance analysis

Displacements of the rib cage are determined by the intrinsic passive properties of the rib cage, rib cage musculature, pleural and abdominal pressures, and the diaphragm. The diaphragm's mechanical actions on the rib cage are inferred from a force-balance analysis in which the diaphragm is seen to cause expansion of the rib cage by pulling cephalad at its insertions on the lower ribs (insertional component) and by raising intra-abdominal pressure, which pushes outward on the diaphragm's zone of apposition to the rib cage (appositional component). Goldman and Mead suggested that the diaphragm, acting alone, could drive both the rib cage and abdomen on their passive characteristics. The force-balance analysis shows that the diaphragm's inspiratory action on the rib cage is less than predicted by Goldman and Mead, but that in the special circumstances of their experiment (low lung volumes), the appositional component is large and the rib cage can be driven close to its passive characteristics. The force-balance analysis is consistent with recent observations by other investigations and is incompatible with the model proposed by Macklem and colleagues and with the Goldman-Mead hypothesis. Experiments on three subjects produced data consistent with the force-balance analysis, showing that the inspiratory action of the diaphragm on the rib cage is greatest at low lung volumes.     

Mechanical coupling of the rib cage, abdomen, and diaphragm through their area of apposition

Although volumetric displacements of the chest wall are often analyzed in terms of two independent parallel pathways (rib cage and abdomen), Loring and Mead have argued that these pathways are not mechanically independent (J. Appl. Physiol. 53: 756-760, 1982). Because of its apposition with the diaphragm, the rib cage is exposed to two distinct pressure differences, one of which depends on abdominal pressure. Using the analysis of Loring and Mead as a point of departure, we developed a complementary analysis in which mechanical coupling of the rib cage, abdomen, and diaphragm is modeled by a linear translational transformer. This model has the advantage that it possesses a precise electrical analogue. Pressure differences and compartmental displacements are related by the transformation ratio (n), which is the mechanical advantage of abdominal over pleural pressure changes in displacing the rib cage. In the limiting case of very high lung volume, n----0 and the pathways uncouple. In the limit of very small lung volume, n----infinity and the pathways remain coupled; both rib cage and abdomen are driven by abdominal pressure alone, in accord with the Goldman-Mead hypothesis. A good fit was obtained between the model and the previously reported data for the human chest wall from 0.5 to 4 Hz (J. Appl. Physiol. 66:350-359, 1989). The model was then used to estimate rib cage, diaphragm, and abdominal elastance, resistance, and inertance. The abdomen was a high-elastance high-inertance highly damped compartment, and the rib cage a low-elastance low-inertance more lightly damped compartment. Our estimate that n = 1.9 is consistent with the findings of Loring and Mead and suggests substantial pathway coupling.     

Effect of position on the mechanical interaction between the rib cage and abdomen in preterm infants.

To determine the influence of body position on chest wall and pulmonary function, we studied the ventilatory, pulmonary mechanics, and thoracoabdominal motion profiles in 20 preterm infants recovering from respiratory disease who were positioned in both the supine and prone position. Thoracoabdominal motion was assessed from measurements of relative rib cage and abdominal movement and the calculated phase angle (an index of thoracoabdominal synchrony) of the rib and abdomen Lissajous figures. The ventilatory and pulmonary function profiles were assessed from simultaneous measurements of transpulmonary pressure, airflow, and tidal volume. The infants were studied in quiet sleep, and the order of positioning was randomized across patients. The results demonstrated no significant difference in ventilatory and pulmonary function measurements as a function of position. In contrast, there was a significant reduction (-49%) in the phase angle of the Lissajous figures and an increase (+66%) in rib cage motion in prone compared with the supine position. In addition, the degree of improvement in phase angle in the prone position was correlated to the severity of asynchrony in the supine position. We speculate that the improvement in thoracoabdominal synchrony in the prone position is related to alterations of chest wall mechanics and respiratory muscle tone mediated by a posturally related shift in the area of apposition of the diaphragm to the anterior inner rib cage wall and increase in passive tension of the muscles of the rib cage. This study suggests that the mechanical advantage associated with prone positioning may confer a useful alternative breathing pattern to the preterm infant in whom elevated respiratory work loads and respiratory musculoskeletal immaturity may predispose to respiratory failure.     

Transdiaphragmatic pressure and rib motion in area of apposition during paralysis

Changes in pleural surface pressure in area of apposition of diaphragm to rib cage (delta Ppl,ap), changes in abdominal pressure (delta Pab), and redial displacement of the 11th rib have been recorded in anesthetized, paralyzed dogs during lung inflation or deflation. Above functional residual capacity (FRC) changes in transdiaphragmatic pressure in area of apposition (delta Pdi,ap) were essentially nil in intact (INT) dogs either in lateral or supine posture, and in partially eviscerated (EVS) dogs in lateral posture, either in the 10th or 11th intercostal space. Below FRC delta Pdi,ap could be positive (INT lateral and EVS), nil (EVS), or negative (INT supine and EVS); it could be different in the 10th and 11th intercostal spaces. Hence, with stretched (like with contracted) diaphragm, delta Ppl,ap measured at one site often differs from delta Pab and is not representative of average pressure acting on area of apposition. With volume increase above FRC, the 11th rib moved slightly in and then out in EVS and linearly out in INT. With volume decrease below FRC it moved out progressively in EVS, and it moved in and eventually reversed in INT. In paralyzed dogs in lateral posture the factor having the greatest influence on displacement of the abdominal rib cage is Pab. Mechanical linkage with pulmonary rib cage becomes relevant at large volume, whereas insertional traction of diaphragm becomes relevant at low volume.     

Theoretical analysis of chest wall mechanics

A mathematical model of the chest wall partitioned into rib cage, diaphragmatic and abdominal components is developed consistent with published experimental observations. The model describes not only the orthodox chest wall movements (rib cage and abdomen expand together during inspiration) of the quietly breathing standing adult, but also Mueller maneuvers (inspiration against an occluded airway opening) and the paradoxical breathing patterns (rib cage contracts while abdomen expands during inspiration) observed in quadriplegia and in the newborn. The abdomen is inferred to act as a cylinder reinforced by the abdominal muscles functioning similarly to bands around a barrel. The rib cage and abdominal wall are inferred to act not as though they were directly attached to one another, but as though they were being pressed together by the skeleton. Furthermore, transabdominal pressure is visualized as acting, not across the rib cage isolated from the diaphragm, as has been suggested previously, but instead, across the combined rib cage and diaphragm acting as a deformable unit containing the lungs.     

Pleural pressure increases during inspiration in the zone of apposition of diaphragm to rib cage

The zone of apposition of diaphragm to rib cage provides a theoretical mechanism that may, in part, contribute to rib cage expansion during inspiration. Increases in intra-abdominal pressure (Pab) that are generated by diaphragmatic contraction are indirectly applied to the inner rib cage wall in the zone of apposition. We explored this mechanism, with the expectation that pleural pressure in this zone (Pap) would increase during inspiration and that local transdiaphragmatic pressure in this zone (Pdiap) must be different from conventionally determined transdiaphragmatic pressure (Pdi) during inspiration. Direct measurements of Pap, as well as measurements of pleural pressure (Ppl) cephalad to the zone of apposition, were made during tidal inspiration, during phrenic stimulation, and during inspiratory efforts in anesthetized dogs. Pab and esophageal pressure (Pes) were measured simultaneously. By measuring Ppl's with cannulas placed through ribs, we found that Pap consistently increased during both maneuvers, whereas Ppl and Pes decreased. Whereas changes in Pdi of up to -19 cmH2O were measured, Pdiap never departed from zero by greater than -4.5 cmH2O. We conclude that there can be marked regional differences in Ppl and Pdi between the zone of apposition and regions cephalad to the zone. Our results support the concept of the zone of apposition as an anatomic region where Pab is transmitted to the interior surface of the lower rib cage.     

The diaphragm of the newborn infant: anatomical and ultrasonographic studies.

In the newborn infant, the diaphragm seems badly adapted to perform the burden of respiratory work. Indeed, due to the large angle of insertion on the rib cage and the small area of apposition, the flat diaphragm of the newborn infant seems better designed to suck in the rib cage rather than air. To better understand this paradox, and get insight in the structure-function relationship, the anatomical connections between the diaphragm and the rib cage were studied in 16 infants of various postmenstrual and postnatal ages. It was concluded (1) that the diaphragm inserts on the rib cage border only in the anterior costo-diaphragmatic triangle. From antero-laterally to posteriorly it inserts at increasingly greater distance from the rib cage border; (2) that the dorsal diaphragm ends its free course at the 11th rib and continues caudally as a spur ending between the 12th rib and the crista iliaca. From echographic studies of the right diaphragm with simultaneous measurement of the caudad displacement of the diaphragm and abdominal circumference change, the dynamics of the diaphragmatic movements could be better understood. It was concluded that, in contrast with the adult diaphragm, acting as a piston within the rib cage, the diaphragm of the newborn infant acts as a below moving mainly in the posterior part.(ABSTRACT TRUNCATED AT 250 WORDS)     

Action of neck accessory muscles on rib cage in dogs

To investigate the action of the neck accessory muscles on the rib cage, we stimulated the sternocleidomastoid and the scalenus muscles separately in supine anesthetized dogs. Hooks screwed into the sternum and ribs were used to measure their axial displacements and the changes in anteroposterior (AP) and transverse (T) diameters of the rib cage. We found that the sternocleidomastoid and scalenus muscles, when they contract alone, cause a large axial displacement of the sternum and the ribs in a cephalad direction and expand the rib cage along both its AP and T diameters. Opening the abdomen increased the cephalad displacement of the ribs and the expansion of the lower rib cage, particularly along its T diameter, but reduced the increase in lung volume. These experiments indicate 1) that the action of the sternocleidomastoid and scalenus muscles on the rib cage is essentially the consequence of a rotation of the ribs' neck axes, resulting from the cephalad displacement of the ribs, and 2) that the fall in abdominal pressure, almost certainly by acting through the zone of apposition of the diaphragm to the rib cage, has a deflationary action on the lower rib cage, more markedly so on its lateral than its anterior wall. The experiments also suggest that the fall in abdominal pressure prevents the diaphragm from moving cephalad and aids the neck accessory muscles in inflating the lungs.     

Shape and size of the human diaphragm in vivo

Serial computerized tomograph (CT) sections at 5-mm intervals of a human diaphragm in relaxed and contracted states were obtained in one subject while he held his breath and lay supine in a CT scanner. All sections for one state were scanned at the same chest wall configuration as monitored by rib cage and abdominal dimensions, using magnetometers. Sections were scanned at relaxed functional residual capacity and after inspiring approximately 1 liter in such a way that rib cage dimensions increased only slightly. Models of the diaphragm dome in the two states were constructed from the sets of serial sections. Diaphragm length and volume displaced were measured, the zone of apposition of diaphragm to rib cage was mapped, and the line of the diaphragm silhouette in anteroposterior and lateral X-rays identified. Coronal and sagittal sections were constructed. In the inspiration studied, the diaphragm movement displaced 680 ml. Meridian lines in sagittal, coronal, and transverse directions over the right hemidiaphragm dome shortened by 6.7-7.2 cm, but over the left dome by only 4.0-4.3 cm. Lines of X-ray silhouettes were close to meridian lines, and estimates of shortening were similar to those made previously from X-rays. The peculiar saddle shape of the muscle may help the hemidiaphragms to operate independently, the fibers of the saddle acting as an anchor for midline directed fibers of the hemidiaphragm domes. The shape of the diaphragm also has implications for the distribution of transdiaphragmatic pressure and for the kind of distortion of the lower rib cage margin that is seen during inspirations at high lung volume.     

A model for studies of the deformable rib cage.

An earlier model for the study of rib cage mechanics was modified so that rib deformity in scoliosis could be better represented. The rigid ribs of that model were replaced by five-segment deformable ribs. Literature data on cadaver rib mechanical behavior were used to assign stiffnesses to the new individual model ribs so that experimental and model rib deflections agreed. Shear and tension/compression stiffnesses had little effect on individual rib deformation, but bending stiffnesses had a major effect. Level-to-level differences in mechanical behavior could be explained almost exclusively by level to level differences in the rib shape. The model ribs were then assembled into a whole rib cage. Computer simulations of whole rib cage behaviors, both in vivo and in vitro, showed a reasonable agreement with the measured behaviors. The model was used to study rib cage mechanics in two scolioses, one with a 43 degrees and the other with a 70 degrees Cobb angle. Scoliotic rib cage deformities were quantified by parameters measuring the rib cage lateral offset, rib cage axial rotation, rib cage volume and rib distortion. Rib distortion was quantified both in best-fit and simulated computer tomography (CT) scan planes. Model rib distortion was much smaller in best-fit planes than in CT planes. The total rib cage volume changed little in the presence of the scolioses, but it became asymmetrically distributed.     

Chest wall mechanics: effects of acute and chronic lung disease

Data from the literature show that lung tissue properties affect the chest wall compliance, Ccw, which is the change in lung volume, Vl, with respect to the pleural pressure, Ppl. to analyze the difference between acute and chronic lung tissue changes, we used a mathematical model that describes the static, nonlinear mechanics of the ventilatory system in terms of its major elements: rib cage; abdomen; diaphragm and lung. With this model we derived the relationship between chest wall, rib-cage and diaphragm compliances. Although the Vl-Ppl relation is independent of lung mechanics, the volume operating point (FRC) of the ventilatory system depends on lung tissue properties. This accounts for the effect of acute lung abnormalities. In the presence of chronic lung abnormalities, the properties of the rib-cage are changed which shifts the entire Vl-Ppl curve. In general, valid comparisons of (extra-pulmonary) chest wall mechanics can only be made using the entire Vl-Ppl relation, or at least a sufficiently large part of the relation about FRC. Differentiation of the rib-cage and diaphragm mechanics requires additional measurements of the rib-cage A-P distance and the relative position of the diaphragm.     

Relationships among pressure, tension, and shape of the diaphragm

The shape of the diaphragm dome was calculated from transdiaphragmatic pressure and tension in the diaphragm. It was assumed that the muscle acts as a free membrane, attached at its edges to the inside of a vertical rib cage circular in cross section, that the attachments are inferior to the point at which the dome makes contract with the rib cage, and that the abdomen is filled with fluid with a hydrostatic gradient in pressure. The shape is different from a section of a sphere, with a radius of curvature substantially greater at the apex of the dome than at the sides. Observed shapes of human hemidiaphragm domes at functional residual capacity are not spherical but closely match the calculated shapes. Best-fitting shapes correspond to transdiaphragmatic pressures of about 3 cmH2O transdiaphragmatic pressure, suggesting that such a pressure and corresponding tension are present in the human diaphragm when it is at rest in an erect subject. In this model; as lung volume increases and the diaphragm shortens, its shape changes in such a way that the ratio between transdiaphragmatic pressure and tension in the diaphragm remains nearly constant, rather than increasing with volume. Such a model can explain the observation that the length-tension relationship of the muscle is much more important than curvature in determining the effectiveness of the diaphragm as a pressure generator.     

Effect of lower rib cage expansion and diaphragm shortening on the zone of apposition

The relationship among diaphragm length (LD), the width of the zone of apposition (WZapp), and transverse chest diameter (Drc) was developed from model equations and statistical analysis. We present a theoretical model of diaphragm motion that predicts that the decrease in WZapp during inspiration is the result not only of shortening of the diaphragm muscle but also of expansion of the lower rib cage. To test our model, static lengths of costal LD, WZapp, and Drc were measured in 15 normal volunteers using posteroanterior chest X-ray films taken at four or five lung volumes spanning the vital capacity. We found a strong correlation between WZapp and LD: WZapp = 0.95 LD - 15.2 (R2 = 0.81). Expressing WZapp as a combined function of LD and Drc significantly reduced the unexplained variance in WZapp: WZapp = 0.96 LD - 0.47 Drc - 2.18 (R2 = 0.95). The coefficients for LD and Drc derived statistically are close to those predicted from our theoretical model. Repeating the analysis with LD as the dependent variable, we obtained similar results: LD = 0.85 WZapp + 17.1 (R2 = 0.81) and LD = 0.98 WZapp + 0.46 Drc + 3.48 (R2 = 0.94). We conclude that shortening of WZapp is dependent on both diaphragm shortening and rib cage expansion and that roentgenographic measurements of Drc and WZapp can be used to predict diaphragm length and length change.     

Analysis of human chest wall motion using a two-compartment rib cage model.

We present a model of chest wall mechanics that extends the model described previously by Macklem et al. (J. Appl. Physiol. 55: 547-557, 1983) and incorporates a two-compartment rib cage. We divide the rib cage into that apposed to the lung (RCpul) and that apposed to the diaphragm (RCab). We apply this model to determine rib cage distortability, the mechanical coupling between RCpul and RCab, the contribution of the rib cage muscles to the pressure change during spontaneous inspiration (Prcm), and the insertional component of transdiaphragmatic pressure in humans. We define distortability as the relationship between distortion and transdiaphragmatic pressure (Pdi) and mechanical coupling as the relationship between rib cage distortion and the pressure acting to restore the rib cage to its relaxed configuration (Plink), as assessed during bilateral transcutaneous phrenic nerve stimulation. Prcm was calculated at end inspiration as the component of the pressure displacing RCpul not accounted for by Plink or pleural pressure. Prcm and Plink were approximately equal during quiet breathing, contributing 3.7 and 3.3 cmH2O on average during breaths associated with a change in Pdi of 3.9 cmH2O. The insertional component of Pdi was measured as the pressure acting on RCab not accounted for by the change in abdominal pressure during an inspiration without rib cage distortion and was 40 +/- 12% (SD) of total Pdi. We conclude that there is substantial resistance of the human rib cage to distortion, that, along with rib cage muscles, contributes importantly to the fall in pleural pressure over the costal surface of the lung.     

Chest wall kinematic determinants of diaphragm length by optoelectronic plethysmography and ultrasonography.

To estimate diaphragm fiber length from thoracoabdominal configuration, we measured axial motion of the right-sided area of apposition by ultrasonography and volumes displaced by chest wall compartments [pulmonary, abdominal rib cage, and abdomen (Vab)] by optoelectronic plethysmography in four normal men during quiet breathing and incremental exercise without and with expiratory flow limitation. Points at the cephalic area of apposition border were digitized from echo images and mapped into three-dimensional space, and the axial distance from the xyphoidal transverse plane (D(ap)) was measured simultaneously with the volumes. Linear regression analysis between changes (Delta) in D(ap) and the measured volume changes under all conditions showed that 1) DeltaD(ap) was linearly related more to DeltaVab than to changes in pulmonary and abdominal rib cage volumes; and 2) this was highly repeatable between measures. Multiple stepwise regression analysis showed that DeltaVab accounted for 89-96% of the variability of DeltaD(ap), whereas the rib cage compartments added <1%. We conclude that, under conditions of quiet breathing and exercise, with and without expiratory flow limitation, instantaneous DeltaD(ap) can be estimated from DeltaVab.     

Pleural pressure between diaphragm and rib cage during inspiratory muscle activity

We measured the changes in pleural surface pressure (delta Ppl) in the area of apposition of the rib cage to the diaphragm (Aap) in anesthetized dogs during spontaneous breathing, inspiratory efforts after airway occlusion at functional residual capacity, and phrenic stimulation. Intact dogs were in supine or lateral posture; partially eviscerated dogs were in lateral posture. delta Ppl,ap often differed significantly from changes in abdominal pressure (delta Pab); sometimes they differed in sign (except during phrenic stimulation). Changes in transdiaphragmatic pressure in Aap (delta Pdi,ap) could be positive or negative and were less in eviscerated than in intact dogs. delta Pdi,ap could differ in sign among respiratory maneuvers and over different parts of Aap. Hence average delta Pdi,ap should be closer to zero than delta Pdi,ap at a given site. Since delta Ppl,ap = delta Prc,ap, where Prc,ap represents rib cage pressure in Aap, delta Pdi,ap = delta Pab - delta Prc,ap. Hence, considering that delta Pab and delta Prc depend on different factors, delta Pdi,ap may differ from zero. This pressure difference seems related to the interaction between two semisolid structures (contracted diaphragm and rib cage in Aap) constrained to the same shape and position.     

Diaphragm function and respiratory response after upper abdominal surgery in dogs

Decreased diaphragm activity has been demonstrated after cholecystectomy in humans (Am. Rev. Respir. Dis. 127: 431-436, 1983). To investigate the mechanism(s) of postoperative diaphragm dysfunction we have established a dog model. Three groups of mongrel dogs were studied under general anesthesia: six dogs received no surgery (control); nine dogs underwent upper abdominal surgery (cholecystectomy); and six dogs underwent lower abdominal surgery (pseudoappendectomy). Diaphragm function was assessed by changes in transdiaphragmatic pressure swings, the ratio of changes in gastric to esophageal pressure swings, and the ratio of changes in abdominal to rib cage diameters during quiet tidal breathing. In the upper abdominal surgery group there were significant postoperative decreases in all parameters of diaphragm function and an increase in minute ventilation and respiratory frequency. However, there were no significant postoperative changes in the parameters of diaphragm function in the control or lower abdominal surgery groups. These studies establish that general anesthesia is not responsible for the reduced diaphragm activity seen postoperatively and that diaphragm function is not affected by lower abdominal surgery in dogs.     

An analysis of action of intercostal muscles in human upper rib cage

The actions of the intercostal and paraspinal muscles in stabilizing the human upper rib cage have been analyzed using a geometrically realistic mathematical model of the first six ribs, vertebrae, and associated musculature. The model suggests roles of the deep layers of erector spinae in stabilizing the vertebral column so that it can support the loads placed upon it by the ribs under physiological load. If we assume that the tension exerted by an intercostal muscle is proportional to its local thickness, the model predicts that the observed distribution of intercostal thickness is close to that which minimizes the stresses in ribs when the model is subjected to peak physiological load. The observed shape of the ribs are optimal to withstand the calculated pattern of loading along their length. These calculations raise the hypothesis that the arrangement of intercostal musculature and rib geometry result in an optimally light rib cage, which is capable of withstanding the loads placed upon it. The analysis of the mechanics of the entire model indicates that the geometrical simplifications made in Hamberger's model are not valid when applied to the rib cage.     

Relative strengths of the chest wall muscles

We hypothesized that during maximal respiratory efforts involving the simultaneous activation of two or more chest wall muscles (or muscle groups), differences in muscle strength require that the activity of the stronger muscle be submaximal to prevent changes in thoracoabdominal configuration. Furthermore we predicted that maximal respiratory pressures are limited by the strength of the weaker muscle involved. To test these hypotheses, we measured the pleural pressure, abdominal pressure (Pab), and transdiaphragmatic pressure (Pdi) generated during maximal inspiratory, open-glottis and closed-glottis expulsive, and combined inspiratory and expulsive maneuvers in four adults. We then determined the activation of the diaphragm and abdominal muscles during selected maximal respiratory maneuvers, using electromyography and phrenic nerve stimulation. In all subjects, the Pdi generated during maximal inspiratory efforts was significantly lower than the Pdi generated during open-glottis expulsive or combined efforts, suggesting that rib cage, not diaphragm, strength limits maximal inspiratory pressure. Similarly, at high lung volumes, the Pab generated during closed-glottis expulsive efforts was significantly greater than that generated during open-glottis efforts, suggesting that the latter pressure is limited by diaphragm, not abdominal muscle, strength. As predicted, diaphragm activation was submaximal during maximal inspiratory efforts, and abdominal muscle activation was submaximal during open-glottis expulsive efforts at midlung volume. Additionally, assisting the inspiratory muscles of the rib cage with negative body-surface pressure significantly increased maximal inspiratory pressure, whereas loading the rib cage muscles with rib cage compression decreased maximal inspiratory pressure. We conclude that activation of the chest wall muscles during static respiratory efforts is determined by the relative strengths and mechanical advantage of the muscles involved.