https://www.researchgate.net/...diaphragm_muscle.../56321c3f08ae13bc6c3745d8.pdf
to the body axis and apposed to the inner aspect of the rib cage. represent cranial and caudad force vectors generated by contraction of the diaphragm. DMT indicates the thickness of diaphragm muscle. pressure is exerted, that is, the cross-sectional area of the thorax.
MAXIMUM CONTRACTILE FORCE OF HUMAN DIAPHRAGM MUSCLE, DETERMINED IN VIVO DUDLEY F. ROCHESTER and (BY INVITATION) NARINDER S. ARORA AND NORMA M.T. BRAUN CHARLOWTESVILLE
The diaphragm is a critical component of the respiratory muscle air pump apparatus (1). Diaphragmatic contractility, vital to life, may be compromised in several ways (2, 3). For example, in obstructive lung disease, contractile force of the otherwise normal diaphragm is reduced when hyperinflation of the lung shortens diaphragm muscle resting length. Undernutrition weakens the diaphragm by reducing its muscle mass. Conditions such as myopathy, hypoxemia, acidosis, hypophosphatemia and electrolyte imbalance compromise the integrity of the contractile elements per se. Because several of these mechanisms may coexist, it would be desirable to identify the relative contributions of each one to impaired diaphragmatic contractility. The purposes of this communication are to describe a method for assessing the strength of the contractile elements of the human diaphragm in vivo, and to indicate how the relative contributions to transdiaphragmatic pressure of altered diaphragm muscle mass and contractile element strength can be quantified. THEORY The contractile force of a muscle depends on its resting length, the velocity of shortening during contraction, and the frequency of neural stimulation (4, 5). Maximum contractile force is produced when contraction begins from an optimum resting length, and when the muscle is restrained from shortening so that it contracts isometrically. The optimum tetanic stimulation frequency for in vivo muscle is usually above 50 Hz. In man, the optimum resting length of the diaphragm appears to occur at a lung volume which lies between the normal breathing position and full expiration (6). Diaphragmatic contraction is nearly isometric during maximum voluntary inspiratory efforts against a closed airway, or during maximum expulsive efforts with the glottis open (6). Maximum voluntary efforts involve neural stimulation frequencies of up to 80 Hz (7), and with percutaneous tetanic stimulation of the phrenic nerve in man, transdiaphragmatic pressure is 95% maximal at 50 Hz (5). Hence by making maximum static voluntary efforts from near the full expiratory Department of Internal Medicine, University of Virginia School of Medicine, Charlottesville, and Department of Medicine, College of Physicians and Surgeons, Columbia University, New York. 200
MAXIMUM CONTRACTILE FORCE OF HUMAN DIAPHRAGM MUSCLE
201
position, the conditions for optimizing muscle contractile force are essentially met. The configuration of the diaphragm at its optimum length is something like a German army helmet, cut out in front, and dipping low along the sides and posteriorly. At the level of the lower thoracic vertebrae there is a sleeve of diaphragm muscle lining virtually the entire circumference of the body cavity (Figure 1). A coronal section through the torso is P.-,0za
FIG. 1. Shape of the human diaphragm inside the rib cage when the diaphragm is at its optimum resting length (see text). In this position most of the diaphragm muscle is parallel to the body axis and apposed to the inner aspect of the rib cage.
202
DUDLEY F. ROCHESTER ET AL.
F,
II
DMT
~~F2
FIG. 2. Schematic coronal section of the human torso, showing that at the full expiratory position diaphragm muscle (heavy line) is oriented parallel to the body axis for most of its length. Pab and Ppl indicate abdominal and thoracic pressures, respectively. F, and F2 represent cranial and caudad force vectors generated by contraction of the diaphragm. DMT indicates the thickness of diaphragm muscle.
shown schematically in Figure 2. The dome of the diaphragm is comprised partly of muscle, represented by the thick line, and partly of central tendon, represented by the thin horizontal segment in the center. The thickness of the muscular sleeve is designated DMT. The long axis of the diaphragm muscle fibers are parallel to the body axis over most of the muscle length. Contraction of the diaphragm produces negative pressure in the thorax (Ppl), and positive pressure in the abdomen (Pab). Transdiaphragmatic pressure (Pdi) is the difference between Pab and Ppl. With diaphragmatic contraction, there is a force vector, F1, directed craniad, and an opposing vector, F2, directed caudad. F1 can be calculated as the product of transdiaphragmatic pressure and the cross-sectional area over which the pressure is exerted, that is, the cross-sectional area of the thorax. F2 can be calculated as the product of tension in diaphragm muscle and the circumference and thickness over which the tension is exerted. We hypothesize that the curvature of the diaphragm dome is relatively without influence on transdiaphragmatic pressure and tension in diaphragm muscle. We speculate that the liver redirects diaphragmatic force vectors, from transverse to parallel to the body axis, much as a pulley redirects tension in a rope. Two lines of evidence support this hypothesis. Loring and Mead (personal communication) analyzed the shape of the dome of the human diaphragm on postero-anterior and lateral chest roentgenograms taken at four lung volumes ranging from full inspiration to full expiration. They measured the length of the arc inscribed by the dome, and the length of the chord connecting the ends of the arc. In both
MAXIMUM CONTRACTILE FORCE OF HUMAN DIAPHRAGM MUSCLE
203
FIG. 3. Tracing of computerized tomographic image of the human torso at the level of the 10th thoracic vertebrae. The heavy line represents the sleeve of diaphragm muscle; its thickness and circumference are labeled DMT and C, respectively. The cross-sectional area of the thorax is labeled A; the transverse and antero-posterior diameters are labeled DI and D2, respectively.
PA and lateral projections, the ratio of arc to chord length was nearly constant at all four lung volumes. Kim and her colleagues measured transdiaphragmatic pressure (Pdi) and diaphragm muscle active tension (Tdi) simultaneously in the dog (8). Over a wide range of lung volume, the ratio Tdi/Pdi was also remarkably constant. According to the Laplace relationship, the ratio of tension in the wall of a container to pressure within the container is a function of the radius of wall curvature. Thus, if the ratio of tension to pressure is constant at different lung volumes, curvature must not change appreciably as lung volume is varied. The diaphragm muscular sleeve is viewed in cross section in Figure 3. This diagram is actually a tracing of a computerized tomographic image of the body at the level of the 11th thoracic vertebra. The area over which Pdi is exerted is labeled "A". The circumference of the muscular sleeve is labeled "C". The transverse and antero-posterior diameters of the thoracic cross-section are labeled "D1" and "D2", respectively. Again, DMT represents diaphragm muscle thickness. The thoracic cross-sectional area, A, the diaphragm muscle circumference, C, and the ratio of area to circumference, A/C, are closely approximated by the formulae: A = IT (D1D2)/4 [1] C = 7TD1 [2] A/C = D2/4 [3] Contractile tension in diaphragm muscle (Tdi) can be calculated from transdiaphragmatic pressure (Pdi), diaphragm muscle thickness (DMT), thoracic cross-sectional area (A), and circumference (C) in the following
204 manner:
DUDLEY F. ROCHESTER ET AL.
F1 = Pdi x A F2= Tdi x DMT x C During an isometric contraction, F1 = F2. Thus, by rearranging, Tdi = (Pdi/DMT) x (A/C) The units of Tdi are force per unit of muscle cross-section area, expressed as kg/cm2.
[4] [5] [6] here
METHODS Each term in equation 6 can be evaluated. Pdi can be measured directly, using esophageal and gastric balloon catheters to record Pab and Ppl. Thoracic aia and circumference could be measured from computerized tomograph images, but this is costly and involves considerable radiation exposure. However, as discussed below, the ratio A/C can be closely approximated using equation 3. Diaphragm muscle thickness cannot be accurately measured in vivo, but it can be predicted within 15% accuracy, using data from a necropsy study of diaphragmatic dimensions. We analyzed tracings from 30 computerized-tomographic images of the lower thorax (T9-T12) to validate the simple formula for calculating the ratio A/C in Equation 3. Thoracic area was measured planimetrically, thoracic circumference was measured using a map wheel, and the ratio of measured area to measured circumference was determined. The calculated values of these variables were obtained using equations 1-3. A comparison of actual and calculated values for A, C, and A/C is summarized in Table 1. Although the differences for A and A/C are statistically significant, they are small, each calculated value agreeing with the actual value within 5%. This analysis is independent of the thoracic level at which the measurements were made. The significance of this analysis is that the term A/C in equation 6 can be evaluated simply by measuring the antero-posterior diameter of the lower thorax (D2) on a lateral chest roentgenogram. TABLE 1. Comparison of calculated and measured values of thoracic cross-sectional area (A), circumference of diaphragm muscle (C), and A/C. P SD mean Variable (A%)*
