thickness referenced to myocardial volume: a new noninvasive framework for cardiac mechanics. J. Appl. Physiol. 87(1): 211-221, 1999.-Dimensional variables measured for study of left ventricular mechanics are subject to errors arising from difficulty in determining zero-stress dimensions for use as a reference. Based on a method validated for measurements within individuals, we have devised an approach that facilitates comparison between individuals while minimizing random scatter. We define an

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... exact mathematical index of strain, ln(h 0 /h), using wall thickness (h) referenced to extrapolated wall thickness at zero-luminal volume (h 0 ). Noninvasive data from rabbits, pigs, and humans all yielded highly similar myocardial stress, ln(h 0 /h), and work values. The stress-ln(h 0 /h) relationship during afterload variation was constant among individual pigs with a twofold variation in ventricular mass. Stress-ln(h 0 /h) data from our analysis displayed lower scatter than either pressure-volume data normalized to myocardial mass or stress-ln(h 0 /h) data referenced to end-diastolic dimensions. A Frank-Starling-like curve with high correlation (r 2 ϭ 0.96) was constructed from single points from different pigs, suggesting a low level of size and intersubject scatter. This method offers high precision for noninvasive characterization of ventricular and myocardial mechanics and for comparisons between subjects and between species. ventricular function; wall stress; ventricular geometry RECENT REPORTS HAVE DESCRIBED a framework for noninvasive analysis of myocardial behavior based on mean wall stress and a strainlike quantity, the natural logarithm of reciprocal of wall thickness, ln(1/h) (21-23). Wall thickness is used as a precise index of myocardial area under the assumption of the approximate constancy of myocardial volume. This approach has been shown to provide accurate estimates of myocardial work per unit volume of tissue (21, 22). Within individuals, it is sensitive to the effects of ␤-blockers and other inotropes (21). It has the further advantage of being based on easily obtainable echocardiographic measurements. The above investigations avoided the inclusion of a reference value for wall thickness. When stress-strain analysis is used to investigate constitutive relationships, such a reference measurement is generally made at a point of zero net stress, a point not obtainable under clinical conditions. Thus all analysis in these studies was in terms of increments in the variable ln(1/h) that indexed strain. The lack of a reference, although practical for determining energetic and geometric changes, prevents direct comparison of values between different individuals. This lack also causes the units of the strainlike variable to be ambiguous. We investigated whether use of a calculated reference would provide a basis for comparison of values between individuals, as well as avoided the use of the ambiguous units of natural logarithm of reciprocal distance. Because myocardial mass has been shown to be effective in normalizing other descriptors of myocardial behavior (4, 15), we specifically examined references calculated as cuberoot functions of this quantity to produce a value with units of length rather than volume. The present paper discusses results obtained by using a reference that is the extrapolated value of wall thickness that would occur if the luminal volume could go to zero. Glossary A Area of a truncated conical section of myocardium, cm 2 D Instantaneous endocardial short-axis of left ventricle, cm D m Instantaneous midwall short-axis of left ventricle, cm D m0 Midwall short-axis of left ventricle at zeroluminal volume, cm ESPVR End-systolic pressure-volume ratio FS Fractional shortening of the left ventricle h Instantaneous measured wall thickness, cm h 0 Wall thickness at zero-luminal volume, cm L Endocardial long-axis of left ventricle, cm; mean sarcomere length, µm LV Left ventricle L 0 Mean sarcomere length at zero-luminal volume, µm P Blood pressure in ventricular lumen, g/cm 2 p, q, r, a, b Arbitrary intermediate quantities for solving a cubic equation T Mean of circumferential and meridional tension, g/cm V Volume of a truncated conical section of myocardium, cm 3 V c Cavity volume of the left ventricle, cm 3 V lum Left ventricular luminal volume, cm 3 V myo Left ventricular myocardial volume, cm 3 V T Left ventricular total volume (luminal ϩ myocardial volume), cm 3 V w Left ventricular wall volume, cm 3 V 0 Extrapolated left ventricular luminal volume at zero pressure, cm 3 VCF Velocity of circumferential fiber shortening, circumferences/s The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 8750-7587/99 $5.00