Geometric similarity of aorta, venae cavae, and certain of their branches in mammals J. P. HOLT, E. A. RHODE, W. W. HOLT, AND H. KINES Department of Heart Research, University of Louisville School of Medicine Health Sciences Center, Louisville, Kentucky 40202; and Department of Medicine, School of Veterinary Medicine, University of California, Davis, California 95616 Holt, J. P., E. A. Rhode, W. VV. Holt, and H. Kines. length of the mammalian aorta. In earlier reports we Geometric similarity of aorta, venae cavae, and certain of presented evidence that allometric equations apply to their branches in mammals. Am. J. Physiol. 241 (Regulatory the geometric and functional characteristics ofthe mam- Integrative Comp. Physiol. 10): R100-R104, 1981.—The diam- malian heart (8,10). The present studies were undertaken eters of the aorta and venae cavae at various points throughout to determine whether the geometry of these vessels can their lengths, the diameters of their major branches, and the be described by p0wer-law equations relating diameter lengths of various aortic and vena caval segments were meas- and { h bod ^. ^ (n) ured in plastic corrosion casts of the artenai and venous systems ° jo of the normal adult mouse, rat, rabbit, dog, goat, horse, and cow, extending over a body weight range of 38,000-fold (arterial) METHODSMETHODS •and .«•*» 1,100-fold l j(venous). u j u It i is Plasticshown that corrosionthe diameters andcasts t>i„„*:„Plastic of„«™„„;«», corrosionnormal ™,^ casts ~eadult ™,-™oiof normal mice,««4«1t adult ™,-o« mice,rats, r-nfc-rats, rab- rab*«u lengths of these vessels are described bv power-law equations . , , , , relating the particular diameter or length to body weight (BW)bits, £lte, dogs, dogs goats, goats, horses, horses, and and cows cows werewere preparedprepared as raised to a particular power, i.e., diameter = a BW6. Equationsfollows: follows: after after attaining attaining a deepa deep anesthetic anesthetic level,1 level, cannu- for the diameters and lengths of the vessels are given for slightlylation lation of ofthe the carotid carotid and and femoral femoral arteries arteries and and exposureexposure to distended vessels and for vessels distended in the physiologicalsevere severe hemorrhage, hemorrhage, the the animals animals were were killed killed byby injectinginjecting range. either a large dose of pentobarbitaleither a large dose of pentobarbitalsodium sodiumor concen- or concen trated KCL solution into the arch of the aorta. This was arteries; veins; mouse; rat; rabbit; dog; goat; cow; horse; similar followed by perfusion of the arterial system with physi ity ological saline by way of the carotid artery for 2 min. then bleeding from the femoral artery for 2 min. BatsonV Compound (Polysciences, Paul Valley Industrial Park following Thompson's discussion (21) of the effects Warrington, PA 18976) was then quickly mixed and of scale in biology, Huxley (12) employed allometric or injected under 100 mmHg pressure into the carotid ar power-law equations for somatic form analysis, and more tery. Bleeding was continued from the femoral arten recently several investigators have described power-law until plastic was seen to pass from the cannula at which equations relating various physiological variables to body time the plastic solution was injected under 100 mmHg weight (5). Evidence has been presented that power-law pressure into the femoral artery as well as the carotid ir equations describe quantitative morphological and func all animals except mice. In these animals injection wa^ tional characteristics of the kidney, heart, respiratory by way of the left ventricle. The infusion was continued system, and certain other organs over an approximately maintaining pressure at 100 mmHg, until the plastic 70 X 106-fold variation in body weight of mammals (1, 2, hardened. This took between 30 and 60 min in differen'. 5, 8-10, 19). As this evidence has grown a number of experiments. Following this, the animal was decapitated intriguing theories of biologic similarity have been for skinned, and the carcass placed in concentrated potas mulated (6, 14). sium hydroxide solution (15-33%) for a period varying A full understanding of hemodynamics is not possible from 18 h to 3 days. At the end of this time most of th without a knowledge of the dimensions of the vascular tissue had been macerated and the remaining arteria segments through which blood flows. For example the cast was washed with water until it was free of tissue. Reynolds number, the Pouiselle-Hagen relation, and In another group of animals venous casts were pre pressure gradients are related to the geometry of the pared in a similar manner except that the plastic wa.c tubular system. Although a number of investigators (16, injected by way of the femoral vein and a .catheter wa 17, 20) have reported quantitative measurements of di ameters and lengths of certain vessel segments in one 1 Mouse (pentobarbital sodium, 120 mg/kg), rat (pentobarbital so species, insofar as we are aware no data are available dium, 55 mg/kg), rabbit (pentobarbital sodium, 18" mg/kg; Dial-Ure thane, 0.3 ml solution/kg), dog (morphine, 3 mg/kg; Dial-Urethant concerning the comparative quantitative geometric pat- 0.125 ml solution/kg; pentobarbital sodium, 7.5 mg/kg), goat (pento aug^aEi barbital sodium, 12-20 mg/kg; acepromazine, 0.15 mg/kg), horse of mammals, large and small, other than that of Clark (chloral hydrate, 85-169 mg/kg), and cow (chloral hydrate, 76-122 mg/ (3) and Gunther (5) regarding the diameter and total kg). 0363-6119/81/0000-0000$01.25 Copyright© 1981 the American Physiological Societ GEOMETRIC SIMILARITY OF AORTA, VENAE CAVAE, AND BRANCHES placed in the vena cava near the right atrium by way of corrected for 1% shrinkage of the plastic that took place the external jugular vein. The plastic was injected under after solidification. In some cases the vessels were slightly, a pressure of 100 mmHg for 1 or 2 min until it was seen oval instead of circular. In these cases the average value to pass from the open end of the catheter in the vena of the greatest and least diameters were recorded. cava. At this time the pressure was decreased to 25 Log-log plots were prepared of the relationship be mmHg and the vena caval catheter occluded. Pressure tween body weight and diameter of the aorta at various was maintained at 25 mmHg until the plastic hardened. points throughout its length, diameter of each branch The remainder of the procedure was the same as that from the aorta, and the length of aortic segments between employed in the arterial preparations. the points where each branch originated. Similar log-log The weight of each animal was recorded in kilograms plots were prepared for the venae cavae and their prior to an experiment. Twenty -one animals were utilized branches. The data were transformed to base 10 loga in arterial injections; and an additional 14 animals were rithms and the linear regression calculated by the method used in venous injections. The individual body weights of least squares to give the parameters in the power-law are presented in Table 1. ■ Venous pressure varies considerably in different por equation tions of the mammalian venous system and the state of y\saXb collapse of these vessels varies accordingly (4, 7). Early y is any variable experiments utilizing injection pressures of 5 mmHg con sistently produced casts inadequate for the measurement X is mass of body weight in kilograms of vessel dimensions; many vessels were seen to be in Statistical analysis of the logarithmic equations included: the correlation coefficient (r), 95% confidence limits for r p n n i t n / J U . - . ^ ( Z + r . I ~ - . _ J „ \ 1 ^ 1 _ j _ l i r . measured. The casts w ~..^ v^vU..ui.v, i_-t, "iiii.ii nao mu^ii me sdiiie fcigiimcance for a logarithmic regression line as the standard deviation cavae with th for a mean, i.e., two SE limits should include 95% of the cases. With the log-log analysis, +SE and -SE differ slightly; the values shown in Tables 1-3 are the mean of Lengths of vessel segments were measured from the the two absolute values. midpoint of a branch to the midpoint of the next branch. Larger vessels were measured with calipers and smaller branches with a microscope. These measurements were RESULTS table 1. Body weight of individual experimental Table 2 presents the coefficients for the power-law animals regression equations, as well as statistical measures for the relationships to body weight of the' diameters and lengths of the aorta, superior and inferior vena cava, and Arterial Injections Venous Injections their major branches. The results extend over a body 0.017 weight range of more than 38,000-fold for arteries and 0.023 0.024 1,100-fold for veins. In Table 2 and in the equations given 0.025 below the diameters and lengths are in centimeters and body weight is in kilograms. 0.431 0.415 Aorta and its branches. The logarithmic relationship 0.431 0.490 between body weight and the diameter of the ascending 0.441 0.500 0.472 aorta, AID, the length of the ascending aorta to the point where the brachiocephalic artery comes off, AIL, and the Rabbits 2.40 2.50 total length of the aorta AL, are shown in Fig. 1, A-C. 2.55 2.80 Equations describing these relationships, as well as sim 3.70 2.80 ilar relationships for the left coronary, LCD, right renal 4.30 RRD, and right iliac, RID, arteries are given below Canine 19.25 9.75 25.50 15.20 AID = 0.41 BW036 LCD = 0.097 BW036 27.70 22.70 AL = 16.12 BW032 RRD = 0.169 BW030 23.20 AIL = 1.00 BW028 RID = 0.177 BW031 32.30 63.50 50.90 It is of interest to note that whereas heart weight is a 95.50 function of BW1, kidney weight is a function of BW085 ._ , Bovine 480.90 258.50 (5), while the diameters of the left coronary and right 659.00 renal arteries are functions of BW036 and BW030, respec Equine tively.