hormones, the binding of the hormone with proteins, and the exchanges and interconversions of hormones in plasma and tissues, the kinetic law of hormone is very complicated; it must be described by complicated differential equations such as eqns. 7 or 8, in whichf ' is always a very complicated nonlinear function of hormone concentrations (and other factors). Therefore, the decay law of hormones cannot be so simple as eqns. 1 or 2. Thus, in general, almost all hormones cannot have a constant half-life, i.e. the so-called half-life changes with time and concentration (consequently with a dose of exogeneous hormone) and loses its original meaning.

Therefore, to describe the decay of hormones (especially endogeneous hormones) in plasma, the half-life has little meaning by itself and is not a good characteristic quantity for hormones. On the other band, the metabolic clearance rate MCR and the metabolic clearance coefficient ,~ are directly well defined quantities (see eqns. 11 and 17, although in some cases 2 may have no definite value). Therefore, we consider both MCR and 2 are rather better characteristic quantities than the half-life for hormones.

Nevertheless, the life (residence or turnover) time may be a more directly perceived quantity than MCR and 2; we suggest calling 1/), the time constant or simply the life (residence or turnover) time instead of the half-life, and mean life time to describe the hormone metabolic character.

References

DISTEFANO, L L III. (1982): 'Noncompartmental vs. compartmental analysis: some bases for choice', Am. J. PhysioL, 243, pp. R1-R6

FINK, G., GENNSER, G., LIEDHOLM, P., THORELL, J., and MULDER, J. (1974): 'Comparison of plasma levels of luteinizing hormone releasing hormone in men after intravenous of intranasal adminis- tration', J. Endocr., 63, pp. 351-360

OFPENHE~cIER, J. H., and GL~tr'IDE, E. (1979): 'Quantitation of the production, distn~bution and interr of hormones', in DEGROOT, L. (Ed.) 'Endocrinology' (Grune & Stratton, New York) Vol. 2, pp. 2029-2036

PETEttSON, IL E. (1959): 'The miscible pool and turnover rate of adrenocortical steroids in man', Recent Progr Hormone Res., 15, p. 231

SCHURMEYER, T. H., AVOEPdNOS, P. C., GOLD, P. "vV., GALLUCCI, W. T., TOMAI, "1". E, and CUTLER, G. B., LORIAUX, D. L., and CHROUSOS, G. E (1984): 'Human corticotropin-releasing factor in man: pharmakokinetic properties and dose-response of plasma adreno- corticotropin and cortisol secretion', s Clin. Endocr. Metab., 59, 1103

STALLA, G. IC, HARTWlMMER, J., VON WEP.ER, K., and MULLER, O. A. (1986): 'Intravenous spplieation of ovine and man CRF levels', Neuroendocrinol., 42, p. 1

TAIT J. E, T&IT, S. A. S., LITTLE, B., and LAUMAS, tC R. (1961): 'The disappearance of 7-H-D-aldosterorte in the plasma of normal subjects', J Clin. Invest., 40, p. 72

( Communication

In vivo measurement of arterial pre-tension

~ .

S. I. Green 1 G . S . Schajer 1 D . R . Parker ~ A . J . Post 1 Y. N.-H. Hsiang 2

1 Department of Mechanical Engineering, 2 Department of Vascular Surgery, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4

Keywords---Anastomosis, Arteries, Compliance, Instrumentation, Measurement, Pre- tension, Rabbit, Tensiometer, Tension

Med. & Biol. Eng. & Comput., 1995, 33, 826-829

, J

1 Introduct ion

ONE OF the more conspicuous events that occurs after arterial transection during a surgical procedure is a substantial axial retraction of the cut vascular segments. This axial retraction arises from the release of a preexisting tensile axial force, here called the arterial pretension. The pre-tension force is large enough to cause approximately a 50% axial stretching of the artery, relative to its totally relaxed state ( F ~ G et aL, 1979).

The arterial pre-tension may have several physiological functions. Perhaps the most significant fi_n, etion is to reduce the tendency of the artery walls to buckle during flexure. A pre- tensioned artery has better resistance to eotlapse during limb motion. A second potential function is to support the viscous drag caused by the internal blood flow, and to inhibit possible

First received 27 July 1994 and in final form 20 April 1995

�9 IFMBE: 1995

fluttering and collapse of the otherwise very flexible arterial wall (PEDI,LrY, 1992). The pre-tension may also be significant in the mechanics of the blood vessel endothelium (Frog and Lro, 1993).

Quantifying arterial pre-tension is important for several reasons. The level of pre-tension may indicate significant changes in arterial properties due to disease, ageing, hypertension, the effects of drugs etc. ha addition, the pre- tension force defines a reference axial stress state used when modelling the ela,.~c (or compliance) properties of the artery (Ftmo et al., 1979).

At least two methods have been developed to measure arterial pretension. 1anicki and Patel designed an electrical gauge to measure ~the force rex~red to maintain arterial stretching after an arterial segment.is excised (JANICKI and PATEL, 1968). This procedure gives reliable results, but its destructive nature severely limits its application. Lee et aL described a different force gauge concept using a 'slingshot' desing (LEE et al., 1968). In this gauge, the arterial pre-tension

826 Medical & Biological Engineering & Computing November 1995

T~ To

fixed post

Fig. 1

mounting rail

- " ' : ~: movable post

~ ~ ~ artedat clamps

binocular beam post

Tensiometer design; post on the left is fixed; central post is of a binocular beam design and is strain-gauged; post on the right is moved towards central post after zeroing the tensiometer

is determined by measuring the lateral force required to deflect the artery by a given amount from a straight line. Force gauges using a similar principle have been developed to measure tendon and ligament tension (BARNES and PINDER, 1974; K~STAL et aL, 1993). The 'slingshot' method is non- destructive, but is less reliable because local bending of the artery wall at the support points makes it difficult to determine the lateral deflection accurately. The device does not maintain arterial pressure during the measurement (the vessel is 'milked'). The non-maintenance of arterial pressure is also a problem with this device. As pointed out by Bergel and others, the internal pressure within an artery and its longitudinal elastic response are interrelated (B~GEL, 196t). Thus, releasing the internal pressure reduces the arterial pretension, perhaps by one-half or more.

In this study, a new design of non-destructive arterial pre- tension force transducer is described. The use of the new transducer is illustrated by a preliminary study, where femoral artery pre-tension is measured in I0 New Zealand White rabbits. The effect of limb extension and of local anaesthesia are monitored, and the two treatments are found to alter the arterial pre-tension substantially.

2 Tensiometer design, calibration and testing

A customised arterial pretension device was designed and built for non-destructive use /n vivo. The 'blood vessel tensiometer' shown in Fig. I consists of three posts mounted on a 10 cm rail. The positioins of the three posts are adjustable to accommodate arteries or veins with exposed lengths of 4- 8 em. Modified drafting compass nibs are attached to the ends of the posts to secure the exposed vessel. The tips of the nibs are coated in soR plastic, and the clan!ping forces are adjustable with set screws to avoid slippage and local damage to the vessel.

The central post contains a lateral force transducer of the binocular beam type (MEASURF2aEtCrs GROUP, 1988). This design was chosen because of its high swdn sensitivity and high bending stiffness. The strain gauges on this transducer are arranged in a '~ear beam' configuration, This strain gauge arrangement indicates lateral forces only, independent of any axial and bending loads. Thus, the transducer reading is not sensitive to the exact vertical location of the vessel contained within the attached clamp.

To confirm the insensitivity of this design to axial and bending loads, two tests were carried out on the central post. In the first test, purely axial loads of between 0.30 N and 0.81 N

artery with pre-tensioning To a

To three clamps attached to artery

b

T~ T~ T=O

right post moved and resecured G

Fig. 2

T> To

Tensiometer operation; when the right clamp is moved inwards (c), the tension T in the right-central pore'on o f artery falls to zero; central clamp is then exposed to only the pre-tension on the left To

were applied to the post. The central post recorded these axial loads as a specious 'tension force' (see below) of 0.003 N or less, implying that there is only a 1% cross-talk between the applied axial force and the measured pre-tensiou. To test the sensitivity of the binocular beam design to bendLug loads, known 'tensile forces' of between 0.50 N and 0-66 N were applied at two different distances from the end of the clamp post. The measured 'tensile forces' were the same for these two cases (with quite different bending loads) to within 1%.

The operation of the tensiometer is shown schematicaUy in Fig. 2. The three clamps of the tensiometer are placed wound a portion of a pre-tensioned artery. The outer clamps, followed by the central clamp, are carefially tightened and fixed to the sample artery. The transducer reading is then zeroed. The right post is moved towards the central p o ~ releasing the pre- tension in the arterial segment labelled T = 0 in Fig. 2c. The forces on either side of the central force-measuring post are now unbalanced, subjecting the central post to a net force equal to the pre-tcnsioning force. The central force tranaducer directly indicates this force.

The response of the tensiometer was found to be highly linear (Fig. 3); the calibration data show a standard deviation of less than 2% of the mean from a linear regression best fit (the slight offset is an artefact of the testing procedure). Extensive testing of the tensiometer in simulated/n vivo conditions has shown it to have a maximum error of 4- 15"/'o. During/n vivo measan~ments, care is needed to ensure that the central force measuring post does not touch any surrounding tissue.

3 Animal experiment procedure

The tensiomcter was used to meas~e the pre-tension in both the right and teR femoral arteries of ten female New Zealand White rabbits. The rabbits ranged in weight from 3.5 to 6 kg. Each rabbit was pre-anaesthetised with xylazine hydrochloride (7 nag kg -l) and ketamine (35mgkg-1). Anaesthesia was maintained throughout the experiments with halothane (I- 2%). Endotraeheal intubation was used, ventilation was

Medical & Biological Engineering & Computing November 1995 827

0-8 0'7

136 0-5

0"4

0'3

0'2

0"1 0

2 4 10 transducer reading

12

Fig. 3 Tensiometer calibration; measured data are represented by squares; regression line is also shown; non-zero y-intercept is an artefact of the calibration procedure

maintained with a mechanical respirator, and the rabbits were placed in a supine position. Intravascular volume was maintained with 0.9% saline solution. Using standard operat- ing room procedures, both femoral arteries were then exposed and stripped of their adventitia, for a length of 4.5-5 era. Branch arteries over this length were tied with sutures and cut. The tensiometer was attached to each exposed arterial segment and the arterial pre-tension was measured, as described above.

During testing, the arteries were kept viable by repeated irrigation "with 0.9% saline. A complete set of arterial pre- tension measurements was completed in less than 20 rain; less exposure time than for many vascular surgery procedures.

In order to examine the effect of limb orientation and local anasthesia on vessel preteusioning, three distinct experimental procedures were followed. Each artery was first measured for pre-tension with the leg of the rabbit in a relaxed position. The pre-tertsion was then remeasured with the leg in an extended position. Finally, with the leg remaining in the extended position, the local anaesthetic Lidocaine ( t% Xylocaine) was applied by liberally spraying the artery from a syringe, Pre- tension in the anaesthetised artery was then measured.

4 R e s u l t s

Table I Measured pre-tension in 20 rabbit femoral arteries

rabbit number extended relaxed l imb, extended and limb timb, N N limb with

Lidocaine, N

1 right 0.085 0-021 0.078 1 left 0.111 0.069 0.031 2 fight 0-155 0.075 0.113 2 left 0.107 0.070 0.069 3 right 0-t55 0.080 0.072 3 left 0-103 0-077 0-080 4 fight 0.071 0.039 0.064 4 left 0.064 0.098 0.066 5 fight 0.080 0-065 0,062 5 left 0-080 0-074 0.070 6 right 0.083 0.070 0.067 6 left 0.086 0-078 0-077 7 right 0- 112 0-094 0.110 7 left 0.066 0.068 0.044 8 fight 0-154 0.072 0.129 8 left 0.123 0-086 0-123 9 right 0-045 0.036 ** 9 left 0-290 0.095 0.110

10 fight 0.120 ** 0,110 10 left 0.170 0.080 0-130 average: 0.113 0-071 0.084 zk SD 0-038 0-014 0-025

** reliable measurement not possible

When Lidocaine was applied to the extended leg, the arterial pre-tension was measured as 0-084 N 4-0.025 N. The mean ratio of Lidoeaine tension to the tension without Lidocaine is 0.774-0.21. Clearly, the application of local anaesthesia diminishes the arterial pre-tension (p < 0.05),

A limited number of arteries were measured with the leg in the relaxed position with Lidocaine applied. A significant reduction in pre-tension was still observed. Unfortunately, it was difficult to measure the pre-tension reliably in this configuration (due to both the small magnitude of the pretension and the upward bias of the tension measurement caused by buckling of the artery on the right-hand side of the cenWal post in Fig. 2).

In total, the pre-tension in 20 rabbit femoral arteries was measured (Table 1). The mean value of the pre-tension with the rabbit leg extended was 0-113 N, with a standard deviation of 0.038 N. The large standard deviation arises from several factors. The experimental error is estimated to account for about 0.016 N of the deviation. The remainder of the deviation is caused by individual animal variations in pre-tension and arterial side branch location (which affects pre-tension distribution along a vessd). Other factors include variable amounts of vessel spastieity arising from manipulation during surgery, the amounts of anaesthetic applied to the vessel to facilitate exposure of the artery, and the exact amount of leg extension.

The mean pre-tension with the leg in a relaxed position was 0-071 N, with a standard deviation of 0.014 N. The ratio of the pre-tension in a relaxed position relative to the pre-tension in an extended position is 0-71 4-0.29. The arterial pre-tension in a relaxed leg is thus significasatl-y tess (at the 99% confidence level p < 0.01) than the pretension in an extended leg*.

* Two of 19 measurements snow the pre-tension increases when the leg is moved to a relaxed position, One of 19 measurements shows an increase in pre4ension when Lidocaine was applied. These w e r e almost certainly specious measurements caused by inadvertent contact of the central force-measuring post with surrounding tissue,

5 D i s c u s s i o n

The actual pre-tension that exists in an undisturbed artery within the body is extremely difficult to determine. We have developed a device to measure the in vivo pre-tension of an artery as it would be prepared for vascular surgery.

The measured arterial pre-tension was always positive, independent of limb orientation and arterial anaesthesia. Although the artery is known to tmdergo spasm when exposed during surgery (which will lead to increased arterial pre- tension), the existence of signi~cant pre-tension even after topical application of anaesthetic suggests that the measured pre-tension is not solely caused by arterial spasticity. Connective tissues that are separated from the artery before the tensiometer measurements no doubt affect the ~ pre- tension. Nonetheless, our pre-tension" measurements are probably indicative of the level o f pre~tension that exists in the artery before surgery, i.e. we would anticipate arterial pre- tensions in the undisturbed body in the order of 50--I 00 raN. Based on an average rabbit femoral artery perimeter of 4960 t~m and a wall thickness of 42 I~m (HSlANG et al., 1995), these pretensions correspond to average arterial wall axial stresses of 240-480 kPa. It is interesting, and perhaps physiologically salient, that these axial wall stresses are very

828 Medical & Biological Engineering & Comput ing November 1995

similar in magnitude to the circumferential stresses (approxi- mately 300 kPa) induced by the arterial systolic pressure.

Other research groups have also made measurements involving pre-tension. Lee et al. measured pre-tensions in the order of 0-5 N for the carotid artery of a dog (LEE et aL, 1968). Two groups have measured the pre-tension in the canine thoracic aorta. The measurements of Janicki and Patel imply pre-tensions of approximately 0.9 N, whereas Plowman et al. have measured pre-tensions averaging 1.8 N (JANICKI and PATEL, 1968; PLOWMAN et al. 1974). The significantly higher pretensions measxtred in the dog experiments implies an intra- species variation in arterial pre-tension. Not surprisingly, the rabbit has lower arterial pre-tension than the much larger dog.

The influence of shear stress caused by blood flow is relatively small. Giddens et al. have shown that the axial shearing stress at the wall arising from blood flow in mammalian arteries is 1-2 N m -2 (Gn~DENS et al., 1990). The total axial force due to blood flow, acting on the portion of blood vessel between the aorta mid the femoral artery of rabbits, is therefore approximately 4 mN (the average diameter of the vessel is 4 ram, and the distance between the aorta and the femoral artery is 15 cm in this estimate). This force is an order of magnitude less than the pre-tension measured here, which strongly suggests that arteries throughout the vascular system are under tension.

Femoral artery pre-tension has been shown to increase substantially (59%) when the leg is extended. Such an increase in pre-tension is consistent with the fact that the length of the femoral artery increases as the leg is extended, and elongation of any elastic member will cause a consequent tension increase. The significant reduction (26%) in pre-tension upon application of a tropica anaesthesia implies that the biochem- istry of the arterial wall also affects the pre-tension. The anaesthetic appears to relax the tissues of the arterial wall, causing the observed reduction in pretension.

6 Conclusions

A 'blood vessel tensiometer' has been designed and developed to measure arterial pretension in vivo. The device does not require trans~'~tion of the artery and does not appear to cause any additional tissue damage beyond that required to expose the artery for a sttrgieal procedure. Tests suggested that the measured pre-tensions are reliable within a range of + 15%.

The tensiometer was used to measure the pre-tension of both left and fight femoral arteries of ten female New Zealand White rabbits. The average pretension with the leg relaxed was found to be 0.017 N, with the leg extended it was 0.t 13 N, and with the leg extended and a local anaesthetic applied it was 0,048 N. As may be expected, leg extension increases the arterial pre-tension, whereas local anaesthetic

relaxes the arterial wall and reduces pre-tension. The axial stress associated with these pre-tensions is comparable in magnitude to the circumferential stress caused by arterial systolic pressure.

Acknowledgments---The authors would like to thank Michael Boyd and Tess Crespo of the Animal Care Unit at UBC for their invaluable assitanee.

This research was sponsored in part by the Natural Sciences and Engineering Research Council of Canada.

Dr. Hsiang is a BC Health Research Scholar.

References

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BEKGEL, D. H. (1961): 'The static elastic propeties of the arterial walt,' d. PhysioL, 156, pp. 445-457

FIING, Y. C., FRONEK, K., and PATrrUcct, P. (1979): 'Paeudoplasticity of armries and the choice of its mathematical expression,' Am. J. PhysioL, 237, pp. H620-H631

FUNG, Y. C., and LIU, S. Q. (1993): 'Elementary mechanics of the endothelium ofblood vessels,' ASME s Biomech. Eng., 115, pp. 1- 12

GIODENS, D. P., ZARINS, C. K., and GLAGOV, S. (1990): 'Response of arteries to near-wall fluid dynamic behaviour,' AppL Mech. Rex., 43, pp. 598-5102

HSIANG, Y. N., HOUSTON, G. T. M., CRESPO, T., TO, E. E., TODD, M. E. SOBEH, M. S., and BOWER, R. D. (1995): 'Preventing intimal hyperplasia with photodynamic therapy using an intmvascular probe,' Ann. Vase. Surg., 9, pp. 80-86

JANICKI, J. S., and PATEL, D. J. (1968): 'A force gauge for measurement of longitudinal stresses in a blood vessel in situ,' J. Biomech, I, pp. I9-21

K1NLEY, C. E., and MARBLE, A. E. (1980): 'Compliance: a continuing problem with vascular grafls,' J Car~ovasc. Surg., 21, pp. 163-170

KRLqTAL, P., TENCER, A. F., TRUMBLE, T. E., NORTH, E., and PARVlN, D. (1993): 'Method for meazna'ing tension in small ligaments: an application to the ligaments of the wrist carpus,' ASME d. Biomech. Eng., 115, pp. 218-224

LEE, J. S., FRASHER, W. G., and FryiNG, Y. C. (1968): 'Comparison of elasticity of an artery in vivo and in excision,' d Appl. Phys., 25, pp. 799-801

MEASLrg.EMENTS GROUP TECh,'NICAL STAFF (1988): 'Strain gauge based tmnsdoeers.' Measurements Group Inc., Raleigh, North Carolina, USA

PEDLEY, I". J. (1992): 'Longitudinal tension ~ o n in collapsible vessels: a new mechanism for the breakdown of steady flow,' ASME J. Biomech. Eng., 114, pp. 60--67

PLOWMAN, F., YOUNG, J. T., and JANICKI, J. S. (1975): 'An instrument for d ~ c ~ e n t of longitudinal s ~ s and swains ha a blood vessel/n situ," BiorheoL, 12, pp. 21-25

WALDEN, R., I2ITALmr~, G. J., MEGEreMAN, J., and ABBOTT, W. M. (1980): 'Matched elastic properties and successful arterial gras Arch. Surg., 115, pp. 1166-1169

Med'mal & Biological Engineering & Computing November 1995 819