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SHORT REPORTS

Spiral laminar flow

in arteries?

Spiral blood-flow patterns in infrainguinal bloodvessels were observed at angioscopy in 54 patients who underwent peripheral vascular reconstruction; the endoluminal surface had spiral folds in 51 of 75 Spiral flow patterns, congruous with inherent endoluminal anatomical features, might more accurately represent blood-flow in infrainguinal arteries than current models of laminar arteries examined.

flow.

Numerous mathematical and experimental models have been devised in attempts to depict the configuration of flow within blood vessels. The mathematical description of blood-flow in arteries usually begins with a solution to the problem of steady flow of an incompressible newtonian fluid in a uniform rigid pipe, and the classic description is that of laminar flow, which describes the velocity profile of a parabola. But several factors must be accounted for to extrapolate this model to in-vivo conditions: arteries are not rigid tubes but elastic; vessels progressively taper, curve, and branch; blood-flow is pulsatile; and blood is a nonnewtonian fluid. Mathematically, these factors are nonlinear. Moreover, the principal difficulty of hydrodynamics in general is that the convective acceleration term in Euler’s equation of motion is non-linear, and the viscous force term also becomes non-linear with non-newtonian fluids.1 Thus, blood-flow models rely on rigid assumptions that fit our mathematical limitations but do not necessarily describe what actually happens.

Fibre-optic angioscopy is a novel technique which allows examination of endoluminal anatomy in vivo and direct, end-on, three-dimensional assessment2 of blood-flow, with stream patterns measured in a similar fashion to dye flow-patterns in experimental glass models.3 Although the column of fluid in the intubated vessel is static, blood from major collaterals enters this vessel under normal flow conditions and the technique allows for the effects of the endoluminal structural attributes of arterial walls, including elasticity.

Angioscopic examination of blood-flow patterns in arteries during infrainguinal reconstruction indicated that the inner surface of the blood-vessels was often not smooth but organised in a series of spiral folds. Moreover, when blood had been cleared from the vessel lumen, the flow pattern as blood entered the column of clear irrigation fluid was often a spiral, the direction of this spiral flow appeared to be constant, and these spiral flow-patterns were maintained at bifurcations. Review of videotaped records of 54 consecutive

diagnostic angioscopies during infrainguinal bypass grafting showed ribbing and spiral folds in the endoluminal surfaces of 51 of 75 arteries examined (see table); very faint spiral folds were also seen in normal and minimally diseased arteries. The angioscopic observation of spiral flow and the presence of spiral folds on the endoluminal surface could be explained in three ways: spiral flow may represent an artifact

of angioscopy, but this explanation is unlikely because spiral flow has been observed with other investigative techniques.s It may represent a phenomenon that occurs in diseased arteries because of turbulence generated by atherosclerosis. Alternatively, spiral flow may be physiological. Other observations lend support to the concept of spiral bloodas a normal process, at least in parts of the circulation. The heart is twisted on its axis and the aortic arch is tapered,

flow

curved, and twisted.1 Measurement of blood velocities across the ascending aorta with a doppler ultrasound probe in 8 patients during coronary artery bypass surgery showed that blood appeared to "rotate in a clockwise direction",4 "secondary spiral flow patterns" have been observed in the ascending aorta and at bifurcations,s and a rotational nature to blood-flow has also been reported in the descending thoracic aorta.6 Computer simulations of pulsatile flow in curved distensible vessels also indicate that the dominant flow pattern was spiraland "spiral shallow folds" have been described in diseased coronary arteries during 8 percutaneous coronary angioscopy. ANGIOSCOPIC APPEARANCES DURING INFRAINGUINAL BYPASS GRAFTING

We suggest that blood-flow may have a spiral pattern, possibly propagated as a result of the anatomy of the arterial tree, even in the absence of atherosclerosis. A spiral configuration of blood-flow may protect the arterial wall from damage by reduction of laterally directed forces, rather as a bullet from a rifle has directional stability conferred by the spiral configuration within the gun barrel. This forward-directed, rotationally induced stability might also prevent disturbance of normal blood-flow patterns at stenoses. It is also possible that stable spiral flow is more efficient and requires less energy to drive blood through the tapering and branching arterial system. A rifled endoluminal arterial surface, as observed in many of the arteries that we studied by angioscopy, may reflect inherent structural features in the elastic wall of the vessel that induce a spiral torque on each pulse of blood as it passes through the vessel. Although these small folds have not been described in anatomical casts of blood-vessels, or in pathological specimens of diseased arteries, they may be obliterated

during preparation. The concept of spiral blood-flow in peripheral vessels needs further assessment, in both experimental and in three-dimensional computerised models. If confirmed, the existence of spiral rather than laminar blood-flow in peripheral arteries would have striking implications for our understanding of haemodynamics, arterial wall function, the pathogenesis of atherosclerosis and intimal hyperplasia, and the design of prosthetic graft materials. We thank Dr A. Miller and Dr F. W. LoGerfo of Harvard Medical School,

Boston, USA, for their support, encouragement, and advice.

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REFERENCES 1. Fung YC. Biodynamics: circulation. New York:

Springer-Verlag,

1984:

77-165. 2. Miller A, Stonebridge PA, Jepsen SJ, et al. Continued experience with intraoperative angioscopy for monitoring infrainguinal bypass grafting. Surgery 1991; 109: 286-93. 3. LoGerfo FW, Nowak MD, Quist WC. Structural details of boundary layer separation in a model of human carotid bifurcation under steady and pulsatile flow conditions. J Vasc Surg 1985; 2: 263-69. 4. Segadal L, Matre K. Blood velocity distribution in the human ascending aorta. Circulation 1987; 76: 90-100. 5. Karino T, Goldsmith HL, Motomiya M, Mabuchi S, Sohara Y. Flow patterns in vessels of simple and complex geometries. In: Leonard EF, Turitto VT, Vroman L, eds. Blood in contact with natural and artificial surfaces. New York: Academy Press, 1987: 422-41. 6. Frazin L, Lanza G, Mehlman D, et al. Rotational blood flow in the thoracic aorta. Clin Res 1990; 38: 331A. 7. Hung TH. Pulsating spiral blood flow in curved arteries. In: Norman J, ed. Cardiovascular science and technology, basic and applied. Louisville, Kentucky: Oxymoron Press, 1989: 124-26. 8. Uchida Y, Tomaru T, Nakamure F, Furuse A, Fujimori Y, Hasegawa K. Percutaneous coronary angioscopy in patients with ischemic heart disease. Am Heart J 1987; 114: 1216-22.

ADDRESSES

Vascular UK (P. A. Vascular Surgery, Yale

Surgery Unit, Royal Infirmary, Stonebridge, FRCSE) and Division of University School of Medicine, New Haven, Connecticut, USA (C. M. Brophy, MD). Correspondence to Mr P. A. Stonebridge, Vascular Surgery Unit, Royal Infirmary, Edinburgh EH3 9YW, UK.

Edinburgh,

Erythropoietin and spontaneous platelet aggregation in haemodialysis patients

Erythropoietin significantly, reversibly, and reproducibly increased in-vitro whole-blood spontaneous platelet aggregation in 15 patients on haemodialysis. During erythropoietin treatment, spontaneous platelet aggregation was significantly higher in these subjects than in non-uraemic controls; concomitant treatment with 300 mg aspirin platelet hyperaggregability. daily reversed thrombosis may promote by an effect Erythropoietin on

haemodialysis patients with anaemia (haemoglobin below 8-5 g/dl) solely attributable to renal failure were treated with erythropoietin (Boehringer Mannheim, Livingston, UK) at an initial weekly dose of 120 IU/kg. They were randomly assigned 15

platelet function.

Erythropoietin is an effective treatment for anaemia in chronic renal failure; side-effects, particularly hypertension and thrombosis, have generally been attributed to changes in blood viscosity, cardiac output, and peripheral resistance associated with increased haemoglobin concentrations. More direct effects of erythropoietin have also been suggested.2,3 Adhesion, aggregation, and activation of platelets are central to the initiation of thrombus formation. Despite evidence for defective platelet function in uraemia,44 haemodialysis patients have an increased risk of thrombosis in arteriovenous fistulas and their overall cardiovascular mortality is high.5 In vitro, platelets tend to aggregate spontaneously both in whole blood6 and in platelet-rich plasma—a tendency which is increased in patients at risk of thrombosis. We measured in-vitro whole-blood spontaneous platelet aggregation in 15 haemodialysis patients who were treated with erythropoietin, and studied the effects of withdrawal and resumption of erythropoietin and ofcotreatment with aspirin or dipyridamole.

subcutaneous or intravenous treatment. After correction of anaemia a target haemoglobin concentration of 10-12 g/dl was maintained for 8 weeks (first maintenance phase), then treatment was withdrawn. When haemoglobin had fallen to pretreatment values the patients were again treated with erythropoietin by the alternative route (second maintenance phase). Platelet studies were done before treatment and during and between each maintenance

phase. patients on haemodialysis and 4 on continuous ambulatory peritoneal dialysis (CAPD) who were stable on erythropoietin therapy for at least 2 months underwent platelet aggregation studies before, and 4-8 weeks after, the start of treatment with 300 mg enteric-coated aspirin daily. 4 haemodialysis and 2 CAPD patients who had a history of allergy to aspirin or of peptic ulceration were similarly studied before and after the start of treatment with 100 mg dipyridamole daily. 10 haemodialysis patients, who had haemoglobin concentrations above 9-0 g/dl, and 23 healthy volunteers were studied as untreated uraemic and normal controls, and platelet aggregation was also measured in 3 iron-deficient haemodialysis patients (serum ferritin below 100 gg/1) who received 10

iron dextran as

an

alternative treatment.

5 ml venous blood was taken before routine dialysis at 0900-1000 h, and was anticoagulated with 3-8% trisodium citrate (9:1 by volume). Platelets were counted before and after 6 min gentle rotation at 37°C. The fall in platelet count was used to determine the percentage of platelets that spontaneously aggregated.6 Results are expressed as median (range). Wilcoxon’s rank-sum test was used to analyse matched-paired data in erythropoietin-treated patients, and the Mann-Whitney U test to compare patients with untreated haemodialysis and normal controls.

All 15 patients responded to erythropoietin: haemoglobin increased from 6-8 (5-3-8-1) g/dl before treatment to 11-11 (101-128) g/dl in the first maintenance phase, fell to 6-9 (4-8-8-3) g/dl during withdrawal, and rose again to 10-7 (9-6-13-2) g/dl after the second phase of treatment. The 10 haemodialysis controls had similar haemoglobin concentrations to erythropoietin-treated patients during the first and second maintenance phases, but significantly higher concentrations (10-6 [9’1-12’4] g/dl; p 0-05; figure). After erythropoietin, spontaneous platelet aggregation was significantly increased (first maintenance 64 (38-91)%; second maintenance 71 (21-92)%; p < 0-01; figure). This difference was not influenced by the mode of erythropoietin administration. The 10 haemodialysis controls with haemoglobin concentrations above 9 g/dl showed intermediate results, with spontaneous platelet aggregation of 41-5 (36-91) %-less than patients on the first (p 0-003) and second (p 0-013) maintenance phases, but higher than patients during withdrawal of erythropoietin (p 0-013) and in normal controls (p 0-034; figure). The 3 patients treated with iron dextran had greater spontaneous platelet aggregation (41, 18, and 27% to 47, 75, and 36%, respectively) and a small rise in haemoglobin concentration (7-2,9-1, and 8-4 g/dl to9-l,l 1-3, and 9.1g/dl, respectively). Of the 14 patients on erythropoietin who also received 300 mg aspirin daily, 2 were withdrawn because of recurrent =

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Spiral laminar flow in arteries?

Spiral blood-flow patterns in infrainguinal blood-vessels were observed at angioscopy in 54 patients who underwent peripheral vascular reconstruction;...
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