[list]CONSERVATIVE SURGERY IN THE TREATMENT OF THE SUPERFICIAL VENOUS SYSTEM
Paolo Zamboni
Edizioni C.E.L.I.
Gruppo Editoriale Faenza Editrice
CONSERVATIVE SURGERY IN THE TREATMENT OF THE SUPERFICIAL VENOUS SYSTEM
Paolo Zamboni
Co-authors:
Massimo Capelli Phlebology Clinic, Florence
Stefano Ermini Phlebology Clinic, Florence
Maria Grazia Marcellino Graduate in Vascular Surgery, University of Ferrara
Raffaello Molino-Lova Phlebology Clinic, Florence
Co-workers:
Claudia Castaldini Technical Assistant, Institute of General Surgery, University of Ferrara
Anna Paola Murgia Graduate in Emergency Medicine and Surgery, University of Ferrara
Luca Pisano Graduate in Emergency Medicine and Surgery, University of Ferrara
Andrea Stabellini Technical Assistant, Institute of General Surgery, University of Ferrara
Diego Quaglio Graduate in General Surgery, University of Ferrara
Edizioni C.E.L.I.
Gruppo Editoriale Faenza Editrice
Paolo Zamboni, 39, is currently a Research Professor and Assistant Chief of Service of the Institute of General Surgery of the University of Ferrara,
PHOTO under the chairmanship of Professor Liboni MD. He received his training in general and vascular surgery at the Institute of General Surgery of the University of Ferrara under the chairmanship of Professor Donini MD. He was a Fellow in the Department of Surgery of the University of California at San Francisco and director of the vascular laboratory in the Institute of Surgical Pathology of the University of Sassari. He is a co-founder and member of the board of directors of the Italian Association of Phlebology-Lymphology, a member of the American Venous Forum and of the Phlebo-Club. He has authored more than a hundred publications on phlebology topics.
ISBN 88-8138-026-9
Diagnostic and therapeutic advice given in the text reflects the personal opinion of the author.
All rights reserved by the publishers. No part of this book may be translated, reprinted, reproduced in any form by any electronic, mechanical, or other means, including photocopying or micro-reproduction, or recorded for use or dissemination in any information storage or retrieval system without permission in writing from the publishers.
© 1996 by Edizioni C.E.L.I.
Gruppo Editoriale Faenza Editrice S.p.A.
Via Pier De Crescenzi 44, 48018 Faenza (Ra), Italy
Tel.: (0546) 663488 Fax: (0546) 660440
July 1996. Printed in Italy
by Litografia Faenza S.r.l., Faenza (Ra)
TABLE OF CONTENTS
Page
PREFACE (Prof. I. Donini)
FOREWORD (Prof. A. Liboni)
CHAPTER 1. Some Common Assumptions in Phlebology
CHAPTER 2. Aims of Conservative Surgery
Introduction
Compliance marker in varicosity progression
Compliance measurement
Noninvasive measurement of venous compliance
CHAPTER 3. Hemodynamic Principles and Venous Ultrasonography
Physical principles of venous hemodynamics
Functional anatomy of the inferior limb veins
Venous drainage from the lower limb
"Private Circulations"
CHAPTER 4. External Valvuloplasty
Surgical rationale
Patient selection
Anesthesia and preparation of the patient
Manual valvuloplasty
Stapler valvuloplasty
Results
Conclusions
CHAPTER 5. CHIVA: Hemodynamic Correction of Varicose Syndrome
Theoretical basis
Preoperative mapping
Anesthesia and surgery
"CHIVA 2" method
Indications for "CHIVA 2" method
Results from CHIVA method
Complications of CHIVA method
CHAPTER 6. High Ligation of the Saphenofemoral Junction and Adjunctive Peripheral Vein Avulsion
Introduction
Anesthesia and surgery
Adjunctive stab avulsion method
Treatment of recurrences
Emergency high ligation of the saphenofemoral junction for ascending superficial thrombophlebitis
References
PREFACE
When Babcock, Keller, Homans and Myers performed stripping at the beginning of the present century, it was a minimally invasive procedure for the time; they attempted ablation of the main varices using only two incisions.
With this simple procedure they tried to ablate the greater part of the superficial venous system: the greater saphenous vein and its tributaries and communicating veins. This was a step forward, in fact, since at the time extirpation was obtained at the price of devastating surgery that resulted in diminished drainage of the lower limb by interruption of the lymphatic system. Veins were ablated by huge incisions: S-shaped, longitudinal and transverse.
Analysis of stripping results, however, has shown extirpation to be an empty promise. A high percentage of varicosed patients suffered recurrences even after technically faultless procedures. Results analysis indicated how presumptuous it was to claim that surgery – and even less so, sclerotherapy – represented definitive treatment for a chronic progressive disease.
Almost a century later, this book again proposes minimally invasive approaches to surgery of the varices, one of the most common diseases to afflict humanity. We are looking at approaches based on a modern original pathophysiology in which hydraulic physics is applied and confirmed through vascular ultrasound.
The surgical procedures described here show that it is possible, with appropriate follow-up, to perform minimally invasive procedures in an outpatient setting that will both preserve the native veins and generate long-term results not unlike those obtained by stripping; for a successful outcome, however, indications must be appropriate. Such procedures correct the hemodynamic changes caused by varicose disease seeing that surgery cannot modify the factors that promote venous wall injury. What reflux elimination and termination of old "private circulations" (parasitic circuits) do is to slow down the disease, which can then remain compensated and asymptomatic for long periods.
This has become possible for us today, unlike the pioneers of stripping, because we have at our disposal not only our eyes, hands and hemostatic tourniquets but also plethysmography of many kinds, slender flexible angioscopes and, above all, high-frequency, high-resolution ultrasonography. While Doppler ultrasound and color Doppler flow imaging have a signal display that is well codified, standardized and widely used for arterial wall analysis, their use with venous walls is sparse and certainly underutilized in the light of their enormous potential.
Interpretation of venous hemodynamics using ultrasound signals is the major achievement of this book; it demolishes assumptions and principles that were never verified but still became the basis of the pathophysiology and therapy of varices. The originality and scientific integrity of the diagnostic tests for noninvasive measurement of venous compliance and venous pressure that have been designed by Dr. Zamboni during his work with this type of surgery and described for the first time in a book are becoming the key to comprehension of the pathophysiology of refluxing venous systems.
We are now capable of treating patients in an almost nontraumatic manner with an extremely selective surgical procedure that preserves the saphenous trunks by relieving them of hemodynamic overload.
I hope that this book – valuable both for its originality of content and wealth of documentation – will lead to wholehearted approval and widespread use of these surgical techniques that are customized for the treatment of varices of the lower limbs.
This would be a well-earned and the best reward for the skillful efforts lavished by Dr. Zamboni upon the design and application of these diagnostic tests and preparation of this volume.
Prof. Ippolito Donini, Director
Surgical Clinic and Graduate Division
Institute of Vascular Surgery
University of Ferrara
FOREWORD
At the beginning of the Seventies, when DeAnna, the youngest students and I began to perform stripping under the guidance of Professors Donini and Bresadola, we did it with the utmost care and enthusiasm, both because it was the first of our clinical duties and because we did not wish to be ever shamed by recurrences.
We took great care in preparing the saphenofemoral junction, ligating and dividing all the branches; the time element involved in meticulous peripheral phlebectomy could make this procedure last even 3–4 hours.
Our experience over the years as well as confirmatory reports in the literature led us to understand that even well planned and executed procedures were not exempt from recurrences. Radical surgery therefore was a chimera, frequently incapable of halting the course and progression of the disease.
While I was chairman of the Institute of Surgical Pathology of the University of Sassari, one of my colleagues, Dr. Zamboni, along with a group of enthusiastic young disciples attempted to convert the surgical treatment of varicosities to an outpatient procedure. With appropriate diagnostic selection, they used resurrected older methods, such as high ligation of the saphenofemoral junction with multiple stab vein avulsion, as well as imported methods such as CHIVA and original methods such as valvuloplasty of the saphenofemoral junction.
Their dedication, use of technological monitoring of events before and after surgery, exchange of experiences with colleagues that was not just marker pen sketching of veins to be excised but a search for reasons – all of these have led to rewriting of a large part of the pathophysiologic theory on which modern varicose surgery is based.
I confess that initially I demanded strict follow-up, confident as I was of my own prior radical approach. I recognized immediately an improvement in the postoperative condition of these patients, secondary to the minor surgical trauma involved.
The passage of time and results analysis have convinced me that with careful preoperative work-up these techniques offer results that are not unlike, if indeed not superior to, those obtainable through radical procedures.
Screening for possible recurrences is done either in the medical office or outpatient surgical clinic. Physician-patient encounters during varicose therapy are therefore few, painless and very short even in worst-case scenarios. This not insignificant benefit derives from the orderly and predictable pattern of recurrences following surgery performed for conservative and hemodynamic reasons and on the basis of rigid preoperative evaluation. This contrasts strongly with the mostly chaotic pattern of recurrences after surgical ablation.
In this way we manage to control the disease and maintain efficiency in our best vascular prosthesis. This experience has been a step forward for me since I have always pursued minimal invasiveness in surgical methods.
Prof. Alberto Liboni, Chairman
Institute of General Surgery
University of Ferrara
CHAPTER 1
SOME COMMON ASSUMPTIONS IN PHLEBOLOGY
P. Zamboni
We believe it may be useful as an introduction to the reading of this book to engage in a discussion of some key issues that will help the reader, along with the literature resources, to understand the motivation that drove us to change our surgical behavior in the treatment of varices of the lower limbs.
The discussion is introduced by questions that serve to focus attention on some positions that have managed to get beyond debate and become accepted assumptions in venous surgery. We maintain, however, that like any concepts that fail to keep pace with diagnostic and therapeutic progress, these may have become so platitudinous as to hinder progress in the field.
DOES STRIPPING GUARANTEE A HIGHER SUCCESS RATE?
Despite the large number of procedures performed on the superficial venous system, the relevant literature is sparse and there are few controlled trials comparing conservative surgery to stripping. The unwary researcher will indeed find that most studies tend to show a lower level of recurrences during follow-up whenever the surgery involves ablation of the saphenous trunk.117, 135, 136, 150, 152, 170
But it is equally true that other trials show the exact opposite. Three of these studies in particular, which are both authoritative and extensive, indicate that the two procedures (high ligation of the saphenofemoral junction* with peripheral phlebectomy and the stripping procedure) give similar results, on condition that the prior procedure be preceded by careful accurate identification of reflux points.80, 81, 106, 107, 201
[*Called "crossectomy" by non-English authors, based on the French word ‘crosse’ meaning the saphenofemoral junction – Translator].
Hammarstern (using preoperative venography) and Dormandy and Fligelstone (using ultrasound) have in fact demonstrated that a well-executed high ligation of the saphenofemoral junction followed by selective radical ligation of all the incompetent perforating veins does not differ significantly from stripping in terms of long-term results. If we take into account that most recurrences within either procedure group always involve the saphenofemoral junction, it is inconceivable that stripping could produce fewer long-term recurrences at the saphenofemoral junction than a carefully performed high ligation. The only criticism one can make against Hammarstern’s work is that he goes too far in insisting upon preoperative venography as a routine requirement for all varicosed patients undergoing surgery.
In addition, Cappelli and co-workers45 have published a comparison between their results from treatment of patients with the CHIVA** method and results reported in the literature on patient treatment using stripping; follow-up was similar: 3 years. Allowing for the limitations implicit in their metanalysis, the data they present clearly favor the CHIVA approach (see Chapter 5). In any case, it is indisputable that modern ultrasound permits optimal preoperative mapping, a precondition for an equally effective procedure.
[**CHIVA: a surgical approach developed in France, meaning ‘ambulatory conservative hemodynamic surgery for the treatment of venous insufficiency’ – Translator]
Another argument made against conservative surgery is that if the saphenous trunk is left intact, it will continue to "reflux."147, 170 These authors are confusing retrograde flow related to emptying of the blood contained in the valveless saphenous that is coming solely from the skin and subcutaneous tissue (or ‘outflow’; see below) with retrograde flow resulting from regurgitation of blood that is coming also from the deep circulation (or ‘reflux’; see below). Differentiation is possible from a diagnostic viewpoint only by Doppler detection of the actual presence of a reflux point from the deep circulation; this is represented in most cases by a positive result on the Valsalva maneuver. In Figure 1 we see how the Doppler signal from a reflux – in the case of a typical ostial incompetence – is characterized by a biphasic waveform: the first wave, activated in the standing position by squeezing the calf muscle pump, illustrates the forward drainage of the saphenous system during muscular systole; the second wave illustrates retrograde flow inside the saphenous trunk in muscular diastole.
Figure 1
[Callouts]
Systole Diastole
Emptying Reflux
[Caption]
Figure 1, 1a. Pulsed-wave Doppler scan of a saphenous reflux and its conversion (1a) to a retrograde flow after interruption of the saphenofemoral junction.
During this phase a more or less conspicuous volume of blood flows within the saphenous trunk to reenter the deep circulation via the perforators, supported in its course by decreased pressure in the deep circulation during muscular diastole.
Retrograde flow is caused by interruption of a vein, whether by surgery or external compression. It is characterized by a monophasic reverse flow waveform on Doppler. If the saphenous is ligated at the saphenofemoral junction, it cannot empty in a forward direction – it lacks an anterograde component. It then reverses its direction of flow and proceeds to empty toward a perforating vein that reenters in the direction of the propulsive or deep system. Should this drainage outlet be cut off also, the likely result for the saphenous would be a thrombosis.
In addition to the qualitative difference there exists also a quantitative difference in the volume of blood transferred during the reflux/outflow processes. This is easily demonstrated by measuring ambulatory venous pressure, refilling time on plethysmography and other standard tests of venous volume in the limb before and after interruption of the saphenofemoral junction.15, 24, 50, 69, 173, 226
IS IT HEMODYNAMICALLY BENEFICIAL TO SAVE THE SAPHENOUS?
An important point of knowledge often passed over is that in the case of a patent saphenous trunk, the incompetent perforators left intact do not significantly increase ambulatory venous pressure (AVP) whenever saphenous flow is interrupted by finger pressure, application of a tourniquet or high ligation of the saphenofemoral junction.9, 11, 22, 24, 180
Elimination of saphenofemoral reflux while maintaining a patent saphenous trunk is basically sufficient to lower the AVP significantly, even if the perforators are incompetent.
The fact that elevated pressures decrease almost to normal levels during walking whenever long refluxes are eliminated is proof that incompetent perforators are able to transport saphenous blood back into the deep circulation during walking because of the pressure gradient.
This means that we should regard these vessels not only as reflux points but also as reentry points. These concepts have been known for more than a quarter of a century through the hypotheses of Bassi and the pathophysiologic research of Hojersgard, Sturup and Bjordal. Bjordal in fact had already established the pathophysiologic basis for the CHIVA method by simultaneously recording venous pressure and the direction and quantity of flow with use of a needle transducer and electromagnetic flowmeter respectively.22–24
We should not, therefore, visualize the venous structure of the limb as segregated compartments, as the study of surgical anatomy has trained us to do, but as three hydraulic systems engaged in interactive balancing: the superficial, deep and perforator systems.
Every time that reflux appears, the quantity of blood that descends along the limb reaches the deep venous system through the perforator veins, especially under conditions of favorable pressure gradients such as during walking or exercise. For every reflux point there are basically one or more underlying reentry points. Ablation of the saphenous trunk, regardless of the degree of clinical or hemodynamic seriousness of the varicosity syndrome, is a rejection of the concept of the venous drainage system as a single system in physical and functional equilibrium. In fact, it has often been found that the appearance of an incompetent perforator after surgery or its incomplete treatment during the previous surgery produce a hemodynamic compensation that can be objectively substantiated through the increase in AVP.
This behavioral difference between a perforator inserted into a saphenous system that is no longer refluxing and a perforator that has been avulsed is the key to understanding the hemodynamic difference between a limb with its saphenous removed and one that has its saphenous saved, patent and free of a long reflux.
Patients that have post-stripping recurrences basically present two classes of recurrence, based on Doppler ultrasound examination:
a) varicose recurrences associated with reflux from the deep vein circulation;
b) varicose recurrences not associated with reflux from the deep vein circulation.
The first class results partly from surgical mistakes in the preparation of the saphenofemoral junction and partly from still unknown factors.
The second class is composed in fact of "outflow varices." Normal outflow from the superficial network to the deep network begins between the superficial venous plexi and the saphenous collaterals, continues from there to the saphenous trunks and lastly reenters the deep veins through the saphenous perforators and the saphenofemoral junction.
The saphenous trunks therefore are true receiving and discharge reservoirs for the blood contained in the superficial network that flows to the deep network. In the absence of saphenous trunks the collaterals are obliged to act as saphenous substitutes, but since for anatomical reasons the collaterals are deprived of capacitance structures, it is obvious that they will tend to dilate whenever subjected to loading as a result of their vicarious role-playing.
WHAT IS MEANT BY COMPENSATED VARICOSE SYNDROME?
All of us in our clinical practice encounter patients with primary varices, often of voluminous size, but with little or no symptoms, whether subjective or objective. They belong therefore to classes 0–II of the newly accepted international classification of chronic venous insufficiency (CVI).115, 161, 204 Other patients who have had varices for the same length of time that are far less prominent have been classified as CVI classes III–VI. Patients with severe lipodermatosclerotic edema or ulcers are found whose venous refilling time (measured by plethysmography), ambulatory venous pressure (measured by needle transducer ) or degree of saphenofemoral reflux (measured by Doppler) are identical to those in patients with slight edema that resolves itself during rest or light exercise. Therefore, hemodynamic severity of reflux does not always correlate with clinical severity of the disease.
Patients in so-called hemodynamic compensation (with no edema or slight edema) owe their favorable situation to the following factors:
Efficacy of the muscular pump and reentry points through the perforators – marvelous pathophysiologic players commissioned by nature to defend it against varicosity and enable the limb to drain.
This mechanism deteriorates whenever the reflux-reentry interplay fails and stagnating blood volume becomes greater than reentry volume. Vessels become incapable of emptying whenever overload occurs; more precisely, for reasons of physics that we will explain later, the collaterals do not succeed in discharging the normal outflow from the venous territory into the saphenous. Consequently, stasis and edema increase and the resulting cascade of events involving the microcirculation and skin tissues significantly increase the degree of CVI.
B) Duration of the disease: the longer the wall and skin tissues are exposed to the cascade of stasis events, the more overt the signs of disease progression become.
C) Co-involvement of the deep venous system in "private circulations." As indicated above, a reflux-shunt-reentry system identifies a so-called "private circulation" and the phenomena of stasis. Sometimes hemodynamic compensation is such that it overloads the deep system also. In such cases, the result is a functional dilation of the wall, with related valvular insufficiency, and coexisting insufficiency of the deep venous circulation.
John Bergan’s observation that in these cases elimination of the saphenofemoral reflux will restore competency of the deep circulation may be an indirect proof of this pathogenic hypothesis. On the other hand, several epidemiological studies demonstrate how in the more advanced stages of CVI there exists a pattern of concomitant primary insufficiency of both superficial and deep circulations, which becomes the starting point for a unique, chronic and progressive disease that we can call primary venous insufficiency.103, 108, 200
However, patterns of primary deep valvular dilation ab initio are in our experience extremely rare.
DOES A VARICOSED INTERNAL SAPHENOUS EXIST?
Hearing or seeing descriptions of a varicosed internal saphenous often brings one into direct confrontation with a serious error perpetuated for years by classic physical symptomatology. In clinical practice one often observes a large varicosed branch that zigzags downward on the medial surface of the thigh, somewhat anteriorly to the internal saphenous; it is engorged from a saphenofemoral reflux, as may be established by performing a Rima-Trendelenburg test. But 14 years of performing vascular ultrasound has taught us that in the field of varicosities what one sees is not always what it is. This branch in fact is usually described as the internal saphenous. Our practice, however, of subjecting all varicose conditions to duplex scanning has demonstrated to us that it is an anterior branch, a tributary of the internal saphenous at the saphenofemoral junction (Fig. 2).40
Duplex evaluation of the internal saphenous shows how it lies deeply embedded in the superficial fascia at the level of the thigh; the fascia appears to be doubled around the saphenous as if to reinforce its wall. This feature makes the saphenous unmistakable on high-resolution transverse access sonograms; it creates the image of a "saphenous eye." 40 The saphenous is therefore a vessel that nature has designed and executed anatomically in a highly distinctive manner, permitting it to support volume and pressure overloads for a longer time without becoming varicosed.
Figure 2 illustrates how without duplex scanning a patient might have been subjected to stripping of a healthy vessel while an incompetent varicosed vessel would have simply been ligated during preparation of the saphenofemoral junction, with the surgeon all the while imagining it had been ablated by stripping.
Unfortunately, preoperative duplex scanning is not widely used. A recent survey of developments in England provides data that make one shiver; we believe they are not unlike what we would find in Italy in a similar study. During preoperative work-up, 68% of vascular surgeons use at least acoustic Doppler, while only 23% of general surgeons do so; however, only 33% of vascular surgeons and 15% of others use duplex scanning. In such conditions, it is obvious that stripping becomes a necessity, as it was at the beginning of the century (202).
Figure 2.
[Callouts]
[Top] Collateral Branch (or R3)
Saphenous (or R2)
Superficial Fascia Duplication
[Bottom] Subpapillary Hypoderm / Collateral Branch (or R3) / Subpapillary Hypoderm
Reticular Hypoderm / Saphenous (or R2) / Reticular Hypoderm
[Caption] Figure 2. At left, a characteristic feature: the "saphenous eye" which is the marker for this vessel on noninvasive transverse access sonography. This feature enables the saphenous to be differentiated (right graphic) from a dilated collateral vein (R3).
Ultrasonographic evaluation of the limb, however, will also improve the surgical quality stripping. Just think of how frequently situations similar to that in Figure 2 occur: the stripper sticks just for a moment and then is inevitably threaded into the straighter vessel instead of the tortuous dilated one. Blind stripping inevitably leads to ablation of the saphenous and preservation of the damaged diseased collateral!176
DOES VEIN DISEASE INCLUDE VENOUS HYPERTENSION?
This question presents an obvious paradox, but it is not pointless to ask it because of all one hears at phlebology conferences.
The varicosed patient presents with venous hypertension in the superficial circulation only during walking, in the sense that venous pressure decreases less than it would in a healthy subject (Fig. 3).
Since every organ and system contains a functional reserve, the smaller decrease in pressure experienced by a varicosed patient during walking largely represents the measurable decrease in its own functional reserve.
In the quiet standing position, however, a healthy subject of the same height as the most varicosed patient presents identical venous pressure values in the saphenous system or any other vein, provided that the measurements (with needle transducer and not Doppler of course!) are made at the same distance from the right atrium in both subjects.112, 160
Venous pressure during standing is identical in healthy and varicosed subjects; it is equivalent to hydrostatic pressure. This means that in a setting of prolonged hydrostasis, the valves of the healthy subject do not totally segregate the column to reduce venous pressure; venous pressure is equivalent to a column of blood will be formed extending from the right side of the heart to the feet. The taller the person, the higher the venous pressure at the ankle during standing; of itself, this is not a risk factor. Likewise, ligating and dividing a vein is not capable of reducing hydrostatic pressure in a more distal segment during quiet standing.
Preservation of valvular function helps to prevent reflux and hemodynamic overload during walking, which is the major factor in transferring blood, along with changes in posture and respiration.
Every therapeutic action, therefore, ought to be oriented toward reducing venous pressure during walking to a significant and lasting extent or to modify the pressure-related indices provided by noninvasive plethysmography. (Fig. 3).
Figure 3. Reduction of venous pressure (P) and lengthening of refilling time (RT) in saphenous insufficiency with tourniquet application during walking (Exercise 2) compared to values obtained without tourniquet application (Exercise 1). Elimination of saphenofemoral reflux improves the venous system functional reserve.
CHAPTER 2
AIMS OF CONSERVATIVE SURGERY
Paolo Zamboni
Introduction
Conservative surgery of the superficial venous system has basically four aims:
1. Performance of effective treatment of the varicosed saphenous by constructing the most stable emptying system possible for the superficial blood.
This treatment plan helps to blunt progress of the varicose disease by reducing the hemodynamic overload that accelerates development of chronic venous insufficiency (CVI).
2. Performance of the treatment in an office or day-surgery setting with a view to cost containment and reduction of the waiting period, since the disease has high social impact.
3. Performance of corrective surgery, in cases of recurrence, with equally nontraumatic procedures on an outpatient basis; this is possible because of the logical and orderly manner of recurrence, which contrasts with the chaotic recurrences associated with ablative surgery.
4. Preservation of our best vascular prosthesis in good working order.
All conservative therapy basically consists in the elimination of the negative effects of reflux from the deep circulation to the superficial; both symptomatic and esthetic dimensions are involved.
Successful therapy will bring about a reduction in venous pressure during walking and/or prolongation of venous refilling time after exercise; measurement of the latter is performed noninvasively by photoplethysmography or light reflection rheography, or also by improvement on air plethysmographic indices: venous filling index, systolic ejection fraction, residual volume, etc.15, 25, 49, 50, 132, 173
Vein diameters should reduce over time, provided that the system is made anatomically and functionally capable of draining the blood to the propulsive system. A competent deep venous system and an efficient muscular pump that stimulate aspiration of blood from the superficial circulation should maintain disease compensation for a prolonged period.
But our own experience as well as reports in the international literature indicate that not all that the surgeon hopes for will in fact occur. A number of patients who undergo conservative therapy will in fact develop postoperative thrombosis recurrences in the short-term.
Our practice of mapping our cases has helped us learn that the most positive and stable results are obtained when the surgeon does not restrict the procedure to elimination of refluxes but also engages in construction of drainage systems (see Chapters 4 and 5). It is obvious that the therapy must be individualized and adapted to each hemodynamic situation. The success of the procedure will depend on the ability of the surgeon to evaluate these choices and carry them out.
A physical indicator that will enhance understanding of these and other aspects of the pathophysiology of incompetent saphenous systems and related corrective procedures is venous compliance.
Venous compliance is the property of the vessel to adapt its volume to differences in pressure loading.1, 5-7, 59, 63-65,119, 138 Compliance is a characteristic of every hollow system and in practice correlates volumetric variation in contents with variation of pressure inside the container. When we apply this concept to a venous compartment or system, it is evident that if the system possesses high compliance, it can accept a large volume of blood with only slight increase in pressure; on the contrary, if system compliance is low, even a slight increase in blood volume within the system induces a sizable increase in pressure.
The compliance of a hollow system such as the venous system is determined by three types of factor:
a) Mechanical Characteristics of the Constituent Material of the Hollow System.
When this concept in physics is converted to phlebological terms, we find that the mechanical characteristics of the vein in question depend on the amount of elastic and especially smooth muscle fiber present in the vessel wall.
The more changes a venous wall presents secondary to phlebosclerosis, the more the excess rigid components will contribute to reducing compliance.
b) Geometric Characteristics of the System.
In a hollow tubular system such as the saphenous, compliance depends on the length of the system and to a lesser extent on the diameter. A saphenous with primary varicosity may be evaluated in terms of the length and diameter of the refluxing segment.
c) Degree of Refill of the System.
The degree of refill of a hemodynamic system such as the saphenous is determined by the ratio between the input and output volumes. If a saphenous system is refluxing, the input volume is equal to the normal volume of superficial emptying collected into the saphenous, plus the refluxing amount. The output volume, however, is equal to the sum of the volume of blood emptying in the anterograde direction in systole and the volume that reenters the deep circulation in the retrograde direction via the perforators in diastole.
COMPLIANCE: A MARKER OF PROGRESSION OF VARICOSE DISEASE
With the single indicator of compliance, we are able in practice to express many parameters tied to the functionality of the saphenous system and the superficial venous system. We are thereby expressing the mechanical characteristics of the vein wall and, above all, the balance between inputs and outputs of the system, which ultimately describe the degree of circulatory efficiency in the superficial system.
In the more advanced stages of primary varicose disease, the superficial blood is no longer sufficiently drained because of the discrepancy between reflux volume and drainage volume; the walls also present a higher degree of phlebosclerosis. Therefore, lower compliance values are matched by higher degrees of chronic venous insufficiency.215-217, 222
This also means that if our surgical interventions – with stripping, high ligation of the saphenofemoral junction and phlebectomy without hemodynamic analysis of the evacuation pathways, CHIVA with inappropriate reentry’s, etc.– do not maintain a well-drained superficial venous system, then the veins will lose their ability to perform because of drainage difficulties (even if they retain moderate residual elastomechanical properties) and ineffective therapy will result.
Even a slight increase in volume of blood within a poorly draining system is enough to induce a significant increase in pressure and consequently a decline in compliance. These nondraining systems seek an outlet, at least through the collateral circulation (recurrence due to the "ligature bypass" or reconnection phenomenon) or perforators are opened to permit the blood trapped at the surface to drain to the deep circulation during walking.
This is the reason why conservative surgery, although it eliminates reflux and lowers ambulatory venous pressure, can be completely successful only if it does not compromise system emptying.
MEASURING COMPLIANCE
It is obvious how important it is pathophysiologically to have a method for clinical measurement of saphenous compliance available.
In vascular surgery, compliance is classically expressed by the Baird formula5-7 as the ratio between pressure and diameter:
Compliance = 2(Di-D0) / D0(Pi-P0) x 100
It is measured in percentages of variation of the diameter of the vessel / mmHg x 10-2, indicating the difference in diameter variation per unit of pressure variation.
Several methods have been proposed for measuring venous compliance.
One uses venous wall elliptical tissue specimens inserted into a pressure chamber.5 This method obviously requires a venous biopsy and it has been criticized also because the forces acting upon the elliptical tissue are different from those acting in nature upon a cylindrical section.
In 1992 Davies proposed two noninvasive methods for clinical calculation of venous compliance.63-65 These methods were able to demonstrate that low compliance levels correlate with histological abnormalities of a venous wall biopsy when the saphenous was excised for use as a peripheral arterial bypass.
The author, however, does admit that this measure of compliance is an indicator of a physical value rather than an absolute measurement. In fact, the pressure component required for calculating the compliance was obtained by Davies through Doppler measurement of venous pressure.
The latter method has not been validated by comparison with the gold standard, represented by measurement with an intravenous needle transducer, and none of Davies’ data correlates his results with intravenous pressure, not even with measures of compliance obtained in vitro.
Doppler measurements of venous pressure, in our experience, have always shown notable variation from measures obtained by needle transducer. For that reason we initiated a research program to identify a method of measurement of venous compliance that would correlate with measurements obtained in vitro and would be noninvasive, simple, reproducible and repeatable.215-217, 222, 225
The test (as indicated below) was constructed in such a way that very uniform test conditions would be obtained. Calculations were in fact made on refluxing saphenous veins at very similar distances from the saphenofemoral junction and with constant postural changes so as to obtain compliance measurements at different levels of saphenous system filling.
We measured compliance on a group of patients representing all classes of primary varicosities, using a fully noninvasive method that was checked and validated by correlation with a semi-invasive method and one performed in vitro. Calculation of compliance was performed on a straight uniform segment of saphenous vein, selected between the lower third of the thigh and the upper third below the knee; this segment was involved in the long saphenofemoral reflux and located above the first reentry point. We assessed compliance in both hydrostatic and dynamic conditions.
Compliance of the superficial venous compartment using a semi-invasive method
Since, in Baird’s formula, diameter and pressure are the only two variables to be determined, we calculated the first with duplex scanning and the second with a needle transducer inserted into the saphenous at the same point where the diameter was measured.
While no validated method for measuring compliance exists, both of the methods chosen to calculate the variables that constitute compliance are in fact universally accepted.69, 112, 116, 132, 153, 160,180-182
Figure 4. A semi-invasive test for measuring compliance in hydrostatic conditions.
For a base point or zero point (D0-P0) from which to calculate the successive changes in pressure and diameter we chose the supine position for the patient with the limb elevated to 30∫, since this induces the lowest degree of refilling of the system.
By having the patient change position, a range of measurements of diameter and pressure was obtained and from these the different measurements of compliance were created using the given formula (Fig. 4).
Pressure (P1) and diameter (D1) were first calculated in the supine position without elevation of the limb. Using the given formula, the first compliance value (C1) was obtained.
Then, with the patient sitting, P2 and D2 were determined, giving C2.
The test continues by having the patient stand up and thereby obtaining P3, D3 and C3 in conditions of quiet standing by the patient.
When a prolonged Valsalva maneuver is performed on a patient in the standing position, another two pressure/diameter pairs (P4-D4) and a fourth compliance value (C4) are obtained.
We have emphasized that since we are dealing with a hemodynamic system, it is necessary also to assess the capacity of the saphenous compartment to empty itself. If the superficial system is decompensated on account of the inefficiency of the muscular pump and the reentry points through the perforators, the volume of blood trapped in the saphenous will automatically reduce system compliance.
Just by adding two more detection procedures to the test described above, we can assess compliance in conditions of blood in motion. Detection is performed at the same point on the refluxing segment above the first reentry.
To obtain the first dynamic diameter/pressure pair (D5d-P5d) we can assess the variations in ambulatory diameter and pressure of the refluxing saphenous system simply by measuring values after exercise without tourniquet application.
A needle transducer will give us a measure of ambulatory pressure (saphenous AVP) in the refluxing saphenous system and vascular ultrasonography will give the related reduction in diameter.
The second pair (D6d-P6d) of dynamic compliance measures is obtained after exercise without a reflux component and this represents the point of arrival of our test.
For test purposes it is sufficient to interrupt the saphenofemoral reflux with a tourniquet, cuff or, simply and even better, with a finger; then have the patient do ten tiptoe exercises and measure the diameter and pressure (Fig. 7, 7a).
Using the values obtained from these experiments we have developed some Compliance/Pressure curves that in general are sufficiently typical of each class of CVI secondary to saphenous incompetence; in practice they express the overall emptying and mechanical properties of the system.
The graph in Figure 5 shows the different responses of the saphenous vessel (depending on the severity of the disease) to different levels of mechanical performance of its wall.
By increasing or reducing pressure one can easily see the compliant behavior of the saphenous veins in CVI classes I-II, as indicated by the hyperbolic curve, which contrasts with the more rigid behavior of veins in classes II-IV or V-VI.115, 161
In classes V-VI the increased rigidity of the saphenous wall is very obvious at every pressure level. One will also note that compliance declines progressively with refilling of the saphenous system and the increase in pressure.
Note also that at pressure loads higher than 120–130 mmHg the curves overlap. This occurs because the muscular elastic components of the vessel walls have reached their maximum extensibility. Beyond that pressure level or filling volume, the curves become inelastic, indicating the nonextensibility of the vascular wall.
The diameter/pressure graph from the same patient group indicates that saphenous veins with greater distensibility exist and these most often are found at the early stages of CVI (Fig. 5a).
The graph very clearly shows a wider range of serial diameters sequentially measured in these saphenous veins, in response to the different refill patterns of the saphenous system, than is found in the less compliant and distensible compartments recorded at the other stages.
The inelasticity of the curve is linked not only to the parietal phlebosclerosis factor, but also and primarily to the excessive filling of the system.
To confirm the importance of drainage capacity on a group of saphenous veins with low compliance values and healed or active venous ulcers, we performed an elegant experiment, using a needle transducer inserted into the saphenous trunk refluxing at the lower third of the thigh. After we had the patient perform 10 tiptoe exercises, we recorded no significant reduction in pressure in the saphenous (Fig. 12 – error, possibly Fig. 4 – Tr.), which evidently goes to show that a refluxing saphenous system has drainage insufficiency
Figure 5. Compliance/Pressure graphs representing the mechanical properties of the vascular wall. As the clinical stage of disease advances, increasing inelasticity is apparent in the curves, indicating loss of compliance in the saphenous system. It should also be noted that when the system is full, regardless of the stage of disease, the curves are flat, which indicates saphenous inelasticity under conditions of volume loading.
Figure 5a. The diameter/pressure curves also demonstrate how distensibility is lost with progression of the disease.
Figure 6.
[Callouts] Diameter (mm)
Noninvasive AVP in a refluxing saphenous
Noninvasive AVP with occlusion of the saphenofemoral junction
Pressure (mmHg)
[Caption]
Figure 6. A method for noninvasive extrapolation of saphenous ambulatory pressure (AVP) from a diameter/pressure line when the saphenous is refluxing and the saphenofemoral junction is occluded. It is sufficient to identify the location P on the line that corresponds to the diameters shown on ultrasonography.
The inflow volume (reflux plus superficial drainage) in such cases is not being discharged through the outlets (the pump and reentry system). This effect correlates then with low compliance values – registering between 0.5 and 1.5%!
It is evident therefore that stasis and the more severe clinical classes of CVI in primary varicose disease are related to problems in saphenous system drainage, and since these problems are expressed in low compliance values, they are detectable by our method.
Figure 7, 7a. Compliance in the dynamic phase: diameter variation in the saphenous system during maximum filling (with patient in the standing position) and after exercise using a tourniquet.
Figure 8. Noninvasive test to measure compliance in conditions of hydrostasis.
In vitro Measurement
To validate our clinical methods of measuring compliance, we surgically isolated the saphenous segments from which we made our calculations, exposing them carefully. The vessels were placed on a caliper to measure diameter variation and perfused with saline solution at 37∫ by means of a transducer catheter, in order to reproduce internally the pressures that had been obtained clinically (Fig. 9).
Obviously, we did not obtain compliance values that were numerically identical because of the lack of in vitro tests of the perivascular tissues and of neuroendocrine analysis of the vascular tone.76, 158 However, this investigation demonstrated a very significant correlation between the three methods used, which validates our noninvasive original method.
Figure 9. In vitro measurement of compliance on excised saphenous segments.
NONINVASIVE MEASUREMENT OF VENOUS COMPLIANCE
Our measurement of venous compliance described above, despite its obvious pathophysiologic interest, contains the obvious limitation of being a partially invasive method and therefore is of debatable value for large-scale application.
We therefore devised and applied a method that permits rapid and fully noninvasive detection of saphenous compliance (Fig.
.
To measure the diameter we still used duplex scanning, and to measure pressure we replaced intravenous measurement with noninvasive measurement of hydrostatic pressure, using the two positions in which this is possible – sitting down and standing (P1 and P2). D1 and D2 are the measured diameters of the saphenous on duplex scanning, corresponding to the sitting and standing positions of the patient respectively.
In this case also we chose the supine position with limb elevation of 30∫ as zero point (P0 D0). from which to calculate the series of pressure and diameter changes.
For P0 (which corresponds to the saphenous pressure in a supine patient with limb elevation of 30∫) we assumed a constant value of 7 mmHg; this was the mean value obtained from previous tests performed in our laboratory on patients representing all classes of CVI. D0 is the corresponding diameter determined by ultrasonography. The semi-invasive and noninvasive measurements of wall compliance proved to be practically equivalent (215-217, 222).
The problem remains on how to calculate venous pressure noninvasively during the dynamic phase of the test (saphenous AVP), corresponding to P5d and P6d of the semi-invasive test.
We calculated it on the basis of the diameter/pressure curve shown above in Fig. 5a. This curve is also available noninvasively and is equivalent to a line (Fig. 6). Every saphenous diameter measured by duplex, including those measured after exercise, with and without use of a tourniquet, corresponds to a well-defined point of pressure on the line of the curve. These pressures, extrapolated noninvasively as shown in Fig. 6, did not prove to be significantly different from those obtained invasively using a needle transducer.
When pressures and diameters are known and Baird’s formula is applied, two further compliance values are noninvasively deduced and these permit us to construct a hemodynamic measurement curve for the saphenous system.
If readers are not happy with numbers and graphs, they should not be frightened off by these calculations: we have already created and are in the process of testing software that will permit a sonograph user to calculate compliance values and construct a curve quickly, easily and in a noninvasive manner.
Figure 10. The parallel paths of compliance/pressure curves calculated in vivo and in vitro are proof of the reliability of the measurements performed. The more compliant behavior of CVI class II vessels in comparison with class V is also evident. In this particular case, the flat curve was obtained in a saphenous recanalized after thrombophlebitis; it demonstrates the impossibility of measuring system compliance through this window and in these wall conditions.
Noninvasive Measurement of Compliance in practice as a Single Indicator
With the patient in the quiet standing position, the first act in performing an initial duplex transverse access scan along the full length of the saphenous should be to mark it with a skin marker at a point involved in the saphenofemoral reflux.
It is a good idea, when one wants to obtain comparable results, to measure compliance at a fixed distance from the right atrium, for example 70 cm, which will correspond during quiet standing to a hydrostatic pressure of 54 mmHg.
Using a tape measure, the distance is measured from the right atrium (projecting at the 3rd. intercostal space of the parasternum) to the selected saphenous measurement point on the limb which is then marked (31).
For the zero point one may select either the position used in the experiment, with a 30∫ elevation, or the supine position, which has the advantage of enabling easier and more rapid ultrasonography of the diameter, although it reduces the range of measured pressures and thereby the sensitivity of the method. Diameters are measured both in the position preselected for zero point and in the standing position (D0 and D1). Recalling the formula:
Compliance (% / mmHg x 10-2) = 2(D1-D0) / D0(P1-P0) x 100
P0 is equivalent to 7 mmHg if we chose the -30∫ position as zero point, or 16 mmHg if we took the measurement at the supine position.
D0 is equivalent to the saphenous diameter in the position preselected for zero point.
P1 is equivalent to 54 mmHg.
D1 is the saphenous diameter at the selected point with the patient standing.
Insert the values into the formula and you will easily obtain the compliance values. Try it out – it is not difficult!
In this part of the test (exclusively hydrostatic) we are dealing primarily with the first of the factors on which compliance depends, as we have seen; this is the elasticity pattern of the wall, which itself may be of particular interest to surgeons investigating the properties of the wall in order to assess the mechanical efficiency of the saphenous as a vascular prosthesis. As we know, research on the use of low-compliance veins as arterial prostheses has shown that the latter present significant pathological features, not least a replacement of endothelial elements with nonspecific cells. Indeed, low-compliance saphenous veins used for arterial reconstruction have a worse outcome, with a high percentage of stenoses or occlusion of the bypass itself1, 5-7, 64-65, 157, 228
This part of the test therefore is critical for the phlebologist who must trace a diameter/pressure line in cartesian fashion. It is clear that the more points you have on the diameter/pressure line, the more reliable will be your noninvasive extrapolations of post-exercise pressures; from this perspective, it becomes useful to add measurements of P and D with the patient both in a -30∫ position and a sitting position, as shown in the previous section.
Figure 11. Use of a needle transducer in the saphenous does not demonstrate significant pressure reduction during exercise in patients within CVI classes V and VI. This result is matched by low compliance values and healed or active ulceration. When the input volume is reduced with a tourniquet, compliance increases and pressure decreases.
In any case, we obtain noninvasively two new pressures from the line (see Fig. 6) by sonographic measurement of venous diameter after exercise, with and without saphenous occlusion.
Returning to our formula, if we keep the P0-D0 value, calculated in the supine or -30∫ position, and if we substitute the two new pairs of dynamic pressure and diameter, we will obtain two new compliance values C1d and C2d, which we may call dynamic or hemodynamic compliance.
C1d expresses in a number the real capacity of a refluxing saphenous system to drain into the deep system with forward flow in systole and retrograde flow in diastole.
C2d on the other hand expresses the potential of the same saphenous system, with reflux eliminated, to empty into the deep system with a retrograde flow.
The difference between C1d and C2d – for example, in the case of uncomplicated varices, the range of mean variation in compliance values is 3–8% without tourniquet application and 15–20% with tourniquet application – ultimately expresses and predicts in percentages the hemodynamic improvement induced by high ligation of the saphenofemoral junction, whether the improvement is seen in terms of elimination of saphenofemoral reflux, as has heretofore been the case, or in terms of functional residual drainage capacity.
Intent and Limits of the Method
The measurement of compliance represents an ideal open window to the saphenous system through which we obtain a picture of the pathophysiologic phenomena that characterize the venous compartment both in cases of primary varicosity and after surgery. But although on the one hand it has the advantage of being a simple, reliable, representative and clinical measurement of the physical phenomena taking place, on the other hand it should not be considered an absolute measure.
The Baird formula used includes some important limitations:
1. Since the diameter may be considered an expression of volume, it is necessary that the length of the system in question be a constant – only under this condition can the changes in diameter be correlated in reality to changes in volume. Baird’s assumption has been verified in vitro; however, in some circumstances in vivo, such as during the Valsalva maneuver or the immediate post-exercise phase, the system varies its length in response to closure of the competent valves.
2. The measured compliance not only relates to the vein segment where the measurement took place, i.e., the saphenous, but is influenced by the entire venous system, which is in open communication with the saphenous itself during equilibrium.
3. The saphenous also presents a wall pattern different from that of other structural components of the system, such as the collaterals, perforators or deep veins.
With regard to the dynamic part of the test, one must be quite certain that the reflux has been interrupted. With the Doppler probe located upstream from the cuff, one should verify that at least the reflux produced by lowered gradients (such as with the compression–release technique) has been effectively eliminated; it may always prove useful to provide eccentric compression in addition to the centrad compression of the tourniquet.
Walking is the gold standard for evaluating physiologic saphenous emptying; indeed, good saphenous drainage is not always achieved by the tiptoe maneuver, especially in elderly patients with active or healed ulcers and consequently articular blocks of a structural or analgesic kind.
An important further limitation on this type of investigation is its inclusion of the immediate reactions of the biological tissues in the process of compliance determination, in this case the immediate variations in saphenous diameter. It is known that biological tissues produce three types of reaction in response to mechanical stimulation: an immediate reaction linked to the purely elastic components of the system; a delayed reaction by the visco-elastic components, called "visco-elastic hysteresis" (Guyton) which requires several minutes before onset occurs; a late reaction, involving several weeks, linked to potential structural remodeling of the components of the vascular wall. It is clear that this test assesses the immediate reaction only. In our experience with conservative surgery, we have indeed observed, to give an example, that immediately following a high ligation of the saphenofemoral junction there is a significant decrease in the saphenous diameter in comparison with the preoperative diameter; at follow-up performed a few days after the intervention, however, the diameter may have returned to its original size, and only at later follow-up visits, at three months or greater distance from surgery, was a stabilized diameter observed, with a reduction of up to 30–40%.
Finally, we recommend careful assessment in every case of the role of the mechanical properties of the venous wall. If the venous system still possesses good mechanical parietal properties, that is, if the veins have the capacity to adapt to different filling volumes with the patient at rest (the first part of the test), then the compliance measured in the dynamic phase (the second part of the test) can also express the capacity of the system to empty during exercise, whether the reflux point is open or closed. In the first case it will express the level of compliance of the system under baseline conditions, while in the second it will express the functional condition of the system once the reflux has been surgically corrected.
Let us recall, by the way, that all incompetent saphenous veins will empty during ambulation once reflux has been successfully interrupted.
On the other hand, if the venous system presents only minor residual mechanical properties, that is, if the veins are not capable of adapting to different volumes of filling with the patient at rest (for example, due to a history of postthrombotic saphenous recanalization or complete fibrotic invasion of vein wall components; see Fig. 10), then the compliance measured in the dynamic phase will no longer reflect the drainage capacity of the system, since the veins are too "rigid" to adapt to the reduction in refill volume.
Chapter 3
HEMODYNAMIC PRINCIPLES AND VENOUS ULTRASONOGRAPHY
Massimo Cappelli, Raffaello Molino Lova, Stefano Ermini, Paolo Zamboni
PHYSICAL PRINCIPLES OF VENOUS HEMODYNAMICS
Potential, Pressure and Gravitational Energies in a Hydrostatic System
The venous system functions under conditions both of fluid stasis and fluid dynamics. It is necessary to review some principles of physics in order to define and correctly interpret the phenomena we are going to describe below.33, 41, 42, 59, 162
First we will examine the principles that govern the behavior of venous blood under conditions of stasis.
There is a widespread opinion that fluid motion within a conduit is produced by the pressure difference or gradient between the two ends.
If this were true, then if we stood a closed-end cylinder vertically and filled it with a fluid, we should expect upward motion in the fluid, from the bottom where the pressure on the cylinder walls is greater to the top where the pressure on the cylinder walls is less. But this does not happen.
In reality, pressure on the cylinder walls (or pressure potential energy) represents only one part of the total energy of this system; another part is gravitational potential energy linked to the height level that the fluid occupies. Since pressure potential energy, greater at the bottom and less at the top, is perfectly offset by gravitational potential energy, greater at the top, less at the bottom, then total energy is absolutely identical at all parts of the system.
By analogy with the zero principle of thermodynamics, which states that no exchange of energy can occur between systems or between points within a system at the same energy level, we find no fluid motion (and therefore no exchange of energy) within a cylinder between points that have the same total energy level.
Fluid Motion
Now let us imagine two cylinders placed vertically, connected to each other through a conduit with a removable rigid diaphragm installed internally at the level of the base of the cylinders. If the height of the fluid within the cylinder on the right is greater than the height of the same fluid in the left cylinder, then an energy gradient exists between these two systems. Both pressure and gravitational potential energies in fact are greater in the right than in the left cylinder because the fluid there is at a higher level. The energy gradient in this case is totally independent of the absolute height of the fluid; instead, it depends solely on the inequality of the levels within the two cylinders.
The second principle of thermodynamics states that energy is spontaneously transmitted from a system at a higher energy level to a system at a lower energy level and not vice-versa. Therefore, it is logical to expect fluid motion (i.e., work) and thereby an exchange of energy from the right cylinder to the left cylinder whenever the rigid diaphragm that separates the two systems is removed; this is something that regularly occurs by reason of the principle of communicating vessels (Fig. 12, 12a).
To sum up, we believe it is more correct to regard fluid motion within a conduit as the result of an energy gradient instead of a pressure gradient.
Figures 12, 12a. Principle of communicating vessels and its application in the physiology of the superficial and deep venous system; it is illustrated by columns of different height.
12a.
Title: REENTRY GRADIENTS
Required Elements for Flow Determination
If however we apply energy in the form of pressure to one end of a rigid conduit filled with fluid, while the other end is closed, we do not produce any fluid motion within the conduit. In this situation, the total energy of the system increases in response to the increase in pressure, but pressure at the distal end of the conduit increases immediately and therefore any pressure gradient between the two ends is also immediately eliminated.
The application then of energy in the form of pressure to one end of a conduit clearly represents a n
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