Dear Sir or Madam

I am writing this letter to you with a request for you to look into a matter that has to be resolved in physiology as soon as possible. I would like to invite you to take part in a discussion related to the theoretical foundations of microcirculation. With my research paper on these problems, which is now available to you on the Internet, I have proven that the hypothesis of the English scientist Starling of 100 years ago is not only erroneous, but that it substantially hampers the development of physiology.

In the past eight years I have worked as an independent researcher. This type of work leads to many problems, mostly because the state does not support the research activities of private individuals. Moreover, there are serious difficulties in practice, connected with the publication of the research results. All this means great loss of time, especially for the computer processing of my research. This is why, I am very happy today about what has been achieved and above all that I can present for the first time a part of my work in English. Only now I can explain precisely everything that I wished to write you years ago.

I hope that you will understand the enormous advantages offered by my method for solving the problems of microcirculation. The method not only makes our work easier, but it also broadens our potential as researchers immensely. If you wish, I can demonstrate this to you personally by applying my method for calculation of your own research tasks in the area of physiology in which you are working.

The strictly scientific and mathematical approach in my work allows to reach very categorical conclusions about the present-day situation in the microcirculation theory. I have worked for many years in the engineering sciences, in the sphere of hydrology, and subsequently in medicine and physiology. I assure you that at the moment the development of physiology essentially needs radical changes. However, their implementation can occur only by persistently and uncompromisingly going forward, with correct proof, without assumptions and without hypotheses.

In my opinion, the biggest problem is to understand that the effective filtration pressure in the intact tissue does not depend on the Colloid-Osmotic Pressure (COP). With this I am taking exactly the opposite stand to that of Starling. The meaning of my theory is extremely clear, because it consist in the simple discovery that Nature does not tolerate the wasting of excessive energy in blood circulation constantly to overcome a factor as COP in the tissue.

The important thing is that this principle is one of the secrets of Nature, it has not been invented by me, it exists irrespective of us. I have discovered it by applying a suitable scientific method for analysis (see Fig. 2 in my paper).

The results of my research show that today physiologists have no choice but to examine the capillaries as elements with distributed parameters. The capillary is a porous tube and science does not offer another solution for its fluid dynamics. Today one can no longer work guided by intuition or by one's senses, when there exists a strictly scientific approach that invariably leads to the results presented in my work.

In  1896 Starling assumed that COP was the reason for the refiltration of the fluid filtered in the interstitium. However, he demonstrated experimentally only that most of the fluid filtered in the interstitium returns to the capillaries. This achievement has earned him a permanent place of honour in physiology. However, some of his other ideas, especially the one about the role of COP in the blood, do not comply with the theory of fluid dynamics in the blood. And if Starling were alive today (see Michel, 1997, p. 27), he would probably have been the first to understand the need to apply the theory about distributed parameters for calculating the fluid volume in the tissue. And this theory is more convenient and more understandable than all earlier hypotheses in the sphere of microcirculation.

More than 100 years later, the time has come to change the theoretical foundation of microcirculation, which means that it is necessary to create absolutely new concepts in physiology. In this sense, I am addressing this letter as an appeal not only to physiologists throughout the world, but also to all researches who have an opinion on these matters.

This is an appeal to you personally to choose your position in an inevitable dispute, which will have to decide the future of the theory of microcirculation. There is no time to postpone this problem further, because we all share a responsibility for physiology, science in general and the future generations.

With the present contribution to the theory of microcirculation, today I am giving the start of an extremely needed updating of physiology. There is still a lot to be done in the future and it can be done only with the united efforts of all of us. Not only physiology, but the science about living nature in general, compels us to do our job well. Therefore, I shall be happy to learn that you would be among the first who would understand me and support me.

There is no doubt that it would become necessary for physiologists to work with scientists from domains outside physiology, with mathematicians, physicists, biologists, systems theoreticians, theoreticians in the field of hydrology, etc. Within the frameworks of such interdisciplinary groups on problems related to tissue supply it would be possible to demonstrate best and most quickly the correctness of my conclusions.

Today I am requesting concrete assistance. If you think that it would be a good idea to invite me for a discussion or for joint work, I am entirely at your disposal. Besides, you can invite me to publish my papers in your journal/specialized publication. For a year my work can be found in the State Library of Bavaria and on the Internet: http:\\

Looking forward to hearing from you, I thank you in advance and remain with best wishes,

Yours sincerely,




Jordan M. Petrow



Personal information:

I have doctorates in medicine and systems theory, was educated in physiology at the University of Rostock and acquired the title of "specialist in physiology". I currently work as a doctor in Bad Tölz: Dr.Dr. Jordan M. Petrow, Badstraße 26, 83646 Bad Tölz, Germany, Tel. 0049 8041 799755, E-Mail:

100 Years since Starling's Hypothesis in Physiology: 100 years along the path of a Misunderstanding. Response to C. C. Michel's Laudation on the Occasion of the Centenary

Jordan M. Petrow




Theory of the fluid dynamics of a porous tube, like the capillary, in a limited and elastic space, like the cellular interstitium

Basic rules

Basic mathematical rules

Discussion 1: The opportunities of the new theory of microcirculation

Discussion 2: New interpretation of the isogravimetric method

Discussion 3. The errors in Starling's hypothesis and in the current microcirculation theory


Key words: Microcirculation in tissues, Starling’s hypothesis, blood pressure, oncotic pressure, interstitial hydraulic pressure, lymph formation, filtration, fluid exchange, capillary filtration coefficient.


The present-day theory of microcirculation, based above all on the hypothesis of the British scientist Starling of 100 years ago, treats blood pressure and colloid-osmotic pressure (COP) as opposing forces in the process of tissue perfusion. According to this theory, the blood pressure increases the convective fluid flux through the cellular interstitium, while COP reduced this flux. Since this concerns the nutritive supply of the tissue with essential life-supporting substances, a model like Starling's hypothesis does not seem appropriate for satisfying the extremely strict criteria in the evolutionary course of Nature.

Just the opposite to the statements in Starling's hypothesis is proven in the present work, namely that the blood pressure and COP are mutually complementary in the process of supplying the tissue. COP not only makes respiration possible, as the basis for the emergence of life on land, but it normally doubles the potential for intensification of the tissue perfusion. The value of the effective filtration pressure (EFP) in the intact tissue is not reduced parallel with the COP value, as was believed in physiology until now, because under real conditions and in the absence of transient processes, EFP to the capillary wall is determined above all by the blood pressure and does not depend on COP.

When Starling formulated his hypothesis in 1896, he expressed an assumption about the fluid exchange on the capillary wall. However, 100 years after Starling, it is no longer necessary to restrict ourselves within intuitive notions only.

Unlike Starling, in the present work the solution to the problem is achieved through correct mathematical means, on the basis of the experience accumulated both in physiology and in the systems theory. Since the capillary and the tissues around it are specific elements with distributed parameters, special mathematical methods are needed to solve the problems formulated. From a scientific point of view, the analysis demonstrated in the present work are absolutely mandatory for the microcirculation theory.


1. Introduction

The mechanism of supplying oxygen and other vitally essential substances to the cells of the living organism is an integral part of the eternal question related to the emergence of life on Earth, because every more complex form in the animal world does exist only by a blood and blood circulation system. And it is not accidental that this system has become identified in our conscience with a symbol of vitality, because the quality of supplying the cells defines above all the surviving of every organism, limits its possibilities for action and simply solves the problem: to live or to die.

In medicine, the problems related to the supplying of the cells in tissues are referred to the domain of microcirculation. This is an independent scientific area, which is predominantly within the scope of interest of physiologists.

The known hypothesis of the great British scientist Starling gained prominence in the past 100 years for explaining the problems of microcirculation in physiology. Starling discovered 100 years ago that most of the fluid filtered in the cellular interstitium returns to the capillaries. In this way, he revised other hypotheses of that time and thus he reserved a permanent place of honour for himself in physiology. This fact is particularly well highlighted in C.C. Michel's comprehensive work (1997), marking the centenary of Starling's hypothesis (p. 27):

"I am sure that if Starling were alive today he would be happy to know that his hypothesis had been so fruitful in clarifying thinking and encouraging experimentation."

Starling assumed that the colloid-osmotic pressure (COP) in the blood causes the moving of a part of the interstitial fluid back to the capillaries through reabsorption. The microcirculation theory in our time has accepted this statement by Starling and also presents COP as a force acting directly in the opposite direction to the blood pressure. Otherwise the blood pressure determines the paracapillary interstitial flux (flow), being the most important carrier of oxygen and of other vital substances necessary to the organism. If we assume Starling's claim about COP to be true, we would also have to agree that a benefit to evolution of the type of COP had been irrationally created to oppose the most vital of all life-determining factors. So far no one has thought about the problem that such a questionable "benefit” would inevitably lead to additional energy expenditure in the cardiovascular system. The main task of this system is to supply the cells of the organism, and precisely during this task approximately a quarter of the cardiac power ought to be wasted in the capillary bed for overcoming a relatively constant value, such as the resultant COP. And when it comes to the energy balance in the organism, Nature never tolerates spokes to be put in the wheel of evolution. Therefore, from a purely pragmatic point of view, Starling's idea appears to be extremely inexpedient, even at first glance.

Starling reached his conclusions 100 years ago as a result of the experimental observation that the volume of a tissue starts decreasing when COP in the blood increases, and conversely, that same volume starts growing when the blood pressure increases. This antagonistic effect of the two parameters is so blatantly obvious that it later served as the basis for devising the so-called isogravimetric method for practical research. Using this method, the dependence is sought between the different values of the blood pressure and COP, while at the same time making sure that the volume or the weight of the tissues studied remain constant (Pappenheimer, J.R. and A. Soto-Rivera, 1948).

The convenience of this isogravimetric method consists in the fact that the values studied can be measured outside the tissue, because very soon there appeared a growing awareness in modern physiology as well that researchers would face insurmountable difficulties trying to conduct similar measurements within the tissues and at cellular level. However, experience was accumulated in physiology over the years and already after Starling's death a mathematical expression of his hypothesis was obtained, which can be seen for the first time in the publications of Landis of 1927 (see also Michel, 1997):


Jv/A  = Lp [(Pc-Pi) - ( pc - pi )] =  Lp (DP - Dp),                                                                        (1)


where Jv/A is the fluid rate per unit area of capillary wall. Pc and pc are respectively the capillary pressure and oncotic pressure of the blood; Lp is the hydraulic permeability of the capillary wall and Pi and pi are respectively the hydraulic pressure and oncotic pressure of the interstitial fluid.

Other modifications of equation (1) appeared later, but they do not change essentially the basic construction of Landis:


Jv/A = Lp [(Pc-Pi) - S sr D pr ],                                                                                                                 (2)

                               r =1


where sr is the osmotic reflection coefficient of the microvascular wall to the r-th solute. Dpr = ( pc - pi ) is the difference in the oncotic pressures of the r-th solution flanking the capillary membrane.

To interpret equation (1) means first of all to draw the conclusion that COP represents energy loss of the cardiac activity in the capillary bed. The second interpretation of equation (1) is that the antagonism between the blood pressure and the resultant COP = Dpr = ( pc - pi ) occurs at the level of the capillary wall. This conclusion will be explained in greater detail in the next section.

Bearing in mind that COP has a relatively constant value within the capillaries and that the blood pressure along the capillary length decreases progressively, it is also possible to construct a graphic image of Starling's hypothesis, as shown on Fig. 1. This is a graph that can be seen in any physiology book.

In addition to the already cited energy wasting in the capillary bed, the theoretical concept presented on Fig. 1 contains a range of other shortcomings, which will be only briefly mentioned here:  

1.                    In constructing the graph on Fig. 1, it is assumed without any evidence that the interstitial hydraulic pressure (IHP) is also a constant value. However, how are the values of the hydraulic pressure assumed to remain constant behind a porous wall, when before that same porous wall the values of the hydraulic pressure are to be changed, see also Discussion 3, items 13-19.

2.                    According to the concept in Fig. 1, the system is incapable of meeting even the most elementary stability criteria. The area of its reliability is actually infinitely small and this conclusion does not correlate in any case with the practical observations in living nature.

3.                    If the values of the blood pressure and the resultant COP are nearly equal, the interstitial fluid flow ought to be stopped. What is the meaning of this conclusion, if there are cells behind the capillary wall, for which this interstitial fluid flow is vitally essential?

4.                    If the resultant COP is increased substantially, the interstitium should become dry. This is not observed in practice and the question about the nature of the force which is opposed and which in the long run neutralizes the action of COP remains.

5.                    From a mathematical point of view, it is not possible to operate with a conception similar to equation (1), because it requires the practically impossible condition to measure the values concerned in each point along the capillary wall. Therefore, this concept does not allow to calculate the different parameters in time and in other dimensions, in the beginning of a process (t®0) and at its end (t®¥).

Each of the shortcomings listed above is in itself sufficient for rejecting Starling's hypothesis as inconsistent. However, item 5 expresses the real problem of physiology, from its inception as a science to this day: So far there is no suitable method in the microcirculation theory for calculating the fluid exchange on the capillary wall.


2.0. Theory of the fluid dynamics of a porous tube, like the capillary, in a limited and elastic space, like the cellular interstitium

2.1. Basic rules

We shall divide the theory of porous tubes into two parts. In this Section 2.1 it will be explained descriptively, which will make it easier to understand its meaning and its philosophy. This will be a preparation for Section 2.2, where a mathematical calculation only will be presented.

Creating a theory about the tissue supply necessitates first to have some idea about the structure of the tissues. And if we are talking about fluid dynamics, it is necessary to know what there is behind the capillary wall and above all how the interstitial space ends.

In principle, there are four possibilities, the first of them being that the interstitial space is simply open (Fig. 2a1). Although ostensibly absurd, such a situation cannot be totally ruled out in Nature, e.g., in fish gills. The second possibility is the interstitial space to be closed by a membrane, which is both elastic and very soft (Fig. 2a2). The third possibility is the interstitial space to be closed by a membrane, which is elastic and sufficiently strong, so that together with the cells it can resist some maximum interstitial hydraulic pressure, e.g., about 200-300 mm Hg (Fig. 2a3). The fourth possibility derives from the third one, if the interstitial membrane is supported mechanically by some bone structure. Such is the situation, for example, in the cranial cavity, but this situation will not be considered here, because it can easily be reproduced from Fig. 2a3. Therefore, it is only necessary to make the provision that the elasticity of the interstitial membrane tends to zero.

The second step along the way to creating a theory on tissue supply is to find an explanation of the antagonism observed in practice between the blood pressure and COP. So far no one in physiology has made the distinction that:  

1.        The antagonism between the blood pressure and COP may occur in principle at the level of the capillary wall. However, we shall prove below that this condition is fulfilled only when the tissue interstitium is open. An open interstitium is not a normal phenomenon in Nature, it exists only in the respiratory organs of sea animals (e.g. fish gills). For all other cases of life,

2.        The antagonism between the blood pressure and COP occurs in the tissue at the level of the interstitium, more specifically at the level of the interstitial pressure IHP. This occurs always and for all cases of intact tissue with closed interstitium. This closed interstitium resembles in its most elementary form the construction of a natural osmometer, which consists of a semi-permeable membrane placed in a liquid medium and in a closed space.

The closed interstitium of tissues is the normal state for all living creature on Earth. However, the theory which we are proposing in this chapter and in the next is equally valid both for open and for closed interstitial spaces:

The third step along the way of creating a theory is to accept at first equation (1) and to find the respective situation among the four types of tissue realization, which corresponds to this equation. If along the capillary on Fig. 2a1, the hydraulic pressure on both sides of the capillary wall is measured in many different points, it will show that this gives validity to equation (1). However, the graphic expression of the values measured will not correspond to Fig. 1, but it will fit very well Fig. 5c, which is already calculated according to the new microcirculation theory. Moreover, the experiment will show that equation (1) is valid for the situation on Fig. 2a2 as well.

The construction from Fig. 2a1 can easily be reproduced experimentally and it can even be built using suitable artificial materials. However, no such case exists in living Nature on land. Contrary to this, the situation in Fig. 2a2 can be realized as an experiment with a living tissue, while all of the tissue structures are still completely preserved. Thus, it becomes clear how close it is to assume that the dependence found here (Fig. 2a2) in the form of equation (1) will also be valid for all other situations in Fig. 2. Starling himself conducted his experiments mainly with cell tissues in oedematous state, as in Fig. 2a2. This is probably why he wrote in 1896:

“… and whereas capillary pressure determines transudation, the osmotic pressures of the proteins of the serum determines absorption. Moreover, if we leave the frictional resistance of the capillary wall to the passage of fluid through it out of account, the osmotic attraction of the serum for the extravascular fluid will be proportional to the force expended in the production of this latter, so that, at any given time, there must be a balance between the hydrostatic pressure of the blood in the capillaries and the osmotic attraction of the blood for the surrounding fluids (E.H. Starling, 1896)...“

From this quotation it becomes clear that here COP and the blood pressure are considered as two opposing forces. This is actually the fundamental idea defining Starling's hypothesis, equation (1) and the present-day theory of microcirculation. As we indicated already, this idea is true for Fig. 2a1, because there the capillary wall represents a kind of boundary behind which an interstitium with infinite compliance starts. In this case, for the antagonism between the blood pressure and COP there is no other choice but to exist at the level of that capillary wall. In this way, the capillary wall on Fig. 2a1 is the substrate basis for the validity of equation (1).

However, what is true of the tissue from column 1 cannot in all cases be applied to explaine the situations of the second and third columns of Fig. 2. Here it is not possible for a science to be objective and not to notice that column 1 differs radically from columns 2 and 3, and that this difference is due above all to the membrane closing the interstitium. Practical measurements as those in Fig. 2a1 cannot help in the concrete case, because they inevitably lead to destruction of the membrane closing the interstitium and to creating conditions that are valid for column 1. Therefore, the conditions of columns 2 and 3 on Fig. 2 necessitate another type of analysis, which will be described below:

With the values given in Fig. 2b, it is logical to conclude that the soft tissue oedema from Fig. 2a2 will already be resorbed as a result of the suction effect of COP, whereby the membrane serving as a sheath of the cellular tissue would move towards the cells and would stop after a certain time, because the cellular bodies would prevent it from approaching closer to the capillary wall. When the movement of this membrane stops, the suction force of COP will cause a subatmospheric (negative) hydraulic pressure in the interstitium. Actually, this is precisely the principle of operation of the devices for COP measurements. In this way, a complete equilibrium of the forces is reached in the situation on Fig. 2b2, whereby COP suction force is neutralized by the resistance of the soft membrane covering the cells and is supported by the cell bodies. In this system there are no longer movements either of the membrane, or of the fluid that is still present between the cells in the interstitium. These are the main postulates of Fig. 2b2, which constitute a radical difference from the situation in Fig. 2b1 with an already dry interstitium.

At this point it is necessary to understand that in the steady state of forces on Fig. 2b2, any increase in the blood pressure DPc, = PCA – PCE, even infinitely small, would result in the system being taken out of its steady state. PCA and PCE are respectively the blood pressure at the entrance and the blood pressure at the end of the capillary.

As shown on Fig. 2c2, this very small increase in DPc will immediately cause a convective flow Jvi = DPc/Ri of the interstitial fluid through the interstitial space (i = interstitial, pressure/resistance relation according to Ohm`s Law). Cave: There will be no such convective flow in the situation shown on Fig. 2c1 and there the interstitium will continue to be dry. On the other hand, the processes in Figs. 2b3 and 2c3, respectively will be analog to Figs. 2b2 and 2c2.

There is no doubt that whoever has understood the essential difference between the first and the second columns of Fig. 2 would also understand the basic postulates of the new theory on microcirculation. It should simply be known that the blood pressure even in an interstitium with subatmospheric interstitial hydraulic pressure (IHP) will cause a convective flow, because there is no force that can oppose it, as in the described case the COP force is already completely neutralized with the help of the mechanical support of the tissue membrane. Moreover, in this case it does not matter in the least whether the tissue membrane is very soft, both elastic and soft, elastic and sufficiently strong, or totally rigid, as in a bone cavity. It can be pointed out as an extreme example that in the lungs the role of such a sheath (membrane) is played by the surface tension of the alveolar fluid.

The fourth line on Fig. 2 shows the different responses of the three types of cell tissue to the condition of forced perfusion. In Nature this condition is imposed with every physical loading of the organism. Interstitial fluid flows from the tissue in Fig. 2d1, a pathological oedema develops in Fig. 2d2, and only in Fig. 2d3 the paracapillary flow through the interstitium can be increased many times, as required by the condition for forced perfusion. The examples show that situations as those in Fig. 2d1 cannot exist in the organism, situations as those in Fig. 2d2 should not exist, whereas in the situations in Fig. 2d3 the tissue should possess sufficient internal bonds so as to withstand the loading.

The mechanism of COP neutralization in a closed interstitial space is the most important characteristic feature of the porous capillary. However, this condition is not always completely fulfilled in some capillary constructions. The specificities of the renal glomerules can be cited as an example. This is why, Fig.3 presents more precisely the mechanism of COP neutralization. In a porous tubing placed under suitable conditions, the COP force at the beginning of the tubing is neutralized by the COP force at the end of the tubing, i.e., COP neutralizes COP. In this brilliant construction of Nature, the liquid medium in the interstitium is the link between the opposed COP forces. It is understood now that the tissue sheath (membrane) plays a secondary role in this process, but without it there can be no effect of COP neutralization, because in that case the interstitial space obtains an infinite compliance and thus the interstitial fluid cannot function as a link.

The mechanism for compensation of the COP force means that the blood pressure in a tissue system with COP filters in the same way in the direction of the interstitium as in a tissue system without COP. There is no force opposing the blood pressure in an intact tissue in a steady state. This means that equation (1) is wrong and 100 years after Starling we can write:

The first property of the theory of porous tubings, such as the capillaries, placed in a closed space with finite dimensions, such as the cellular interstitium, is the fact that the paracapillary interstitial flow in a steady state is determined only by the blood pressure and does not depend on the resultant COP, acting along the capillary wall.

In a steady state and with a constant volume of the intact tissue, the suction force of the resultant COP in the capillaries is projected in the interstitium and lowers the interstitial hydraulic pressure IHP.

The second property of the theory of porous tubings, such as the capillaries, placed in a closed space with finite dimensions, such as the cellular interstitium, is the corollary that the interstitial pressure IHP in intact tissues decreases with the value of the resultant COP, acting along the capillary wall.

In the next section these two properties will be derived mathematically.


2.2.                Basic mathematical rules

The capillary is a porous tubing placed in the interstitial space with defined elastic properties. It is completely futile to make attempts to calculate such structures using equation (1), because they are systems with distributed parameters. This definition comes from the scientific domain of the systems theory. Another example of such systems is a telephone circuit over a distance of thousands of miles. Here it is important that the systems with distributed parameters are calculated using special mathematical methods. This is why, the capillary cannot be considered as an ordinary tube, although it does not exceed 1 mm in length. This small tubing is porous and the millions of pores along the capillary length make all parameter values dependent on the place where they are acting. This peculiarity necessitates to treat the capillary as a sum of numerous separate segments, infinitely small in themselves, or at least small enough to the extent of ruling out the already cited distribution of the parameters for the individual segment. This condition leads to a substitutive diagram of the capillary, and this rule is also valid of the cases when numerous capillaries share one interstitial space and form a so-called substituting capillary in a certain part of the cell tissue.

In order to construct the substituting diagram of a capillary, it is necessary to know above all how to express the different properties of the tissue elements taking part in the microcirculation. For this purpose, there is a scientific domain dealing with the so-called electromechanical analogies. The aim here is to create a common scientific base by means of which certain principles in, e.g., hydrology, may already be expressed through familiar electromechanical concepts. We have used the following parameters for the construction of the substituting diagram of the capillary, according to Fig. 4a:

·          The hydraulic resistance inside and along the capillary. Every capillary segment with elementary length Dl opposes the blood flow with a resistance which we have designated with Rcm. Here m is an index of 1 – N, where N is the total number of the capillary segments.

·          Capillary filtration coefficient. This coefficient determines the permeability of the capillary wall for the indicated segment. It is replaced by a resistance Rqm   in each segment and is placed transversely to the capillary wall.

·          The hydraulic resistance of the interstitial space. Each tissue is characterized by its own structure of its interstitial space, which opposes the paracapillary fluid flow with a definite resistance. It may also change for the different segments, hence it also receives an index and is designated with Rim.

·          COP on the capillary wall. The action of COP here is suction depending on the direction of the colloid-osmotic gradient. This property is accepted in full correspondence to all earlier observations of experimental physiology. Similar to the blood pressure, COP is a vector force pd, which is designated as an arrow in a circle and receives a separate index m for each segment.

·          Hydraulic capacity Cm. This value expresses the capacity of the interstitial space to incorporate fluids and characterizes the elastic properties of the interstitial structures.

By means of the listed structures it is possible to obtain the substituting diagram of the capillary, which is shown on Figs. 4a and 4b. Actually, the construction on Fig. 4b is the most important stride forward, because after it the calculation of the separate parameters becomes a purely technical problem. For example, the elementary flux Jvm in the respective segment can be found according to the following formula:


Jvm = mm . PCA + S njm . pdj,                                                                                                                                     (3)



where PCA is the blood pressure at the beginning of the capillary, m and n being coefficients with conductivity dimension. pdj is the resultant COP for the respective segment, N denotes the total number of capillary segments.

The effective filtration pressure EFP at the capillary wall is defined as a pressure decline against the respective resistance Rqm. If this resistance along the capillary remains constant, the graphic image of EFP coincides in principle with that of Jvm by using another dimension.

EFP = Jvm . Rqm                                                                                                                                                        (4)

The blood pressure Pcm along the capillary can also be calculated according to the diagram on Fig. 4b, but for the sake of brevity, we cannot discuss all parameters here. However, the complete calculation of the substituting diagram is much simpler than one can think after the first impression of equation (3). Computer programmes for this purpose have existed for a long time and they offer the biggest details in a ready form.

In this way, the calculation even of the most complicated situation in the sphere of tissue perfusion is reduced to a single click with the computer mouse. Naturally, this is an enormous relief for the researchers of microcirculation, who will be expected in the future only to learn to cope with concepts of electromechanical analogies, in order to be able to construct the substituting diagrams of the objects studied. In this way, microcirculation will thus at long last acquire the advantages that have entered other research branches of science a long time ago.

3.1. Discussion 1: The opportunities of the new theory of microcirculation

So far we presented the theory of fluid dynamics in porous tubing, like the capillaries, when they are in a closed space, like the tissue interstitium. The calculation of the substituting diagram of the capillary produced the same results, which we obtained descriptively in section 2.1. There is no point in doubting the actual calculation, because it is merely a mathematical inventory that has been accepted in science for a long time. Therefore, here we are restricting our discussion only to the type of the substituting diagram of the capillaries.

1.                    The description of the capillary in accordance with Fig. 4b is the only correct way to derive the microcirculation theory. There are no other possibilities in science for calculating elements with distributed parameters. Naturally, the description on Fig. 4b is after all only a model of blood supplying the tissues. However, real science exists only in accordance with a model. Merely verbal notions are not in the least sufficient, because even the simplest practical measurement requires the respective scientific model, according to which the interpretation of the measured value should be made.

2.                    Starling's hypothesis is in itself also a model. The expression from Starling's quotation “... Moreover, if we leave the frictional resistance of the capillary wall to the passage of fluid through it out of account...” (see 2.1), means, for instance, that Starling is proposing here a simplification. However, he could not provide any justification for this simplification, because he lacked the respective mathematical model. However, we specifically indicate on Fig. 4a that Starling referred to the resistance Rqm. Moreover, we can prove that according to the new theory, this resistance plays a role mainly in transient processes by determining their duration. Therefore, in some special cases considered, the resistance Rqm can indeed be ignored. However, such a simplification is not done intuitively, it should obligatorily be scientifically substantiated, see also item 6 below.

3.                    The description on Fig. 4b is universal, because it can be used to calculate capillaries from all kinds of  tissues. This method allows us to study the fluid exchange both in inhomogeneous structures and in non-linear processes in the tissues. In addition, the model in Fig. 4b can be infinitely enlarged, e.g., for increasing the precision or for examining lymph processes. In the concrete case, a homogeneously structured capillary is presented on Fig. 4b, because this model is perfectly sufficient for measuring the essential dependences between the values determining the fluid exchange on the capillary wall.

4.                    The new theory permits studies of the parameters depending on time, which means that for the first time it can also be used to account for the transient processes in microcirculation (Fig. 6). On the other hand, this possibility allows to use certain test functions (Fig. 6c), as this is done in the systems theory. On the basis of the information obtained with the test functions it is possible to determine the unknown values in microcirculation, which cannot be measured directly for one reason or another.

5.                    It should be borne in mind that in a steady state the action of the elastic elements in the tissue, and hence the influence of time, no longer exist, compare with Figs. 6d, 6f, 6g. In this case the interstitium of the tissue is treated as an inelastic and closed compartment with a constant volume.

6.                    One of the most important properties of the theory of porous tubes, like the capillaries, can be seen by comparing the figures 6b and 6d. From the comparison it becomes clear that the quality of the process is invariant with respect to the value of its parameters. In other words, it is shown here that the law binding the elementary values R and C does not depend on the concrete relations between these two values, because whatever values are used to substitute the values R and C, the process remains unchanged in principle. Only the amplitude and the scale in time change on Figs. 6b and 6d.

At this point it is possible to see the advantage of the new microcirculation theory over all earlier attempts to calculate the fluid volume in the tissue. It suddenly becomes clear that it is possible to obtain the basic dependences between the parameters defining it, without the necessity of any practical measurement. In the substituting diagram of the capillary it is sufficient just to write any random values of R and C in order to obtain the type of the dependence sought. This gives enormous relief to the adherents of practical measurements in physiology, because the results of every experiment can be predicted. Then the actual experiment is conducted, if that is necessary at all, merely to confirm or visualize the theoretical formulation of the problem under consideration.

Here we shall describe some of the corollaries of the new microcirculation theory:

1.                    The most important corollary is undoubtedly the finding that the value of the effective hydraulic pressure EFP in the intact tissue is not reduced with the value of COP, as was believed so far. This conclusion, as well as a necessary correction of the earlier values of the capillary filtration coefficient CFC (Petrow, 1990e), face physiologists with the fact that the filtration in the human capillary network for one day is perhaps 100-200 times more than the norm of about 20 litres accepted now. This means the need of radical changes in the existing physiology concepts.

2.                    The advantage which Nature creates for itself by introducing the COP factor consists in the fact that a considerably more intensive tissue perfusion is possible with COP than without COP. Here we are referring to the paracapillary flux through the interstitium, which brings oxygen and vitally necessary substances to the cells, and takes the slag back to the blood and out of the body. Without COP, the same flux through the interstitium would occur with a much higher tensile strength than with COP. With respect to the blood pressure, COP reduces the swelling of the tissue and its sheath 1:1, making it more compact and more viable.

3.                    The application of the new theory to explain the function of the lungs is of particular interest. (1) The lungs can function correctly only if the COP values exceed those of the blood pressure. Under normal conditions, the fluid film in the lung alveoli closes the interstitium of the respiratory capillaries from the side of the air. Here the surface tension of the alveolar fluid acts as a thin membrane, which is completely sufficient for preventing the penetration of air bubbles in the blood. (2) Subatmospheric hydraulic pressure exists in this specific type of "interstitium", which keeps the lungs "dry" and makes respiration possible. (3) Under the effect of the blood pressure, a paracapillary convective flux passes in this interstitium, assisting the function of the lungs. This flux assists the saturation of the blood with oxygen and the elimination of slags, poisons, bacteria and other harmful additives, which penetrate there from the air.

4.                    The condition for prevalence of COP over the blood pressure should also be fulfilled in the soft tissues, e.g., in the subcutaneous tissue or in the tissue below the serous mucosae in the body, otherwise they would develop an oedema and would not be able to perform their functions. With the help of COP, a subatmospheric (negative) hydraulic pressure with suction in the direction of the capillaries is created. Nevertheless, the interstitium of the soft tissues continues to be perfused by a paracapillary convective flux, which is created by the blood pressure. This ingenious invention of Nature is the reason for the close adhesion of the skin and all kinds of mucous membranes to the body or to the internal organs. In this way, the necessary conditions for body movements of the individual are created and for the same reason fluids injected into the subcutaneous tissue are rapidly resorbed.

5.                    The natural capillary contains an infinite number of pores, and equilibrium between the filtration and refiltration with respect to the interstitium is automatically established on this capillary tubing. Life shows that this equilibrium is maintained within the different types of physiological loading of the organism. This means that the actual construction of the porous capillary and the surrounding area creates the conditions for the enormous stability of the tissue perfusion. On the other hand, COP gives an opportunity for additional intensification of this perfusion.

The blood capillary and the area around it in the form of the paracapillary cylinder represent a self-optimizing and a self-adapting system, which guarantees stable and viable blood supplying to the tissues.


3.2. Discussion 2: New interpretation of the isogravimetric method

The isogravimetric method was considered so far in physiology as the most serious proof of Starling's hypothesis (Michel, 1997, p. 14):

“The experimental result of Pappenheimer & Soto-Rivera (1948) were a complete vindication of Starling`s hypothesis that fluid across microvascular walls are determined by differences in hydrostatic and oncotic pressure."

More details in discussing the method of Pappenheimer and Soto-Rivera were already presented in another paper about CFC (Petrow, 1990e), which will be translated into English shortly. Of course, the antagonism between the blood pressure and COP is a fact, because a rise in the blood pressure increases the volume of the cell tissue, whereas a rise in COP reduces this volume. However, this does not mean that blood pressure and COP oppose each other at the level of the capillary wall. According to the new microcirculation theory, the antagonism between the blood pressure and COP concerns not the fluid flux through the capillary wall, but the interstitial hydraulic pressure (IHP). Therefore, the essence of the gravimetric method consists precisely in the presentation of a constant IHP value, with a view to preserving the cell tissue volume also constant. When this is known, the isogravimetric method can already be used not for confirming, but - conversely - for rejecting Starling's hypothesis.

For instance, in the case when the values of the blood pressure and of COP increase, but the difference between these two parameters remains constant, e.g.: 20 - 16 = 40 - 36 = 60 - 56. In this case the convective fluid exchange should remain constant, because the effective filtration pressure, according to Starling's hypothesis, does not change in all three cases. According to the new microcirculation theory, the convective paracapillary flux through the interstitium will increase considerably. Every researcher conducting experiments in this field will confirm this conclusion, if he stains the interstitial fluid and measures the rate of its elimination from the tissue for the different values of the cited parameters. With the higher values of the blood pressure and of COP, the staining substance is eliminated faster, and this fact cannot be explained with Starling's hypothesis. Conversely, it fits perfectly the new theory.

The rise in the blood pressure leads to increased tissue volume for two reasons:

1.                    The elevated blood pressure increases the difference between the averaged pressures in the capillaries and in the interstitium. Consequently, a certain amount of fluid will pass into the interstitium and will increase the interstitial pressure IHP, and hence the tissue volume as well.

2.                    The elevated blood pressure expands the blood vessels from the arterial side. This effect contributes to the additional increase of the tissue volume.

The compensating rise in COP with the isogravimetric method reduces the pressure in the interstitium and hence the tissue volume. However, COP does not influence the volume of the additionally expanded blood vessels. Therefore, the isogravimetric points will occur in this case at a higher COP value than can be expected under the simplified theoretical model, see a real theoretical model by Petrow (1990e).

The isogravimetric curve from bottom to top, i.e., from low blood pressure to high blood pressure, will shift to the right for the cited reason, whereas conversely, top to bottom, it will shift to the left for analogous reasons. The hysteresis effect obtained confirms the new theory. It is specific for each type of tissue and is influenced by the properties of the interstitium and of the blood vessels in it. The isogravimetric method can be used in practice for determining these properties, which is important for making the theoretical tissue model more concrete.

3.3. Discussion 3. The errors in Starling's hypothesis and in the current microcirculation theory

Starling discovered 100 years ago that most of the fluid filtered in the tissue interstitium partially returns to the capillaries, which was a considerable achievement for his time. Even if it had been only for that achievement, Starling would have remained for us a great researcher, whom we would always respect.

However, to make an assumption that, for instance, in Starling's quotation in Section 2.1, or to derive a dependence of the type of equation (1), does not mean in the least that this can happen as an isolated act in itself in a theory. In reality, both the verbal expression and the mathematical formula involve above all an obligation to also define the conditions of the theoretical model for which they are valid (compare with Fig. 2). For the same reason, a practical experiment cannot be an aim in itself, it will only be wasted power if it is not supported 100% by a serious theoretical concept. In all other cases it would have errors.

For example, if a spaceship is sent to Mars, it cannot be claimed that its trajectory was partially correct, because that spaceship finally landed on the Moon. Therefore, "slightly correct" ideas do not exist, they are either correct or incorrect. This rule is universally valid, because every idea can be fragmented ad infinitum into sub-ideas, for which this "yes or no" type of assessment can always be applied.

Unfortunately, no one has thought so far about the extent to which the model devised by Starling is applicable in practice, and whether it can secure an effective supply to the cell in tissues. For this reason, quite a number of fallacies have accumulated in physiology for the past 100 years and we shall examine them below:

1.        Starling's idea that COP in the intact tissue may stop fluid filtration is erroneous. Antagonism between blood pressure and COP does exist, not at the level of the capillary wall, as Starling believed, but at the level of the interstitial hydraulic pressure IHP. In this way, the blood pressure increases IHP, whereas COP reduces it, making IHP the most important factor that can oppose the blood pressure, in order to obtain a sensible equilibrium of the forces in the tissue (action=reaction). The static pressure in the blood vessels is also completely neutralized by IHP, see item 21 below.

2.        This situation also solves the energy problem about which we wrote in Section 1. With the new microcirculation theory, COP does not create energy losses against the blood pressure, because the antagonism between these two parameters is transferred to the level of the interstitium. It is normal to expect such a result of Nature, because it not only does not tolerate empty spaces, but it likewise does not tolerate solutions that are not optimal.

3.        Starling's assumption that the COP factor causes fluid resorption from the interstitium (cf. Starling's quotation in 2.1) is also erroneous, because essentially refiltration and not resorption exists in the intact tissue. We are introducing here the concept of "refiltration" in order to distance ourselves from Starling's "resorption", which he uses not at the place where it actually exists (see item 7 below).

4.        We divide the convective flux in the interstitium on the capillaries into "filtration" in the direction of the interstitium and "refiltration" back to the capillaries. The motive force of this flux is the difference in the blood pressure from the beginning to the end of the capillaries, and the phenomenon follows Ohm's Law, see Fig. 3b1 and Fig. 7. The division into "filtration and refiltration" is purely formal and it is done to differentiate between the part of the flux that enters the interstitium and the other part that leaves it. In a steady state, the filtration and refiltration are "automatically" equalized.

5.        The lymph in the tissue is not formed as a residue of the fluid filtered in the interstitium, as was believed until now. The lymph is actually the result of the accumulation of osmotically active substances in the interstitium, Petrow (1990b, 1991).

6.        Even in the case of the transient processes, such as the sudden rise in COP, an additional part of the interstitial fluid will return to the capillaries, not because it will be resorbed: (1) The rise in COP immediately provokes a decrease in the interstitial pressure (see Figs. 6f and 6g). (2) Because of this, the elastic parameters of the interstitium become unloaded, they shrink and in this way they refilter a part of the interstitial fluid back to the capillaries.

7.        A real resorption occurs, for example, when COP in the blood suddenly increases in the case of tissue oedema. However, this is already a pathological situation, which cannot be valid for the intact tissue as well. This is why, we insist on determining correctly the concepts of resorption and refiltration. Incidentally, Starling conducted his experiments mainly on oedematous tissues, which may be the reason for his erroneous conclusions.

8.        The concept of "refiltration" was not alien to Starling and he defined it in his paper (Starling, 1896) as "back filtration". However, Starling firmly rejects this possibility, assuming that the higher interstitial pressure would cause the venules to collapse, see also C.C. Michel, p. 10. Here we are referring to another of Starling's assumptions, which is also wrong. Theory has shown that the capillaries will not collapse under similar conditions, but will pulsate rhythmically. Elsewhere we have even given an experimental setup that demonstrates this in practice (Petrow, 1991). The blood flow during these pulsations of the venules cannot be interrupted.

9.        The meaning of the new theoretical setup will be understood even by non-specialists, because only now it has become possible to determine correctly the role of COP in the blood. It is known now that the convective flux through the interstitium occurs under all circumstances. However high the resultant COP may be, it cannot prevent the nutrient flux to the cells, if the tissue intactness is preserved. The new theory demonstrates above all an optimum supply of the cells with high stability of the blood supply process of the tissue. These conclusions cannot be obtained either with Starling's formulation, or with the more recent studies, which actually only develop further Starling's ideas.

10.      Equation (1) and the graph on Fig. 1 do not express the interaction of the parameters in the intact tissue, as physiologists still believe. Actually, they refer to a pathological situation in which the lungs are simply filled with water. However, even in that case equation (1) cannot be used for calculating the process. A massive lung oedema, of the type that occurs after drowning, is calculated according to the new theory and in compliance with Fig. 5.

11.      The capillaries are structures with distributed parameters. If equation (1) is used to calculate them, then these complex structures would be reduced to one pore or to a ring of pores (see Fig. 3a). It is more important, however, that there is no rule in mathematics that would allow us to do that.

12.      Precisely in terms of the criticism in item 10, researchers of microcirculation have persistently sought for decades a value of IHP, which they can substitute in equation (1). During that time all kinds of practical methods were proposed for its measurement, which will not be discussed here.

13.      The living organism consists of most varied tissues. It is self-evident that each tissue has is specific IHP. Moreover, it is quite logical to assume that this IHP from the external wall of a porous capillary wall changes according to some law and that it has not one, but an uninterrupted series of values. Similarly, the blood pressure inside and along the same capillary wall changes constantly and declines progressively. Any other assumption would be erroneous.

14.      Therefore, it would be totally pointless to seek any methods for IHP measurement: (1) because no practical method can be so precise as to measure the real IHP values; (2) moreover, even the best IHP measurements bring no benefit, if the experimenter does not know how to interpret them.

15.      We believe that no suitable method for IHP measurement will be found in the future, either. On the other hand, IHP can be easily calculated if some angular parameters are known, e.g. the blood pressure in the beginning and at the end of the capillaries, the COP profile, the permeability of the capillary wall, the elastic properties of the interstitium, etc. Unlike IHP, these parameters can be really measured.

16.      There is not one single reason that would give us evidence to assume that the hydraulic pressure would remain constant in the interstitium on the outer side of a capillary, if at the same time on the inside of that capillary the blood pressure or COP change. "Due to the incredible difficulties in the IHP measurement, we were forced so far to assume IHP to be a constant value in the in vivo experiments"- Pappenfuß, 1993. Unfortunately, such excuses are not accepted in mathematics and it is likewise not acceptable to draw convenient conclusions just because a value allegedly cannot be measured. It is also impossible to measure directly the distance to the Sun with a ruler. However, this is no obstacle for proposing a sensible model for its calculation. It is perfectly natural to introduce simplifications in science, but they have to be very well grounded in order to lead through induction to more general conclusions. The condition IHP = const. cannot be substantiated in the microcirculation theory.

17.      It is not possible to substantiate the property of the infinite capacity of the interstitium. This property, however, is directly required, if the condition IHP = const. is to be accepted. No one can substantiate the claim that the capillaries are actually in an infinitely large compartment filled with fluid, or that the interstitium is simply open. Therefore, IHP = const. cannot be merely an ordinary assumption. According to mathematics, IHP = const. is above all an obligation for certain properties of the interstitium.

18.      In practical experiments it is observed that the intact tissue starts diminishing its volume, if COP increases suddenly. This process stops after a short time and this ostensibly simple fact is the best proof that IHP cannot be a constant value, because there is practically no other force in the tissue, which can neutralize the influence of the suddenly increased COP. Here only the response decrease in IHP is in a position to stop the additional fluid flux to the capillaries and thus to stop the volume reduction of the tissue. At IHP = const., this process would be terminated only if the COP value is diluted by the hypotonic interstitial influx to the initial level. The effect of COP dilution can easily be compensated by a specially designed experimental setup.

19.      IHP = const. in the space behind a permeable wall as that of the capillary requires an interstitium with an infinite capacity to accumulate water. Such an interstitium would have to be open, but there are no such cases in living Nature on land. Here even the lungs present a closed interstitium, which is located between at least two permeable walls in the tissue space from the air to the blood. At the same time, it also prevents air embolism in the blood and achieves in this way one of the most important phenomena of life creation: the respiration by the lungs (for details see 3.1.).

20.      In the case of pulmonary oedema, the interstitium suddenly becomes open (see Fig. 5). The capillaries in fish gills should also have an open interstitium: in the future it would therefore be necessary to focus attention on the mechanisms for regulating the fluid exchange there. In a practical experiment, the capillary interstitium can be open unnaturally, e.g., by destroying the capillary cylinder. In practice, these are the few examples in the animal world, when it is possible to talk about open interstitium.

21.      A component of the blood pressure acts in the lower limbs of a standing human being, which may exceed several times the COP value. This is the static pressure and it can be compensated only by a response increase in IHP. There is no other force in the tissue to compensate this pressure and to stand behind the permeable capillaries. Its value shows that the strength of the interstitial bonds, especially in case of the muscle interstitium, should be sufficient strong to withstand this loading. They also show that it would simply not be serious to try to speak here about an open interstitium. Cave: Soft tissues are not able to compensate static pressures.

22.      Every scientist-physiologist should pose the question how the cell tissue would be fed, if there were truth that a prevalence of COP over the blood pressure would stop the convective flux around the cells. The assumption about the alleged prevalence of the diffusion in that case cannot be substantiated, because the real diffusion is very slow to overcome the relatively large spaces between the capillaries in such a short time. This simple fact has been ignored in physiology until now. Moreover, in semi-permeable membranes like the capillaries and when there is a concentration gradient, the diffusion is always connected with fluid convection in the tissue, Petrow (1991). At the same time, it seems to be difficult to understand that most processes around the capillary wall are easily explained with the well-known classical laws of hydraulics (see Fig. 7).

The contribution of the present paper consists in the application of a new method for calculating the fluid exchange processes around the capillary wall. The new theoretical formulation yields results, which are above all accurate, logical and sensible. Moreover, for the first time it is possible to demonstrate a concept that appeared to be optimal and to work precisely in the way  which is to be expected a priori in living Nature.

The new approach to these problems also shows us that there are other omissions and errors in physiology, which merit most detailed investigation in the future. They refer to problems as: (1) Capillary filtration coefficient, CFC, Petrow (1990e); (2) Edema and formation of lymph, Petrow (1990b); (3) The role of the blood pulsation and blood amplitude, Petrow (1990c) (4) The movement of the colloids through capillary membranes, Petrow (1990d, 1991, and 1992).

No assumptions have been made in the new theory, so that there is no one reason to call it  a hypothesis. The new theory is simply mathematics, therefore it is as true as mathematics can be true generally. The use of the new theory for calculating capillary processes is both convenient and expedient. From a scientific and logical point of view, the new theory is mandatory for solving problems of the type of fluid exchange on the capillary wall.

A more detailed version of this theory can be found in German on the Internet: http:\\


Fig. 1: Profile of the fluxes Jvm through the capillary wall along the capillary in accordance with Starling's hypothesis. The insignificant increase in the blood pressure leads to critical prevalence of the filtration (see the second series of values). If such a construction of the tissue perfusion is to function (to become real), the interstitium around the capillaries should be open. DPm and Dpm are respectively the hydraulic pressure and the oncotic pressure differences flanking the capillary membrane. km presents a dimension coefficient, and CA and CE mark respectively the capillary entrance  and the capillary end.

Fig. 2: Three different possibilities for cell tissue construction. On Fig. 2a1 the interstitium above the capillary wall is open (this is valid of column 1) and here the interstitial hydraulic pressure IHP is constant, being determined by the height of the water column. Fig. 2 a2 shows a soft tissue, e.g., the subcutaneous tissue (this is valid of column 2), in a state of oedema, and Fig. 2a3 presents schematically a cell tissue, which should possess sufficient internal bindings so as to withstand the loading by Pc, e.g. the muscle tissue (this is valid of column 3). A, C and V designate the arterial, capillary and venous part of the blood vessels. Pc and pd are respectively the mean pressure in the capillaries and the oncotic pressure difference upon the capillary wall; I = interstitial space.

Fig. 3: Sometimes the dimensions of the capillary or the way of its incorporation in the surrounding tissues allows it to be considered as an element with only one pore or with a ring of pores. In that case, COP and the blood pressure act opposite each other and the influence of COP cannot be compensated, although the interstitium is closed (Figs. 3a1 and 3 a2).

It can be seen from Figs. 3b1, 3b2, 3b3 and 3b4 that the compensation of COP may occur only with capillaries, which may be presented as elements with at least two or more (Fig. 3a3) pores, or with at least two or more rings of pores, respectively. The liquid medium in the interstitium is the link along the chain, so that, for instance, the suction force of COP at the end of the capillary to be transmitted with the opposite sign to the suction force of COP in the beginning of the capillary, Fig. 3b3. In this way, the forces of COP, acting along the capillary, mutually reduce each other to zero (Fig. 3b4).

Fig. 4. 4a: Describing of a capillary segment with elementary length Dl and the elementary values Cm, Ri, Rq, Rc and pdm. The set of numerous such segments forms the summary substituting configuration, which is shown on Fig. 4b with 11 capillary segments. Rc0 and Rv are here the resistances of the blood vessels before and after the capillary. In Fig. 4b the resultant value of the oncotic pressure pd is designated with the initials COP. PCA and PCE are respectively the blood pressure at the entrance and the blood pressure at the end of the capillary.

Fig. 5. 5a: The pathological situation of lungs filled with water corresponds quite correctly to Starling's hypothesis and can be used for demonstration purposes. 5b: The substituting capillary configuration of pulmonary oedema in accordance with Fig.5a and Figs. 4a and 4b. 5c: Distribution of the transcapillary flux along the capillary at a definite moment in time t = 150s (cf. Fig. 5d). It is interesting to note that the base line in Fig. 5c shifts downwards under the influence of the constant IHP. 5d: Dependence of the transcapillary flux on time for different values of the blood pressure Pc and the oncotic pressure difference pd, designated here with COP, see Fig. 5e.

Fig. 6: Simulation of the capillary fluid exchange for intact tissue according to the substituting configuration on Fig. 4b. 6a: Dependence of the transcapillary flux on time for tissues with a non-elastic interstitium - on Fig. 4b for Ci= 0 in all segments. The positive leap of COP at 150ms has no influence on the processes of filtration and refiltration. On the other hand, the interstitial hydraulic pressure IHP (Fig. 6f) makes a momentary leap in the negative area. 6b: In the tissue with elastic interstitium, each leap in the blood pressure or in COP generates a transient process with a definite duration. 6c: Graphic image of the blood pressure in the beginning of the capillary and of COP for all capillary segments. 6d: Considerable changes in the tissue elasticity Cm and in the values of the resistances Ri : Rq : Rc do not induce qualitative changes in the type of the transient process (cf. Fig. 6b). 6e: Detailed image of the graphs on Fig. 6d around the zero line. 6f: Change in the interstitial hydraulic pressure IHP in a tissue with a non- elastic, and in Fig. 6g - with elastic interstitial space, respectively. 6h: In the intact tissue the ratio between filtration and refiltration is preserved and the system remains stable even after a manifold rise in the blood pressure.

Fig. 7: The blood supply to the tissue with the help of capillaries is normally a pressure-perfusion transversely across the tissue. Moreover, the interstitial flux is distributed according to Ohm's Law in the same way as the small balls placed in a suitable bag are washed by a water jet (Fig. 7a). Here the water pressure regulates the speed of the washing and the system remains stable until the bag in which the balls are placed bursts. With more prolonged washing, the small balls which obstruct the strongest jet line will be pressed to the sides, forming a channel in the middle, as shown on Fig. 7b. The principle of this washing will not change, if a water-permeable membrane is gradually formed on the inner surface of this channel (Fig. 7c). In this way, Ohm's Law as a fundamental principle in hydraulics and the channeling effect of hydraulic pressure are the most important mechanisms facilitating the formation of new capillaries in the traumatized and oedematous tissue after injury. 7d: Stylized presentation of the tissue to visualize the action of Ohm's Law: the areas at a greater distance to the capillary wall are less perfused, because they exercise a higher hydraulic resistance to the fluid flux.

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