Final Affirmative Proof Starling’s Law Wrong and G Tube Hydrodynamic is the Correct Replacement: New Results and Critical Analytical Criticisms of Impactful Landmark Articles

There are 21 reasons affirming Starling law is wrong on both of its forces and equation. The main study based on which Starling’s hypothesis was transferred into a law has a serious experimental error that invalidates it conclusion. The Tree Branching Law corrects 2 widely received misconceptions on capillary physiology: “The capillary crosssection area is greater that the aorta” and “the speed of blood flow in lumen is very slow”


Introduction
This article reports new porous orifice (G) tube results based on new insights, re-analysis, and interpretation of previously reported results. It also addresses issues that critically and analytically articles on the wrong Starling's law [1,2]. The first article is an account on: "Mathematical model to determine the effect of a subglycocalyx space" that aimed to prove the Revised Staring Principle (RSP) as paradigm for reviving Starling's hypothesis. My article here demonstrates that this is a futile attempt. The second article [3] that also defends Starling's hypothesis by highlighting the role of precapillary sphincter in regulating blood flow, speed, and pressure of the capillary to the cerebral cortex in rats, in which it is wrongly concluded it maintains cerebral tissue "perfusion" in the title. It is demonstrated here that the derived calculations are based on wrong formulae producing wrong results, graphs, and conclusions in article [4,5]. The authors are not at fault, but they were misled by wrong hypothesis and inadequate law and formulae. The  law is proved wrong." [6]. I agree with Hahn et al, but I think that their call for further clinical validation of RSP is unnecessary. I predict and warn authors that further clinical validation of RSP or any related research will prove to be total waste of energy, money, efforts, and time. I had previously reported 21 reasons [7] affirming Starling's law on the capillary-interstitial fluid (ISF) transfer wrong and the correct replacement is the hydrodynamic of G tube [8][9][10][11].
All the 21 reasons, plus more added here later, cannot be denied or refuted. Before that of course I had reported the physics study on the G tube as preliminary report at Medical Hypothesis in 2001 [8], emphasized 2017 [9] and the physiological evidence was reported also in 2017 [10] and concluded a plenary evidence reported in 2020 [11], titled: "The Correct Replacement for the Wrong Starling's law is the Hydrodynamic of the Porous Orifice (G) Tube: The Complete Physics and Physiological Evidence with Clinical Relevance and Significance".
This intellectually and experimentally based theory on the hydrodynamic of the G tube as replacement for the wrong Starling's law is probably the most solidly concrete, thoroughly convincing, conclusive, extraordinarily impeccable, and theoretically provable discovery of all time that provides an overwhelmingly clear manifestation of the scientific physics, physiological and medical discovered truth. To clear any misunderstanding, I find discussing the following issues necessary. A "best critic" of mine, I wish I can call him a friend, brought this recently reported article [1] to my attention but refused to have his name mentioned or acknowledged. He also sent me this article published recently in Nature Communication [2]. When I sent him a copy of my Latter to Editor (LTE) of Nature Communications, he replied by email saying: "As an experienced manuscript reviewer, allow me to explain that your letter is immediately unacceptable to a reputable journal because your tone is in places over-effusive and patronizing, and in others insulting.
It shows total disregard to the Journal's Instructions for Authors." The text of this LTE is reproduced as part of section 7 of the discussion in this article. I immediately wrote back to him and apologized for sounding like that; explaining that I have never intended or wanted my tone in writing or saying to be over-effusive, patronizing, or insulting. I always read and follow the journal's instructions for authors. I invited him to demonstrate his criticisms and suggest alternatives that I shall implement in all future writing, He has not replied. I also wanted to say that: "My only interest is to propagate the bare scientific truth based on the results of sound experimental research work with total disregard to politics." I am in the business of science and medicine not politics. If reporting the truth sounds insulting to someone that is tough as he/she will not get an apology for that. What makes my writing sound hierarchical and authoritative is the power bestowed on me while presenting and defending the scientific truth. Personally, however, I am most sincere, polite, easy going person and flexible in life who is easy to convince with the truth but powerfully rejects what is untrue or There is nobody else in the whole world who reported on issues that is self-referenced here or in any other article of mine. The editors, peer reviewers and readers may challenge me on that by producing one reference that may replace any of mine, and I shall replace mine with it immediately.
Also, there seems that nobody is taking notice of what I report or say and the whole Scientific and Medical World seem to be not just asleep but in a state of deep coma [12]. presents with cardiovascular shocks of VOS and later with all the manifestations of the multiple organ dysfunction syndrome (MODS) or ARDS [13,14].
The primary endpoint objective of this article is to provide substantial, solid, unquestionable, and convincing plenary evidence for the theory that the G tube phenomenon as the correct replacement for the wrong Starling's law. The secondary endpoint objective is to cross the firewall and open the closed shut gates to reputable top journal to report this article by convincing its editors and peer reviewers of the validity, correctness and worthiness of the G tube theory presented her. There is also a deeper important objective for reporting this final article. I am certain it will help to save hundreds of thousands of ARDS patients' lives who die all over the World every year [13,14]. The wrong Starling's law is the real culprit inducing VOS [15,16] that cause ARDS [13,14]. This will satisfactorily fulfil my pledge to the 3 patients I witnessed being killed by a condition known in urology as the TURP syndrome [17] as example of VOS1. This was back in 1981 at the Urology Department, District General Hospital, Eastbourne, UK where I was working as Senior House Officer.
The TURP syndrome is induced by sodium-free fluid overload or volumetric overload type 1 (VO1) characterized with acute dilution hyponatraemia [17]. It has similar clinical picture to ARDS of MODS, though coma of hyponatraemia predominates in the TURP syndrome. VOS are of 2 types: VOS1 and VOS2. The TURP syndrome is an example of VOS1. As for VOS2 it is induced by volumetric overload of sodium-based fluids type 2 presenting in theatres with shock or cardiopulmonary arrest. VOS2 Has no clear markers like hyponatraemia of VOS1. Both types of VOS cause ARDS that complicate fluid therapy but are unrecognized and underestimated.
Starling's law misleads treating physicians into giving too much fluid for the resuscitation of shock, acutely ill patients and patients undergoing prolonged major surgery inducing VOS that cause ARDS [13,14]. This explains how and why these major investigations Section 6 shall criticise the report by Pappenheimer and Soto-Rivera on investigating the capillary hydrostatic pressure. This is the report after which Starling's hypothesis was transferred into a law with equations. A serious experimental error by the authors is identified and reported. Section 7 shall demonstrate how this current impactful article [2] was criticized objecting to the word "perfusion" in the title and recommending a correction of serious errors in results, graphs and conclusions highlighted by the use of the word "perfusion" in title that supports Staling's law. Section 11 demonstrates the red blood cells (RBCs) speed or capillary blood speed (CBS) is not "very slow" as generally believed but rather fast as it has a fast speed at start in the pre-capillary sphincter that extends as fluid jet with descending gradient along the wider lumen tube: it ejects from the precapillary sphincter into capillary as it does from the orifice to the wide lumen of the G tube.
Section 12 is on correcting the received error that the crosssection area of all the capillaries is very much greater than the aorta based on which a formula wrongly produces "very slow and fixed speed" of RBCs speed or CBS in the functional capillary. This correction is based on the G tube's newly presented results showing fluid flow (akin to CBS) is fast with a dynamic descending gradient of velocity along the length of the wide section of the tube (G tube and capillary). Section 13 is on missing data from precision engineering microvascular and capillary ultrastructure anatomy, and correct physiology on pressure and RBCs speed or CBS and suggestions for future research. Section 14 is a brief statement testifying that the authors of articles [1] and [2] have not done anything wrong. They were only misled by the many errors and misconceptions gathered over the decades that produced wrong law and formulae which produce wrong results and conclusions in article [2]   shows Poiseuille's tube hydrodynamic with positive side pressure along the entire length of the tube causing fluid to filter out maximum near the inlet and minimum near the exit. This is what Starling had based his hypothesis on regarding the hydrostatic pressure causing filtration maximum near the orifice. This will be compared to the hydrodynamic of the G tube ( Figure 2) built on a scale to capillary ultrastructure of pre-capillary sphincter and intercellular clefts making wide capillary pores that allow the passage of molecules larger than plasma proteins. shows the hydrodynamic of the G tube's with side pressure gradient lower at the inlet where it is negative and turns into positive pressure maximum near the exit, with visible magnetic field-like circulation around it seen at your top right hand quarter of the photo-based on which and other photos shown below, the diagram showing the G-C circulation was drown ( Figure 5). There is negative side pressure gradient over the proximal part of G tube not shown here but is shown in (Figure 4).

Figure 3:
shows a full set of G tubes in the middle fitted with orifice diameter ranging from 2 mm inner diameter to 6 mm, and 7 mm is the G tube inner diameter. Poiseuille's tube of strait uniform diameter (7 mm) with smooth inner surface (G tube without orifice) is at the bottom of the photo. At the top is the G tube enclosed in chamber C (G-C apparatus) with connection for manometers ready for enclosing in a circulatory model (Provided free of charge by Designer Engineer Peter Holder of Eastbourne, UK in 1983).

Figure 4:
shows a rubber orifice tube's negative side pressure gradient maximum near the inlet, turning into positive pressure maximum near the exit as shown in (Figure 2), with visible magnetic field-like circulation around it seen at your top righthand quarter of the photo-based on which and other photos shown here, the diagram showing the G-C circulation was drown ( Figure 5). This rubber orifice tube was also used for measuring the flow pressure (FP) and side pressure (SP) which are dynamic components of the lumen pressure (LP) induced by the proximal pressure (PP)-akin to arterial pressure. See the last 2 figures (Figures 17,18) below for more details on FP and SP of both Poiseuille's tube and the G tube. Figure 5: shows a diagrammatic representation of the hydrodynamic of G tube based on G tubes and chamber C seen in ( Figure  6). This 37-years old diagrammatic representation of the hydrodynamic of G tube in chamber C is based on several photographs shown here. The G tube is the plastic tube with narrow inlet and pores in its wall built on a scale to capillary ultra-structure of precapillary sphincter and wide inter cellular cleft pores, and the chamber C around it is another bigger plastic tube to form the G-C apparatus. The chamber C represents the ISF space. The diagram represents a capillary-ISF unit that should replace Starling's law in every future physiology, medical and surgical textbooks, and added to chapters on hydrodynamics in physics textbooks. The numbers should read as follows: 1.
The inflow pressure pushes fluid through the orifice.

2.
Creating fluid jet in the lumen of the G tube**.

3.
The fluid jet creates negative side pressure gradient causing suction maximal over the proximal part of the G tube near the inlet that sucks fluid into lumen.

4.
The side pressure gradient turns positive pushing fluid out of lumen over the distal part maximally near the outlet.

5.
Thus, the fluid around G tube inside C moves in magnetic field-like circulation (5) taking an opposite direction to lumen flow of G tube.

6.
The inflow pressure 1 and orifice 2 induce the negative side pressure creating the dynamic G-C circulation phenomenon that is rapid, autonomous, and efficient in moving fluid and particles out from the G tube lumen at 4, irrigating C at 5, then sucking it back again at 3,

7.
Maintaining net negative energy pressure inside chamber C.
**Note the shape of the fluid jet inside the G tube (Cone shaped), having a diameter of the inlet on right hand side and the diameter of the exit at left hand side (G tube diameter). I lost the photo on which the fluid jet was drawn, using tea leaves of fine and coarse sizes that runs in the centre of G tube leaving the outer zone near the wall of G tube clear. This may explain the finding in real capillary of the protein-free (and erythrocyte-free) sub-endothelial zone in the Glycocalyx paradigm. It was also noted that fine tea leaves exit the distal pores in small amount maintaining a higher concentration in the circulatory system than that in the C chamber-akin to plasma proteins.

Figure 6:
shows the G tube enclosed in chamber C (The G-C apparatus). The negative side pressure of G tube also creates a negative pressure in C shown here to suck the red water from a jar 300 mm below G tube into the manometers.

Figure 7:
shows the G tube enclosed in a rubber chamber (C) which is sucked in not ballooned out demonstrating the negative pressure in (C) akin to the negative pressure measured by Guyton and Colman [17] using a subcutaneous implanted chamber-a remarkable fact that cannot be explained by Starling's forces.     The fluid inside the surrounding chamber C runs in the opposite direction. This is demonstrated by injected ink into the distal part of the chamber C moving towards the orifice for reabsorption through proximal side holes into the lumen of the G tube. Also, noted the distal pressure (DP), akin to central venous pressure (CVP) of the circulatory system of maximum 12 cm water; usually DP is 7 cm in this model.  Figure 13: shows the G tube in G-C apparatus connected to circulatory model driven by electric pump. The proximal pressure (PP) akin to arterial pressure is above 100 cm water when the distal pressure (DP) is less than 7 cm water. The pressure in the chamber around the G tube is less than DP. Furthermore, the pressure in C manometers is lower near the inlet than it is near the exit. So, suction or reabsorption of fluid occurs through side holes near the inlet while filtration occurs through side holes near the exit. This creates the dynamic magnetic field like circulating fluid inside G tube (capillary) with that in the surrounding C that has net negative pressure akin to ISF space that gets well irrigated without oedema formation. Irregularities of the inner surface of the G tube perturbed the G-C circulation and caused elevation of pressure in C akin to oedema formation, this may explain the importance of Glycocalyx; being normally smooth but sepsis causes irregularities. Also elevating DP akin to elevated CVP augments oedema formation as does low PP akin to hypotension of the circulatory system.  (13), just by elevating the pump above the level of G tube. The DP now reads <12 cm water. PP is >70 cm water. Also, the CP in both manometers turns positive but, still lower than DP of +7 cm water near the inlet and +9 cm water near the exit. So, the flow in Chamber C is in the opposite direction to flow in the system from exit to inlet of the G tube.   [24,25] that cause the acute respiratory distress syndrome (ARDS) [13,14].

Figure 16
: shows the hydrodynamic of the G tube (without surrounding chamber) connected to a garden hose. It shows lower PP of 24 cm water and DP of 12 cm water and the side pressure gradient higher positive maximum at exit. The negative SP near the inlet is not shown here but is demonstrated elsewhere (Figure 4,5). The pressure gradient also demonstrates the direction of flow in the G tube from right to left hand side. The system is continuously overfilled from a water hose to replace the water loss from the holes of the G tube. Please, note that the proximal and distal pressures before and after the G tube shows values of 24 and 12 cm water, respectively, that are lower than and equal to mean pressure at proximal and distal pressure obtained in a real capillary by Landis of 32 and 12 mmHg (see text) and still induce the G tube phenomenon as shown here and in (Figures 2,5). The two insets on the left show that applying DP by increasing DP up to 12 cm water (in the circulatory system by volumetric overload) the G tube phenomenon still operates ( Figure 5). Increasing the DP from 12 to 20 cm reverts the negative SP to positive with increasing volume and pressure in chamber C ( Figure 11). The measurements of the fluid jet as it leaves the exit of the rubber G tube are shown.

New Results on the Hydrodynamic of the G Tube and
Applicability to Hemodynamic of the Capillary    This probably means no relation between FP and the G tube's length. A line connecting PP to DP in the above graph represent the descending gradient of FP from inlet to exit of the G tube.  shows the relationship between SP to tube Diameter and length of the G tube which demonstrate a negative SP starting at the orifice (Point 2) (akin to precapillary sphincter) and extends as high negative pressure gradient over the proximal part of the G tube (Point 2-6) to cross 0 line at point 8 and then turn positive of 7 cm water at Point 9. Data are taken from ( Figure 17). This SP gradient from orifice at Point 2 to G tube lumen {Points 2-6) is negative to become positive DP at point 9 of 7 cm H20 water along the G tube. The wide section diameter of G tube is 7 mm all along the entire tube. The orifice is 5 mm while the distance from orifice to exit represent the tube' length in which the Fluid jet diameter change with increasing gradient ( [2] as shown in the legend of ( Figure 30) written by the authors. At the precapillary sphincter (arterial end) the RBCs speed is 8.7 mm/s and at venous end is 4.7 mm/s at best expectaion that is based on the wide capillary tube diameter for which the equation gives a single value that is wrongly assumed to apply for the whole wide section tube.  b) The SP gradient for (SP and (∆SP) as measured in the G tube ( Figure 17, 18) c) The fluid jet diameter (Dj) at precapillary sphincter and at exit (Dj inlet and DJ Exit) ( Figure 5). d) The fluid jet length (Lj) ( Figure 17) and tube length (L).

e)
The CBS or RBCs speed at start and end of the capillary (CBSinlet and CBSexit) as suggested to be done in future at both arterial and venous ends of the capillary by Stucker et al. [21].
However, as all the above dynamic variables are measurable the equation may be easier than one might think.
To predict the correct speed of RBCs or CBS a line connecting the   (Figure 27&28) is adequate for inducing the G tube phenomenon between the capillary and ISF space.

Figure 28
: shows the RBCs speed or the capillary blood speed (CBS) at the precapillary sphincter and capillary lumen reported by Ivanov et al. [31]. The black line represents the slope of speed gradient. This is very much like the graph in ( Figure 27). This speed gradient is adequate for inducing the magnetic field-like phenomenon of fluid exchange between capillary lumen and the ISF space as demonstrated in the G tube ( Figure 5).
Data from the G tube on FP fits quite well with data from the capillary anatomy and physiology on the same graph (Figures 29).
The capillary is the G tube, and the G tube is the capillary.  shows data on capillary compared with the G tube pressure at inlet and exit. The capillary pressure, speed and diameters at inlet and exit fits well with the G tube pressure at inlet and exit. There is a perfect fit between the G tube and capillary together in one graph. Data source on the capillary are published reports by authors of references [2,23,25]-after correction for the CBS figure in [25], and for the G tube pressure data is taken from (Figure 16). The pressure values are in the same range and thus applicable and compatible. The proximal driving pressure in the capillary is higher than that in the G tube. This may answer the accusations of the G tube Theory concerning applicability of its hydrodynamics to the capillary hemodynamic (See text under Section 10: criticizing the G tube Theory).  (Figure 2g). The authors stated in the figure's legend: "At rest, the average RBC velocity through precapillary sphincters were 8.7 ± 0.6 mm/s (Figure 4c), significantly higher than for the bulb (3.6 ± 0.6 mm/s) and the first order capillary (4.7 ± 0.6 mm/s), but correlated with the relative differences in the resting diameters of the vessel segments. As shown in Figure 2g, high RBC velocity through the narrow lumen of the precapillary sphincter amplifies the reduction in pressure across the sphincter due to high shear, i.e., augments the reduction of pressure from larger proximal PAs to downstream capillaries. From the baseline measures, the pressure drop per unit length is 4-times larger in the sphincter than the first order capillary, assuming that RBC velocity and fluid velocity are equal (see Figure  2g). During whisker stimulation (Figure 4c), both diameter and RBC velocity increased in each segment, but significantly more at the precapillary". In contrast Stücker et al. [26] reported a rather too slow RBCs speed of 0.47 mm/s in human capillaries that cannot be correct. It may be due to a typing error misplacing the decimal point. A study measuring the actual and exact RBCs speed or CBS at both the arterial and venous ends of the capillary remains to be done. This suggested study is strongly recommended for the validation of CBS. Please, note that P, D and L plus (∆P and D2) in the equation above and in Poiseuille's equation need precise definitions to produce accurate results that represent the G tube's diameter at exit and the related accurate RBCs speed or CBS also at exit only. A line connecting CBS at precapillary sphincter of 8.7 mm/s to that at capillary exit of 4.7 mm/s represent the descending gradient of CBS along the capillary lumen ( Figure 29).
all. of the fluid jet inside the lumen of the G tube which changes from 5 to 7 mm or as ratio from 0.7 to 1 as the diameter of the orifice or capillary sphincter and G tube, respectively. This orifice/tube ratio is the equivalent of 0.5 cross section area of the G tube. In a circulatory model the fluid jet is separated from the tube's wall by particle free layer lining the smooth glycocalyx layer that lines the endothelium wall. As all the above variables are measurable, the equation may be easier than it appeared initially.

Discussion
The above results demonstrate that the Poiseuille's tube has a positive SP causing filtration all along its entire length which is maximum near the inlet and lower near the exit (Figure 1). The side pressure in the G tube causes negative pressure gradient exerted on the wall that is maximum negative near the inlet ( Figure 4&5SI) and turns positive pressure maximum near the exit ( Figure 2SI). Thus, absorption of fluid occurs through proximal holes maximum near the inlet and filtration occur through distal holes maximum near the exit of the G tube. This negative SP gradient of the G tube creates unique autonomous rapid magnetic field-like fluid circulation between fluid inside its lumen and that surrounding it in chamber C (Figure 2 & 5SI). The net pressure in a surrounding chamber C is also negative ( Figure 5-7 SI). These findings have important serious implications of relevance to the capillary physiology [7][8][9][10][11] and high clinical significance [13][14][15][16] as summarized here.
The physiological relevance of the hydrodynamic of the G tube to normal capillary physiology. The presented evidence demonstrates that the hydrodynamic of the G tube is totally different from Poiseuille's tube. This is relevant to the physiological function of capillary regarding the capillary-ISF transfer currently attributed to Starling's forces. When Starling proposed his hypothesis on the formation of oedema in 1886 and 1896 [21,22], he assumed that the capillary works as Poiseuille's tube of uniform diameter and its hydrostatic pressure induced by the high arterial pressure is responsible for filtration of fluid higher over the proximal part of the capillary. It was discovered >80 years later in 1967 that the capillary has a narrow orifice; the precapillary sphincter [18].
Hence the capillary is a G tube not Poiseuille's tube. Starling also wrongly assumed that absorption of fluid is induced by the oncotic pressure of plasma proteins (albumin) as he thought that the capillary wall is impermeable to albumin. It was also discovered in 1967 that the capillary has wide pores of intercellular clefts that allow molecules larger than plasma proteins such as horse radish to pass through as reported with photographs by Karnovesky [19]hence nullify oncotic pressure in vivo. Starling's hypothesis was made into a law with equations later after Pappenheimer and Soto-Rivera's report in 1948 [24] despite their serious experimental error. Based on these above facts the capillary hemodynamic should work as G tube not Poiseuille's tube that simply proves Starling's hypothesis and law with equation are wrong on both forces. In fairness to Professor Starling, who was a great physiologist, he never wrote any equations nor proposed a law. I have reported 21 reasons affirming Starling's law is wrong [7]. Here I affirm that Starling's law is wrong on both of its forces [8][9][10][11], and the equations must be also wrong. This applies the principle of what is built on wrongdoing must also be wrong.
Both physics [8][9][10][11] and physiological [10] evidence demonstrate that the capillary works as G tube in which the arterial pressure induce negative side pressure gradient that causes absorption by suction not filtration that occurs maximally near the inlet. This is based on hydrodynamic of the G tube presented here.
It has also been demonstrated that the oncotic pressure does not exist in vivo as the capillary has wide intercellular cleft pores that allow molecules larger than plasma proteins to pass through it [19].
Hence the oncotic pressure does not exist in vivo [7][8][9][10][11]. Starling's law is thus wrong on both of its forces and the equations must also be wrong.
The new results reported above affirm that not only Starling's law is wrong but also provide the correct replacement for it: The  [26]. These errors mislead physicians into giving too much fluid during the resuscitation of shock, acutely ill patients, and prolonged major surgery [27]. It thus induces the volumetric overload shocks (VOS) [15] also reported as volume kinetic (VK) shocks [16] that cause the acute respiratory distress syndrome (ARDS) [11,13,14].
Not only the exact patho-aetiology of ARDS was identified but also a possible prevention and curable therapy is advanced and recommended [13,14]. So, ARDS is not caused by sepsis and Covid-19 only but also by VOS though remaining unrecognized and underestimated. Sepsis is manageable using appropriate and adequate powerful antibiotics that exist today. Covid-19 that kills its victims by inducing ARDS is transient and will soon go away or a vaccination will materialize that puts it dormant in history like other eradicated infectious diseases by the effective vaccination. The faulty Starling's law is the primary culprit responsible for the death of hundreds of thousands of ARDS patients every year all over the World [11,13,14,28]. This is preventable and curable when the truth on the G tube discovery can prevail and shine. All should welcome the new discoveries in physics, physiology, and medicine [12]. The physics, physiological and clinical evidence is so overwhelming that it justifies saying farewell: "Goodbye Starling's law, hello G tube" [29]. The second endpoint objective of this article is a final attempt to persuade editors, peer reviewers as well as my The reported RBCs speed or CBS varies from capillary to another and from report to another both in humans [25], and in rats [1,[30][31][32]. Such variation is expected even in the same capillary from point to another as there is a speed gradient from the precapillary sphincter to exit of the capillary. What matters most here is the speed gradient along the wide lumen tube of G tube and capillary that is responsible for the magnetic field-like flow of fluid between capillary lumen and the surrounding ISF space. Ivanov et al. [31] reported: "The mean linear red cell velocity for 100 cerebral capillaries 2-5 μm in diameter was found to be 0.79 ± 0.03 mm/sec.
In the temporalis muscle the velocity was equal to 1.14 ± 0.04 mm/ sec in 123 capillaries and 2.43 ± 0.08 mm/sec in 34 arterioles and pre-capillaries not more than 5 μm in luminal diameter." Ishikawa et al. [32] reported: "Average RBC velocity in the capillary is between 0.73 and 0.99 mm/s." Guevara et al. [33] reported: "The mean centreline RBC velocity in normal rats varied between 1.0 and 9.0 mm/s (most of the measurements were taken in vessels ranging between 20 and 80 microns in diameter). As the diameter of the pial artery becomes smaller, the blood flow rate (pi x (diameter/2)2 x (mean centreline velocity/1.6)) tends to become smaller." Stücker et al. [25] reported on Resting capillary Blood Velocity in humans: "The mean capillary blood velocity (CBV) rest was 0.47 mm/sec (SD ± 0.37 mm/sec, range 0.14 to 0.93 mm/ sec). The average intraindividual difference between max rCBV and min rCBV was 0.  (Figure 27). This is most important for two fundamental reasons:

1.
It rejects the generally received misconception on RBCs speed in the capillary being "too slow".

2.
It proves that the magnetic field-like phenomenon of G tube occurs between the capillary and ISF space.
Hence, I shall consider the 3 possible scenarios for the RBCs speed in the capillary:

1.
Assume that an error of placing the decimal point was  found to be 0.79 ± 0.03 mm/sec. In the temporalis muscle the velocity was equal to 1.14 ± 0.04 mm/sec in 123 capillaries and 2.43 ± 0.08 mm/sec in 34 arterioles and pre-capillaries not more than 5 μm in luminal diameter." The figure of 2.43 mm/s is that at the precapillary sphincter and 1.14 mm/s is for the speed at the capillary exit. The slope of the speed gradient in that case is shown in (Figure 28)  where we know the speed at the precapillary sphincter is high of 8.7 mm/s and at the exit is 4.7 mm/s. So, there is a definite descending speed gradient along the capillary (Figures 27,28). The SP is also negative causing suction at the orifice or precapillary sphincter well known as Venturi's effect (Figures 23,24). So, a modification of the equation to yield both speed gradient and negative SP gradient is in order, and the graph should show this negative side pressure gradient over the G tube or capillary length.
The low PP shown in (Figure 16) of this report is lower than the MHP measured by Landis at the arterial end of the capillary and is certainly adequate for inducing the dynamic FP and SP in the capillary as shown in the G tube (Figures 19-29). In the capillary as in the G tube, the speed of flow in the capillary shown in Dr Mayrovits' video is "very fast", and certainly cannot be described as "very slow" as generally believed and taught in current classical teaching on the capillary circulation, so there is no "diffusion" here and the word must be corrected in the title of this article [2]. In fairness to Professor Starling, who was a great physiologist, these authors [4] correctly wrote: "When Starling proposed his hypothesis in 1896 [22], on the capillary interstitial fluid (ISF) transfer and oedema formation he never wrote equations nor proposed a law." Starling's hypothesis was transferred into a law after Pappenheimer and Soto-Rivera report in 1948 [24].
The ultrastructure anatomy of the capillary of the precapillary sphincter and the inter-cellular cleft pores were discovered in 1967, by Rhodin [18] and Karnovesky [19] respectively. The wide intercellular capillary pores nullify the oncotic pressure in vivo.
Ghanem reported the hydrodynamics of the G tube as preliminary report in 2001 [8] demonstrating its relevance to the hemodynamics of the capillary and as well as its clinical significance proposing the G tube phenomenon of magnetic fieldlike fluid circulation between the capillary lumen and ISF space as the correct replacement for Starling's law and hypothesis [8][9][10][11]. I shall leave it up to history, that will certainly be kinder and fairer to me than some editors of top Science and Medical Journals, to decide if my name is worth mentioning at the end of the above list as based on my contributions about G tube physics and capillary physiology [6][7][8][9][10][11] and resolving the puzzle of ARDS [11,13,14] as well as identifying 2 new volumetric overload shocks [15,16]. Not only the exact patho-aetiology of ARDS was identified but also a possible preventable and curable therapy was suggested [13,14].
History may record: "Ahmed N. Ghanem is a man doctor surgeon who was Eastbourne and educated up to university degree in Egypt, came to Eastbourne in the United Kingdom for further postgraduate education and training to demonstrate to scholars' peers in the West later that the impossible can be achieved and made possible without external funds whatsoever."

C. Section 3: Hydrodynamics of the porous orifice (G) tube:
What are the new physics discoveries of physiological relevance?
The results of the presented study clearly indicate and recognize the following new discoveries of the G tube: There is a major difference between the hydrodynamic of Poiseuille's tube and that of the G tube as compared in (Figures   1 and 2 SI). There is also a difference between the hydrostatic in this video is "very fast", and certainly cannot be described as "very slow" as generally believed and taught in current classical teaching on the capillary circulation. As mentioned here later the RBCs speed or CBS is 8.7 mm/s at the pre-capillary sphincter and 4.7 mm/s at the exit of the capillary reported in rats [2] and in humans with uncanny similarity after correction [25]. The speed gradient between the two recorded speeds is that that matters in inducing the G tube magnetic field like phenomenon in the capillary. The RBCs speed or CBS run down a slope of gradient from pre-capillary sphincter to exit of the capillary, from 8.7 mm/s to 4.7 mm/s [2]. This speed gradient induces the magnetic fluidlike flow phenomenon of the G tube between the blood flow in capillary lumen and the surrounding ISF space. This FAST capillary-ISF transfer is essential for the viability of tissues and cells under rest conditions and strenuous exercise. Substantial evidence on this issue with supporting graphs is reported here, particularly as the driving pressure in the capillary of 32 mmHg [2] is higher than proximal pressure in the G tube of 24 cm water. In support of the above fact is: High venous pressure, or obstruction, is the main cause of the most common clinical oedema but arterial hypertension though quite common it never causes oedema. Off course neither Starling nor any of the authors who transferred his hypothesis into a law were aware of the brilliant discoveries of precapillary sphincter [18] and wide porous wall of intercellular clefts of the capillary that allow the passage of plasma proteins thus nullifies oncotic pressure in vivo [19] that were discovered later in 1967. The G tube discovery demonstrate PP akin to arterial pressure induce negative pressure gradient exerted on the tube's wall that is maximum near the inlet causing suction or absorption. So, both Starling's forces are wrong.
The same wrong conception that elevating CVP to levels of 20-22 cm H20 may elevate the arterial pressure in shock by infusing too many fluids was prevailing in clinical practice till recently.
Fortunately, such practice has stopped now since it was realized that it induces volume kinetic shocks [15,16] that cause ARDS [13,14,28]. It is worth mentioning the relation of G tube orifice diameter to SP of the G tube and the surrounding chamber C pressure (CP) shown in (Figure 9 SI). This is relevant to the negative ISF pressure measured by Guyton and Coleman subcutaneously to be of -7 cm water [20]. This negative pressure of the ISF space can only be explained by hydrodynamics of the capillary working as G tube (Figures 4-7

This is a common and prevailing physiological misconception that
RBCs speed in the capillary is "very slow" to allow for the slow "perfusion" of fluid and particles from the capillary to ISF space and cells found in all current textbooks and physiological teaching on the capillary-Interstitial fluid (ISF) transfer.
The word "perfusion" is based on the currently accepted physiological law of Starling's forces that are generally believed to regulate the capillary-ISF transfer through "perfusion" balance influenced by its 2 main forces. The 2 main forces of Starling's law believed to induce this "perfusion" balance state are the hydrostatic pressure of the capillary causing filtration, and the osmotic (oncotic) pressure of plasma protein (albumin) causing absorption.
Here I demonstrate that Starling's law is wrong on both forces and the correct replacement for it is the hydrodynamics of the porous orifice (G) tube. The physics evidence was preliminary reported in 2001 [8], emphasized 2017 [9] and concluded in 2020 [11]. The physiological evidence was reported in 2017 [10].
The porous orifice (G) tube was built on a scale to the capillary ultrastructure anatomy of precapillary sphincter [18] and the wide intercellular cleft pores [19] that allow the passage of plasma proteins, hence nullify the oncotic pressure in vivo. Investigating The value of the Venturi's effect or ΔP at the precapillary sphincter should be expressed as a negative unit of pressure (-mmHg, or -cm H 2 o or -Pascal)-the negative sign is a must over in the orifice of precapillary sphincter and the proximal part of the capillary and should also show in the graph (Figure 2). There is no negative sign in Poiseuille's law shown above or its modification that allows for such calculation. So, the graph (Figure 2) is wrong. This is just one example of other graphs using the derived pressure and CBS in the precapillary sphincter as well as the capillary itself particularly over the proximal part. We now know from the G tube experiments that the fast fluid jet coming out of the narrow orifice of the precapillary sphincter and remains fast for a distance inside the lumen of the proximal part of the capillary as in G tube iii. The fluid jet length (Lj) not the tube L? (Figure 17 SI) iv. The G tube or capillary length for L?
The CBS or RBCs speed at inlet and exit of the capillary (CBSinlet and CBSexit) as calculated and reported by Grubb et al. [2] and Ivanov et al. [31], and after correction of value to 4.7 mm/s in the article by Stucker et al. [25] who suggested that RBCs speed should be measured in future at both arterial and venous ends of  Note that P1 and P2 may refer to the hydrostatic pressure in the tube but does not specify whether it is the flow pressure (FP) or MHP? This P is incorrectly assumed to have a single value that apply to the wide section of a tube after constriction i.e., the G tube wall and all! Certainly, the negative side pressure (SP) is not shown in the equation to account for neither the Venturi effect at the orifice nor the Bernoulli effect at the proximal part of the wide tube that are not represented in the Bernoulli's equation. The shown calculated value for V2=V1 A1/ A2 gives an incorrect low value of ∆P which does not reflect the actual speed of the fluid at orifice and proximal part of the wide section of the tube of capillary and G tube. Calculated negative SP cannot be obtained from this equation at all.
The negative SP at the orifice or precapillary sphincter is well known as the Venturi's effect. The equation used by the authors in It becomes clear that this G-C circulation represents the capillary-ISF circulation as shown in (Figure 5). The G tube phenomenon works in capillaries as based on the physiological evidence [10] as well as modern video on the speed of flow in the capillary circulation (The video is available on Thomas Woodcock's Blog [3] and reported by Dr HN Mayrovits-URL is given above).
The speed of blood flow in the capillary shown in this video is fast enough to induce the magnetic field-like flow phenomenon of the G tube in a capillary. It is worth noting the gradient of RBCs speed or CBS, observed by Stücker [21], along the capillary length that is high at the inlet and low at the exit of the capillary. This CBS gradient is responsible for inducing the G tube phenomenon in the capillary. Furthermore, the reported above data of G tube FP in relation to tube's length and fluid jet length is shown in (Figure 16SI &19).
I trust that the authors [2] have adequate data and capability to correct the erroneous conclusions and the title as based on the given references and report back a correction in Nature as soon as possible. Hundreds of thousands of patients lives per year who suffer from ARDS depend on it as summarized here and explained in detail in previous reports [13,14,28].

I. Section 9: Criticizing Dalwadi et al Mathematical Model
to determine the effect of sub-glycocalyx space that the authors themselves report that this space is of doubtful existence. This is the one section of this article and criticism that I despise most being the heaviest on my heart for fear of upsetting the respected authors to the effect that they might hate me for it. I shall do my best to be as humble, kind, sympathetic, commiserative, and considerate as I possibly can while, like a good surgeon, having to do a necessary major lifesaving but may be painful surgery. Allow me to start by pointing out a contradiction in the authors' statements in the article's introduction. The authors stated that: "The endothelial glycocalyx (eGlx) is a coating found on the luminal surface of most blood vessels [1,2]. Later they stated: "It acts as a molecular sieve for plasma proteins." There is an obvious contradiction in these two statements by the authors [1]. The porous eGlx does not act as molecular sieve for plasma proteins if plasma proteins can pass through it. It does act as sieve for the platelets and cellular elements of the blood not for plasma albumin. So, let us agree that eGlx permits the free passage of plasma proteins but, the fact that albumen only passes in small amounts to the ISF space require an explanation.
Observations from the G tube in the G-C model in a circulatory system on the fine tea leaves' behavior in the circulatory model presented in the diagram in (Figure 5 SI) demonstrate that tea leaves like plasma proteins do pass into the surrounding chamber C (akin to the ISF space) in small amount at distal pores governed by only the kinetics of the fluid passing through the lumen of the G tube and capillary. This happens mostly through the distal pores of the G tube as the small size tea leaves behave in the G-C apparatus demonstrated in the diagram ( Figure 5). Thus, the concentration of the fine tea leaves remains high in the circulation than in the surrounding chamber C around the G tube (akin to plasma albumen and ISF space). The authors also stated "As blood plasma drains from the lumen on its way to the interstitium (ISF space), it first passes through the porous eGlx attached to the endothelial cells.
The impermeability of the endothelial cell body means that in nonfenestrated vessels the only route to the interstitium is through the small gaps between these cells, referred to as the intercellular clefts discovered by Karnovesky in 1967 [19].   [1], its legend read " Figure 1. A schematic of the endothelial glycocalyx and the plasma leakage through it as a cross section through the radial and axial directions of the capillary. As blood passes through the lumen, a small amount of plasma leaks across the capillary wall. This plasma travels through the two-layer structure of the eGlx and then down the intercellular clefts between neighbouring endothelial cells before reaching the interstitium." One added note here is: the mentioned plasma leakage occurs through the distal part of the capillary where SP becomes positive causing filtration that crosses the eGlx then down the intercellular clefts before reaching the ISF space.
The authors are correct in saying: "In nonfenestrated vessels (capillary) the only route to the interstitium is through the small gaps between these cells, referred to as the intercellular clefts [19]." These intercellular clefts were most clearly reported by Karnovesky in 1967 [19], who most clearly demonstrated with photographs that horse radish molecules, which are larger than plasma proteins, freely enter these intercellular clefts and pass to the ISF space. This surely nullifies the oncotic pressure in vivo. Surly you should agree that this fact on its own proves Starling's law and its equation wrong as one of its main forces of oncotic pressure has cancelled out.
Accepting the above may prove that all the complex equations and RSP are totally unnecessary and unrequired, particularly as the authors stated that the sub-glycocalyx space is of doubtful existence. It does not make any difference whether it exists or not as it plays no rule in fluid and proteins flux across the capillary wall! It only provides a smooth inner coating of the blood vessels and the capillary that is crucial for the capillary to function as the G tube.
Any irregularities at the inner surface of the capillary disturbed the magnetic field like circulation.
Further discussion and arguments may no longer be necessary.
End of debate? If not, tell us your concerns and criticisms and you will get a satisfactory answer. Having said that, I believe the authors have a real good chance to develop an equation that determines the fluid flux through the inter-cellular capillary cleft pores based on the hydrodynamics of the G tube and hemodynamic of the capillary.
While they are at it they may try to sort out Poiseuille's law and Bernoulli's equation to allow it to calculate and correctly predict the dynamics of SP exerted on the G tube's wall that causes suction proximally and filtration distally in the wide section of the G tube as happens in the capillary. This is an extremely hard job to do but I trust the authors are up to the challenge. I know they have the knowledge, experience, data, and capability that allow them and colleagues to achieve that. I cordially invite them to do that and I would look forward to seeing the results.
Finally, please may I most humbly and kindly request that the authors do the calm and honorable act of accepting the G tube dynamics as the correct replacement for Starling's hypothesis. Hundreds of thousands of ARDS patients' lives who are killed every year all over the world [13,14] depend on it. Please join in and say a farewell: "Goodbye Starling's law, hello G tube." [27]. The results of experiments in macro tubes such as the G tube may not work in micro tubule such as the capillary.
The pressures in the G tube inducing its phenomenon are too high than that in the micro-vessels and the capillary circulation where speed is believed to be "very slow" in current teaching. This is also based on an assumption that the cross-section area of all the capillaries is much greater than that of the aorta. The speed of fluid flow in the G tube is much too high than RBCs speed or CBS in the capillary, hence the G tube phenomenon is impossible to work in the capillary under such slow CBS. This is particularly important as it is generally believed that RBCs speed and CBS is a "very slow" motion in capillaries to allow for the "perfusion balance" of Starling's forces to take place". My best critic informed me that the hydrodynamic of the G tube working in the capillary is a "physics impossibility".
Then please, allow me to answer to the above criticisms one at a time. If it is argued that experiments in macro tubes may not apply to micro tubules such as the capillaries, then Starling's hypothesis should not have been accepted in the first place and it is invalid now as the hypothesis was based on Poiseuille's experiments in long brass tubes of large uniform diameter [18,19]. A double standard is refused. The G tube hydrodynamic is the real correct replacement for the wrong Starling's law as it was designed on the capillary ultrastructure anatomy. The argument that the G tube phenomena requires high pressure that is not available in the capillary is incorrect. In fact, the G tube phenomenon works under low proximal pressure of 24 cm water as the driving proximal pressure as shown in (Figure 16 SI), which is even lower than the pressure recorded in the proximal capillary by Landis of 32 mmHg at the arterial end. So, the G tube phenomenon does work in the capillary at this low pressure. Please see below for further evidence and discussion with graphs. I shall challenge that received wisdom on the sum of all capillaries' cross-section area is greater than that of the aorta later. The issue on RBCs speed or CBF being too slow is also challenged as discussed here, referring to reported data on it from research in human capillaries [21] and rats [2,[29][30][31] that demonstrate a definitive speed gradient between RBCs speed at orifice of 8.7 mm/s and at exit of the capillary of 4.7 mm/s [2]. This speed gradient is adequate for inducing the G tube phenomenon in the capillary. Answering this criticism is best done by most humbly and simply saying based on evidence reported here it seems that: "achieving the impossible and making it possible is my specialty"! Yes, you may call me a debate terminator. reporting it soon. The TBL states that: "A tree trunk does not and cannot give rise to branches at any one level that has a sum of cross section areas that is larger than its own. In other words, A tree's branches at any one level has total sum of cross section areas of less than the trunk or mother branch".  Arterioles and venules are further bound by a second layer of SMCs as well as elastin and collagen fibres. Capillaries have a varying extent of basement membrane and pericyte coverage and can be continuous, fenestrated, or discontinuous. Created with BioRender.com." This diagram violates Crogh's Model [34] of the capillary and the Tree Branching's law (see text above in section 11 and 12 of the discussion). Please draw another one based on real terminal arteriole showing its exact diameter and how many capillaries it branches into. Please give the exact diameter of every capillary in the example and any further branching with number of branches, the diameters and length of the capillaries. Please keep the arterioles in red colour and the venules in blue colour as it is the natural thing to do. In an ideal future studies, the RBCs speed and capillary pressure at both the arteriolar and venous ends of the capillary should be given.

Based on data presented in section 1, the diagram reported by
Fleisher et al. [29] reproduced here as ( Figure 34)

Methods
The lumen pressure (LP) of fluid passing in a tube was found to have not just one hydrostatic pressure at any one point but two

Conclusion
This article presents the final definitive proof that Starling's law is wrong, and the correct replacement is the hydrodynamic of the G tube. The presented evidence is based on reported and new results of the G tube hydrodynamic and critical analytical criticism of landmark and contemporary impactful articles, demonstrating many errors and misconceptions occurring while Starling's hypothesis was being transformed into a law with equations.
Received wisdom on cross section area of the whole number of capillaries is larger than of the aorta is proved wrong and the RBCs speed in the capillaries being "too slow" is also proved wrong.
Unquestionable evidence to show Starling's law is wrong and the revised Starling's principle is futile are given.
The hydrodynamics of the G tube was preliminary reported The results of the presented study clearly indicate and recognize the following new discoveries of the G tube: There is a major difference between the hydrodynamic of Poiseuille's tube and that of the G tube. There is also a difference between the hydrostatic and hydrodynamic pressures of FP and SP.