Paper Info
Title
Results of the oxygen Fick method in a closed blood circulation model including “total arteriovenous diffusive shunt of oxygen”
Abstract
It is considered that arteriovenous diffusive shunts of oxygen may cause inaccuracy of the oxygen Fick method as Up V ̇ O 2 > Q ̇ ( CaO 2 − CvO 2 ) where Up V ̇ O 2 is the pulmonary oxygen uptake, Q ̇ is the cardiac output, and CaO 2 and CvO 2 are the arterial and venous oxygen contents, respectively. A simple circulation model, including the whole circulation with nine well-mixed compartments (C1,…,C9), is constructed: the Q ̇ is assigned as constant as 6000 ml min −1 ; the blood portions of 60 ml move at an interval of 600 ms. C1 and C2 compartments, each having 60 ml volume, represent the blood of pulmonary microcirculation, C3 represents the arterial blood with a volume of 1500 ml, C4,…,C8, each also having a volume of 60 ml, represent the blood of peripheral microcirculation, whereas C9 represents the venous blood with a volume of 3000 ml. The pulmonary oxygen uptake (Up V ̇ O 2 ), related to C1 and C2, the oxygen release (rel V ̇ O 2 ), related to C4,…,C8, as well as a “total arteriovenous diffusive shunt of oxygen” (av V ̇ O 2 ), from the arterial blood (C3) to the venous blood (C9), are calculated simultaneously. The alveolar gas has a constant oxygen partial pressure, and the pulmonary diffusion capacity is also constant; similar to modeling the pulmonary oxygen diffusion, constant partial oxygen pressures for all peripheral tissues as well as constant diffusion capacities for all peripheral oxygen diffusion are also assigned. The diffusion capacities for the av V ̇ O 2 (between C3 and C9) are arbitrarily assigned. The Fick method gives incorrect results, depending on the total arteriovenous diffusive shunt of oxygen (av V ̇ O 2 ). But the mechanism determining the magnitude of av V ̇ O 2 remains unclear. Keywords Computer modeling Diffusion Oxygen uptake Oxygen release Mixed compartment Closed circulation Arteriovenous diffusive shunt Introduction According to the mass balance of Fick (1870) , the pulmonary oxygen uptake (Up V ̇ O 2 ) is expressed as (1) Up V ̇ O 2 = Q ̇ CaO 2 − Q ̇ CvO 2 , where the product of cardiac output ( Q ̇ ) and oxygen content of arterial blood (CaO 2 ) is the oxygen flow from the lung to the peripheral tissues, the product of cardiac output ( Q ̇ ) and oxygen content of venous blood (CvO 2 ) is the oxygen flow from the peripheral tissues to the lung. The Fick method (1), including a mathematical concept so pure in its logic ( Acierno, 2000 ), has been widely used in both clinical and experimental studies. Nevertheless, some recent investigations have indicated that the Fick method for calculation of oxygen uptake (1) may be inadequate ( Smithies et al., 1991 ; Stock and Ryan, 1996 ; Keinänen and Takala, 1997 ; Walsh et al., 1998 ; Epstein et al., 2000 ): the problem is that the calculated oxygen uptake, using the Fick method, was smaller than the value of measured oxygen uptake expressed as follows: (2) Up V ̇ O 2 > Q ̇ (CaO 2 − CvO 2 ), where Up V ̇ O 2 is the measured pulmonary oxygen uptake, and the right-hand side of expression (2) represents the calculated pulmonary oxygen uptake cUp V ̇ O 2 . (This (2) can also mean that the calculated cardiac output is greater than the measured cardiac output as Up V ̇ O 2 / (CaO 2 − CvO 2 )> Q ̇ ). Moreover, the difference between the measured and calculated pulmonary oxygen uptake was remarkably great: according to Smithies et al. (1991) and Keinänen and Takala (1997) , the calculated oxygen uptake was found to be around 85% of the measured oxygen uptake. The inaccuracy in the Fick method for oxygen uptake calculation was more pronounced in the studies of Stock and Ryan (1996) , Walsh et al. (1998) and Epstein et al. (2000) , in which they found the calculated oxygen uptake to be around 75% of the measured value. We have considered that arteriovenous diffusive shunts of oxygen ( Schubert et al., 1978 ; Popel, 1982 ; Stein et al., 1993 ; Buerk et al., 1993 ; Pittman, 2000 ; Kobayashi and Takizawa, 2002 ) may be responsible for oxygen transfer from the venous blood to the arterial blood. This means that the arteriovenous diffusive shunts of oxygen decrease the oxygen content of arterial blood and increase the oxygen content of venous blood—the difference of CaO 2 −CvO 2 in Eq. (1) becomes smaller. Thus, an inaccuracy in the Fick method (2) might indicate the hypothetical effect of arteriovenous diffusive shunts of oxygen. In order to discuss this hypothesis, a simple computer model, including a closed circulation is designed. Model According to the model, the blood flow in pulmonary microcirculation, in the arterial vessels, in the peripheral microcirculation and in the venous vessels comprises the closed blood circulation: the whole “closed” circulation is consisted of nine well-mixed blood compartments (C1,…,C9) as illustrated in Fig. 1 . The oxygen is taken up into the blood compartments of pulmonary microcirculation (C1 and C2) whereas the oxygen release takes place from the blood compartments of peripheral microcirculation (C4,…,C8) into the peripheral tissues. It is assumed that the arterial blood compartment (C3) includes a part of blood of arterioles whereas the venous blood compartment (C9) includes a part of blood of venules. It is also postulated that a certain amount of oxygen, which left the arterioles of arterial blood compartment C3, is not consumed in tissue and it is returned to the blood of venules of venous compartment C9. This postulation is based on the data from the literature that the arteriovenous diffusive shunts of oxygen may take place in different peripheral tissues ( Schubert et al., 1978 ; Popel, 1982 ; Stein et al., 1993 ; Buerk et al., 1993 ; Pittman, 2000 ; Kobayashi and Takizawa, 2002 ): the sum of arteriovenous oxygen shunts is defined as the total arteriovenous diffusive oxygen shunt (av V ̇ O 2 ). The av V ̇ O 2 is represented by a white vertical arrow in Fig. 1 , in the direction from arterial blood compartment (C3) into the venous blood compartment (C9). Each of the pulmonary and peripheral microcirculatory compartments had 60 ml blood. The volumes of arterial blood compartment (C3) and the venous blood compartment (C9) were 1500 and 3000 ml, respectively. It is assumed that the blood circulation takes place by the stepwise motion of 60 ml blood; where the cardiac output is 6000 ml −1 min, each step lasts 600 ms. For the calculation of the pulmonary oxygen uptake (Up V ̇ O 2 ) into the compartments of C1 and C2, both the partial oxygen pressure of mixed alveolar gas (PalvO 2 ) and the pulmonary oxygen diffusion capacity between alveolar gas and the blood of pulmonary microcirculation (Dpul) was assumed to be constant. It is assumed that the oxygen is homogenously distributed also in the peripheral tissues, similar to the modeling of pulmonary oxygen exchange: therefore, we need to assign a constant partial oxygen pressure for all peripheral tissues (PtisO 2 ) as well as an oxygen diffusion capacity (Dtis), for the calculation of oxygen release (rel V ̇ O 2 ), from the blood compartments of peripheral microcirculation (C4,…,C8) into the peripheral tissues. In order to calculate the flow rate of total arteriovenous diffusive oxygen shunt (av V ̇ O 2 ), from the arterial blood compartment (C3) to the venous blood compartment (C9), the diffusion capacities for arteriovenous shunt (Dav) are arbitrarily assigned (see “Discussion”). To perform the above calculations, for oxygen flows of Up V ̇ O 2 , rel V ̇ O 2 and av V ̇ O 2 , we also needed the initial oxygen contents for all blood compartments to be assigned and expect the oxygen contents of the compartments to change until a steady state. It is clear that these depend not only on stepwise circulation but also on diffusion processes. The diffusion-related changes will be calculated with the time interval of 1 ms; it means 600 times repetitive calculations ( t =1,…,600) must be performed, for each step of circulation as explained in the following part. First, for t =1, the initial oxygen content of a compartment (ConO 2(Ck,1) ) is given by neglecting the fraction of dissolved oxygen as (3) ConO 2( Ck ,1) = sO 2( Ck ,1) Hb 1.38, where Ck represents any of nine compartments (numbered as k =1,…,9), sO 2(Ck,1) is the oxygen saturation of compartment Ck, Hb is the hemoglobin content of blood assumed as 150 mg ml −1 , and 1.38 is Hüfner's number. And, the partial oxygen pressure of the compartment Ck(pO 2(Ck,1) ) is calculated from the Hill's equation (4) sO 2( Ck ,1) =( pO 2( Ck ,1) ) n /( pO 2( Ck ,1) ) n +(P 50 ) n , where the P 50 is 26 mmHg, being the oxygen partial pressure at the half oxygen saturation of blood, and n =2.6 being Hill's constant. For a time constant of 1 ms, the oxygen flow V ̇ O 2( Ck ,1) to the compartment or from the compartment is calculated using the following equation: (5) V ̇ O 2( Ck ,1) = ΔpO 2( Ck ,1) D ( Ck ) , where ΔpO 2(Ck,1) is the difference between partial oxygen pressures and it is related to the compartment number ( k =1,…,9); for the pulmonary oxygen diffusion, ΔpO 2(Ck,1) =PalvO 2 −pO 2(Ck,1) ; for the peripheral oxygen diffusion, ΔpO 2(Ck,1) =PtisO 2 −pO 2(Ck,1) ; and, for the total arteriovenous diffusive oxygen shunt ΔpO 2(Ck,1) =pO 2(C3,1) −pO 2(C9,1) , D (Ck) is the related diffusion capacity as Dpul/2 (for Cl and C2) or Dtis/5 (for C4,…,C8) or Dav (between C3 and C9). The axial diffusions between the given compartment (Ck) and the neighboring blood compartments are neglected. The oxygen flow V ̇ O 2( Ck ,1) changes oxygen content of the given compartment, from ConO 2(Ck,1) to ConO 2(Ck,2) : the ConO 2(Ck,2) is calculated by taking into account both the V ̇ O 2( Ck ,1) and the volume of the compartment Ck. And, from the value of ConO 2(Ck,2) , the next oxygen flow V ̇ O 2( Ck ,2) is found by applying the above equation ( Eqs. (3)–(5) ) for t =2. After the similar iterative calculation until the t =600, the oxygen exchange of a given compartment for a circulation step of time interval of 600 ms is (6) V ̇ O 2( Ck ) = ∑ t=1 600 V ̇ O 2( Ck ,t) . The summation of V ̇ O 2( Ck ) values, for C1 and C2, gives the oxygen uptake Up V ̇ O 2 as follows: (7) Up V ̇ O 2 = ∑ k=1 2 V ̇ O 2( Ck ) . And, the oxygen release rel V ̇ O 2 is calculated as (8) rel V ̇ O 2 = ∑ k=4 8 V ̇ O 2( Ck ) . It is clear that, the total arteriovenous diffusive shunt of oxygen is equal to the oxygen loss from the arterial blood compartment ( V ̇ O 2( C3 ) ) or to the oxygen uptake of venous blood compartment ( V ̇ O 2( C9 ) ). The oxygen contents of compartments are changed due to the steps of circulation; as mentioned above the 60 ml of blood moves in steps with a time interval of 600 ms: for the beginning of the following step of circulation, the oxygen content of a given pulmonary or peripheral blood compartments is equal to the oxygen content of the previous compartment, where the volume of compartment is also 60 ml: but, considering the volume of C3 (1500 ml) and of C9 (3000 ml), both the oxygen contents of arterial and venous blood compartments are (0.06 ConO 2( C 2,600) +1.44 ConO 2( C 3,600) )/1.5, and (0.06 ConO 2( C8 ,600) +2.94 ConO 2( C9 ,600) )/3, respectively. The running of the model lasted 6 min to reach a steady state, where the both oxygen content of arterial blood compartment (ConO 2(C3, t ) ) and oxygen content of venous blood compartment (ConO 2(C9, t ) ) change within the circulation step of 600 ms: for each circulation step, the arterial oxygen content (CaO 2 ) as well as the venous oxygen content (CvO 2 ) are calculated, as a mean of related oxygen contents as follows: (9) CaO 2 =1/600 ∑ t=1 600 ConO 2( C3 ,t) and (10) CvO 2 =1/600 ∑ t=1 600 ConO 2( C9 ,t) . According to Fick's principle (1), the calculated oxygen uptake (c Up V ̇ O 2 ) and calculated cardiac output (c Q ̇ ) are given as follows: (11) c Up V ̇ O 2 = Q ̇ ( CaO 2 − CvO 2 ) and (12) c Q ̇ = Up V ̇ O 2 /( CaO 2 − CvO 2 ). Results Fig. 2 shows the results of the model running for a case: the partial oxygen pressure of mixed alveolar gas (PalvO 2 ) is 100 mmHg, the partial oxygen pressure for all peripheral tissues (PtisO 2 ) is 36 mmHg, where the pulmonary oxygen diffusion capacity (Dpul) and the tissue oxygen diffusion capacity (Dtis) are 0.5 and 1.25 ml s −1 mmHg −1 , respectively. The Dav is assigned being 0.01 ml s −1 mmHg −1 to produce total arteriovenous diffusive oxygen flow (av V ̇ O 2 ), as shown in Fig. 2a . At the beginning ( Fig. 2a ), the av V ̇ O 2 is around 18 ml min −1 and it reaches 24.69 ml min −1 at the steady state. Where the cardiac output Q ̇ has a constant value of 6000 ml min −1 , the calculated cardiac output c Q ̇ changes due to av V ̇ O 2 ( Fig. 2b ). Fig. 2c shows the Up V ̇ O 2 , rel V ̇ O 2 and c Up V ̇ O 2 ; in the steady state, the Up V ̇ O 2 is found to be 294.6 ml min −1 simulating the physiological value of the pulmonary oxygen uptake of body. Both the initial arterial oxygen content (CaO 2 ) and initial venous oxygen content (CvO 2 ) are predicted as 0.19 and 0.14, respectively ( Fig. 2d ). The course of av V ̇ O 2 and all other time-related changes in the parameter of Fig. 2 depend on the predicted values of CaO 2 and of CvO 2 . But, obviously, the values obtained in the steady state do not depend on the initial blood oxygen contents. The time course for equilibrium of Up V ̇ O 2 with rel V ̇ O 2 ( Fig. 2c ) is parallel to the increase in both CaO 2 and CvO 2 ( Fig. 2d ). The greater Up V ̇ O 2 in comparison to the rel V ̇ O 2 requires oxygen accumulation in arterial blood and in venous blood—the oxygen mass incoming into the circulating blood is greater than the oxygen mass released from the blood. According to Eqs. (11) and (12) , the calculated pulmonary oxygen uptake (c Up V ̇ O 2 ) is smaller than the pulmonary oxygen uptake (Up V ̇ O 2 ) as given in Fig. 2c , whereas the calculated cardiac output (c Q ̇ ) is greater than the assigned cardiac output ( Q ̇ ) being 6000 ml min −1 ( Fig. 2b ). Using the assumptions for the case of Fig. 2 , we have derived Fig. 3 which shows the time-dependent fluctuations of arterial oxygen pressure (PaO 2 ) and of venous oxygen pressure (PvO 2 ), with the periods of 600 ms: according to definitions, PaO 2 and PvO 2 are, respectively, the partial oxygen pressure of C3 compartment (pO 2(C3, t ) ) and of C9 compartment (pO 2(C9, t ) ). The values of Fig. 3 are obtained, being close to the end of the period of 6 min: the increases in arterial oxygen pressure indicate the mixing of 60 ml blood of C2 compartment to the 1500 ml arterial blood of C3 compartment (upper). Parallel to this, the decreases in venous oxygen partial pressure depend on the mixing of 60 ml blood of C8 compartment to the venous blood of C9 compartment (lower). In contrast, the partial oxygen pressure of arterial blood (C3) decreases (upper) due to the total arteriovenous oxygen shunt av V ̇ O 2 whereas the partial oxygen pressure of venous blood (C9) increases (lower). The results for steady state are summarized in Table 1 : the partial oxygen pressure for mixed alveolar air (PalvO 2 ) as well as the pulmonary diffusion capacity (Dpul) are not changed. In contrast, three different values for the partial oxygen pressure of peripheral tissues (PtisO 2 ) were assigned as 30, 34, and 38 mmHg where the diffusion capacity for peripheral tissues (Dtis) was 0.5 or 1.25 ml s −1 mmHg −1 ; for the total arteriovenous diffusive shunt of oxygen ( av V ̇ O 2 ), three different values of Dav are assigned, 0 or 0.005 or 0.01 ml s −1 mmHg −1 . Considering the oscillations of blood gas parameters in Fig. 3 , we have calculated the mean blood oxygen contents (CaO 2 and CvO 2 ), from Eqs. (9) and (10) , respectively. The calculated values of the pulmonary oxygen uptake (c Up V ̇ O 2 ) and of the calculated cardiac output (c Q ̇ ) were obtained by Eqs. (11) and (12) , respectively. As given in Table 1 , if the Dav is zero, there occurs no oxygen flow between arterial blood compartment and venous blood compartment ( av V ̇ O 2 =0). Therefore, the results of the Fick method have to be correct (Up V ̇ O 2 =c Up V ̇ O 2 and Q ̇ =c Q ̇ ); there is also no difference between Up V ̇ O 2 and rel V ̇ O 2 , at the steady state. If the Dav is different from zero (0.005 or 0.01 ml s −1 mmHg −1 ), the calculated values, from both Eqs. (11) and (12) , were different in comparison to those values representing the measured values ( Table 1) ; we found around 5% and 10% errors in the application of the Fick method, respectively. Note that, in the cases of arteriovenous flow of oxygen, rel V ̇ O 2 is not just equal to the Up V ̇ O 2 ; there are very small differences between rel V ̇ O 2 and Up V ̇ O 2 as given in Table 1 . Discussion The arteriovenous diffusive shunts of oxygen The oxygen diffuses not only across the peripheral capillary wall but also across the wall of arterioles and of venules; moreover, the oxygen can diffuse across the wall of any blood vessels, if there is a transmural difference in partial oxygen pressure (PO 2 ) ( Pittman, 2000 ). The description of arteriovenous diffusive shunt of oxygen comes from the following question: How much of oxygen, which left the arterial system, is returned to the blood across the walls of venules ( Stein et al., 1993 ; Kobayashi and Takizawa, 2002 )? The increase in venous PO 2 , in comparison to the end-capillary PO 2 , was considered as an indicator of the arteriovenous shunt of oxygen, for different tissue circulations; for instance, in hamster retractor muscle ( Stein et al., 1993 ), in the coronary circulation of heart ( Schubert et al., 1978 ; Popel, 1982 ), and in the circulation of eye ( Buerk et al., 1993 ). But more direct evidence for arteriovenous shunt of oxygen was recently obtained by Kobayashi and Takizawa (2002) using the microspectrophotometrical data, for imaging of blood oxygen saturation (SO 2 ) in cremaster muscle of rat: it was clearly shown that the SO 2 profiles of venous blood were skewed toward the vessel wall, on the arterial side ( Kobayashi and Takizawa, 2002 ). Validity of the model Although the diffusive shunt flow of oxygen may take place in several parts of circulation, as mentioned above ( Schubert et al., 1978 ; Popel, 1982 ; Stein et al., 1993 ; Buerk et al., 1993 ; Pittman, 2000 ; Kobayashi and Takizawa, 2002 ), no information about its overall magnitude in a closed circulation system could be found in the literature. Therefore, the values for arteriovenous diffusion capacity (Dav) of model must be arbitrarily assigned to demonstrate that the arteriovenous diffusive shunts may cause incorrect results of the oxygen Fick method: using the Dav, the av V ̇ O 2 is calculated as the rate of overall atreriovenous flux of oxygen between the arterial blood compartment (C3) and the venous blood compartment (C9). The classical Krogh (1919) model of oxygen transfer deals with the partial oxygen pressure drop along a peripheral capillary as well as the partial oxygen pressure distribution of a surrounding cylindrical volume of tissue. For the sake of simplicity, we have postulated a homogenous distribution of oxygen for all peripheral tissues, to calculate oxygen flows from a given well-mixed compartment. The well-mixed compartments concept was also previously used, for instance, to study myocardial oxygen diffusion ( Van der Ploeg et al., 1994 ). To construct a unified model, the calculation of oxygen uptake was performed, being similar to that of oxygen release—the unique difference was the number of compartments—all peripheral microcirculations are represented by five well-mixed blood compartments (C4,…,C8) but pulmonary capillary blood are represented by two compartments (C1,C2). Both the values for alveolar oxygen partial pressure PalvO 2 and the pulmonary diffusion capacity Dpul were assigned prior to the physiological data ( Thews, 1990 ); these were 100 mmHg and 0.5 ml s −1 mmHg −1 , respectively. We have also postulated a constant diffusion capacity, Dtis, for all peripheral tissue, where the partial oxygen pressure of peripheral tissues was 30 or 34 or 38 mmHg. Actually, the tissue partial oxygen pressure is not homogenously distributed for different peripheral tissues ( Grote, 1990 ). As given in Table 1 , the oxygen uptake depends not only on PalvO 2 and Dpul, but also on Dtis and PtisO 2 : the oxygen uptake increases parallel to the decrease in PtisO 2 or to increase in Dtis, vice versa. The Dtis is so assigned, as 0.5 or 1.25 ml s −1 mmHg −1 , that the oxygen release is found to be around the oxygen supply to the whole organism; the first value of Dtis, assigned here, is equal to the oxygen diffusion capacity for the pulmonary system, whereas the second Dtis is assumed to be greater, considering the greater capillary volume of peripheral circulation, in comparison to the pulmonary capillary volume ( Witzleb, 1990 ). Because the venous blood volume is around two times greater than arterial blood volume, we have assigned venous and arterial blood volume as 3000 and 1500 ml, respectively ( Witzleb, 1990 ). As generally accepted, for the application of the Fick method, the arterial blood can be withdrawn from any peripheral artery, because oxygen contents do not differ, including all arteries. But, the venous blood can be obtained from a. pulmonalis because only the blood of a. pulmonalis should represent mixed venous blood—the blood oxygen content of any venous vessel may be different from that of a. Pulmonaris. In the presented model, all arterial blood is represented by one compartment (C3) whereas the venous blood was also represented by one compartment (C9), and both the C3 and C9, include mixed blood. Two different explanations for the inaccuracy in the Fick method? First, the results of the presented model indicate that the av V ̇ O 2 causes a smaller oxygen uptake in comparison with the calculated oxygen uptake (see (2)), as given in Table 1 . The other explanation for this inaccuracy of the Fick method is as follows: the oxygen uptake which was measured on the external airway may not be equal to the oxygen flow, from the alveolar space into the blood of pulmonary microcirculation, because the lung itself may use the oxygen from the inspired gas mixture ( Oudemans-van Straaten et al., 1993 ; Jolliet et al., 1996 ). Thus, the difference between the measured oxygen uptake and calculated oxygen uptake, from the Fick method, should give the intrapulmonary oxygen consumption ( Oudemans-van Straaten et al., 1993 ; Jolliet et al., 1996 ). This explanation was not found to be acceptable, as previously discussed, based on some experimental results ( Weyland et al., 1994 ; Nunn, 1996 ; deBoisblanc et al., 1998 ). On the other hand, Fick method does not always give incorrect results. Some clinical or experimental results showed the oxygen Fick method to be reliable ( Zhang et al., 1985 ; Davies et al., 1987 ; Keinanen et al., 1992 ; Oudemans-van Straaten et al., 1993 ; Thrush et al., 1995 ; Pauli et al., 2002 ). The basic question of the present study would also be this, “why was the Fick method found to be reliable”—consider that the arteriovenous diffusive shunts of oxygen would also take place for those cases with correct results of the Fick method ( Zhang et al., 1985 ; Davies et al., 1987 ; Keinanen et al., 1992 ; Oudemans-van Straaten et al., 1993 ; Thrush et al., 1995 ; Pauli et al., 2002 ): because, in peripheral tissues of all cases, the arterial vessels or arterioles are generally very close to the venous vessels or venules. On the other hand, if the lung uses the oxygen from the alveolar space, as the so-called intrapulmonary oxygen consumption, it would also cause inaccuracy in the Fick method, for all cases. Studies dealing with the questioned reliability of the Fick method were performed in different groups of patients or animals, with different methods ( Zhang et al., 1985 ; Davies et al., 1987 ; Smithies et al., 1991 ; Keinanen et al., 1992 ; Oudemans-van Straaten et al., 1993 ; Thrush et al., 1995 ; Stock and Ryan, 1996 ; Keinänen and Takala, 1997 ; Walsh et al., 1998 ; Epstein et al., 2000 ; Pauli et al., 2002 ): we may speculate that the Fick method may be inaccurate depending on the increase in the av V ̇ O 2 , but, which mechanism/mechanisms could be involved to increase the magnitude of av V ̇ O 2 ? One of these unknown mechanisms might be related to the artificial ventilation. Namely, Stein et al. (1993) have indicated that arteriovenous shunting of oxygen in hamster retractor muscle was pronounced, if the level of the oxygen fraction of inspired gas was elevated. In contrast, no evidence for arteriovenous shunting of oxygen, in hypoxic artificial ventilation ( Stein et al., 1993 ) and in spontaneous breathing ( Swain and Pittman, 1989 ), has been detected. It is concluded that the hypothetical correlation between the arteriovenous shunts of oxygen and the reliability of the Fick method remains to be tested by extended experimental studies. References Acierno (2000) L.J. Acierno Profiles in cardiology Adoph Fick: mathematician, physicist, physiologist Clinical Cardiology 23 2000 390 391 Buerk et al (1993) D.G. Buerk R.D. Shonat C.E. Riva S.D. Cranstoun O 2 gradients and countercurrent exchange in the cat vitreous humor near retinal arterioles and venules Microvascular Research 45 1993 134 148 Davies et al (1987) G.G. Davies D.R. Hess P.J. Jebson Continuous Fick cardiac output compared to continuous pulmonary artery electromagnetic flow measurement in pigs Anesthesiology 66 1987 805 809 deBoisblanc et al (1998) B.P. deBoisblanc E. McClarity K. Lord Oxygen consumption in the intensive care unit indirect calorimetry is the way to go, but where? Critical Care Medicine 26 1998 1153 1154 Epstein et al (2000) C.D. Epstein J.R. Peerless J.E. Martin M.A. Malangoni Comparison of methods of measurements of oxygen consumption in mechanically ventilated patients with multiple trauma the Fick method versus indirect calorimetry Critical Care Medicine 28 2000 1363 1369 Fick (1870) Fick, A., 1870. Über die Messung des Blutquantums in den Herzventrikeln, SB-Phys-Med. Ges. XIV, Sitzung am 9. Juli, Würzburg. Grote (1990) J. Grote Gewebeatmung R.F. Schmidt G. Thews Physiologie des Menschen 1990 Springer Berlin 633 648 Jolliet et al (1996) P. Jolliet J.B. Thorens L. Nicod C. Pichard U. Kyle J.C. Chevrolet Relationship between pulmonary oxygen consumption, lung inflammation, and calculated venous admixture in patients with acute lung injury Intensive Care Medicine 22 1996 277 285 Keinänen and Takala (1997) O. Keinänen J. Takala Calculated versus measured oxygen consumption during and after cardiac surgery. Is it possible to estimate lung oxygen consumption? Acta Anaesthesiologia Scandinavica 41 1997 803 809 Keinänen et al (1992) O. Keinänen J. Takala A. Kari Continuous measurement of cardiac output by the Fick principle clinical validation in intensive care Critical Care Medicine 20 1992 360 365 Kobayashi and Takizawa (2002) H. Kobayashi N. Takizawa Imaging of oxygen transfer among microvessels of rat cremaster muscle Circulation 105 2002 1713 1719 Krogh (1919) A. Krogh Number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue Journal of Physiology (London) 52 1919 409 415 Nunn (1996) J.F. Nunn Pulmonary oxygen consumption Intensive Care Medicine 22 1996 275 276 Oudemans-van Straaten et al (1993) H.M. Oudemans-van Straaten G.J. Scheffer L. Eysman Ch.R.H. Wildevuur Oxygen consumption after cardiopulmonary bypass—implications of different measuring methods Intensive Care Medicine 19 1993 105 110 Pauli et al (2002) C. Pauli U. Fakler T. Genz M. Hennig H.P. Lorenz J. Hess Cardiac output determination in children equivalence of the transpulmonary thermodilution method to the direct Fick principle Intensive Care Medicine 28 2002 947 952 Pittman (2000) R.N. Pittman Oxygen supply to contracting skeletal muscle at the microcirculatory level diffusion vs. convection Acta Physiologica Scandinavica 168 2000 593 602 Popel (1982) A.S. Popel Oxygen diffusive shunts under conditions of heterogeneous oxygen delivery Journal of Theoretical Biology 96 1982 533 541 Schubert et al (1978) R.W. Schubert W.J. Whalen P. Nair Myocardial PO 2 distribution relationship to coronary autoregulation American Journal of Physiology 234 1978 H361 H370 Smithies et al (1991) M.N. Smithies B. Royston K. Makita K. Konieczko J.F. Nunn Comparison of oxygen consumption measurements indirect calorimetry versus the reversed Fick method Critical Care Medicine 19 1991 1401 1406 Stein et al (1993) J.C. Stein C.G. Ellis M.L. Ellsworth Relationship between capillary and systemic venous PO 2 during nonhypoxic and hypoxic ventilation American Journal of Physiology 265 1993 H537 H542 Stock and Ryan (1996) M.C. Stock M.E. Ryan Oxygen consumption calculated from the Fick equation has limited utility Critical Care Medicine 24 1996 86 90 Swain and Pittman (1989) D.P. Swain R.N. Pittman Oxygen exchange in the microcirculation of hamster retractor muscle American Journal of Physiology 256 1989 H247 H255 Thews (1990) Thews, G., 1990. Lungenatmung. In: Schmidt, R.F., Thews, G. (Eds.), Physiologie des Menschen. Springer, Berlin, pp. 574–610. Thrush et al (1995) D. Thrush J.B. Downs R.A. Smith Continuous thermodilution cardiac output agreement with Fick and bolus thermodilution methods Journal of Cardiothoracic and Vascular Anesthesia 9 1995 399 404 Van der Ploeg et al (1994) C.P.B. Van der Ploeg J. Dankelman J.A.E. Spaan Classical Krogh model does not apply well to coronary oxygen exchange Advances in Experimental Medicine and Biology 345 1994 299 304 Walsh et al (1998) T.S. Walsh P. Hopton A.A. Lee Comparison between the Fick method and indirect calorimetry for determining oxygen consumption in patients with fulminant hepatic failure Critical Care Medicine 26 1998 1200 1207 Weyland et al (1994) A. Weyland W. Weyland M. Sydow Reversed Fick principle versus indirect calorimetry do systematic differences between methods represent intrapulmonary oxygen consumption? Intensive Care Medicine 20 1994 457 458 Witzleb (1990) E. Witzleb Funktionen des Gefäßsystems R.F. Schmidt G. 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Year
DOI
Venue
2004
10.1016/j.thbio.2003.09.001
Theory in biosciences = Theorie in den Biowissenschaften
Keywords
Field
DocType
Computer modeling,Diffusion,Oxygen uptake,Oxygen release,Mixed compartment,Closed circulation,Arteriovenous diffusive shunt
Blood circulation,Biology,Oxygen,Shunt (electrical),Fick method,Zoology,Cardiac output,Nuclear magnetic resonance
Journal
Volume
Issue
ISSN
123
2
Theory in Biosciences
Citations 
PageRank 
References 
0
0.34
0
Authors
2
Name
Order
Citations
PageRank
Mustafa Özbek100.34
Ahmet Akay200.34