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Pulmonary Vascular Resistance in Fetal and Neonatal Goats by Raymond Dwight Gilbert), l4  A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1971 ACKNOWLEDGEMENTS The author wishes .to acknowledge all those persons who have helped him in his work as a graduate student. In particular he would like to express his gratitude to his supervisory chairman, Dr. Sidney Cassin, for the time and effort he devoted to this investigation and for the facilities and laboratory space he made available to the author. To the other members of his committee, Dr. A. B. Otis, Dr. Wendell Stainsby and Dr. David Williams go special thanks for their time and helpful suggestions. The author would also like to thank his fellow graduate students for their help and encouragement. To Dr. Jack Hessler the author extends his special appreciation for his assistance throughout this investigation. Also to Dr. Ian Hood for his help in examining sections of lungs the author is grateful. He also wishes to thank his wife, Mrs. Sandra B. Gilbert,, for5:erhelp in the preparation of this dissertation.;_ ;T E i I~~   TABLE OF CONTENTS Page ACKNOWLEDGEMENTS. . .... .. ii LIST OF TABLES. . ... ...... v LIST OF FIGURES . ... . vi ABSTRACT. . .. . ix INTRODUCTION. . ... .... MATERIALS AND METHODS . .... ..... 6 Mathematical Model . .. . 12 Pi Versus Po.. .. . 12 Pi Versus . . 22 Physical Model . . 24 Pi Versus P0o,.. ...... . .... ... 24 Pi Versus Q . . 26 Animals. ......... .. . .... 27 Fetuses .......... . 27 Neonates. . . 35 RESULTS . .. .. . 36 Mathematical Model . ... ... 36 Pi Versus PQ. . . 36 Pi Versus Q.. ................................ Physical Model ... .... . .... 57 Ph Versus . . .. 57 Pi Versus Q. ......... . 77 Animals. . . . 90 Fetuses ... ... .. . .. 90 Neonates. . .. . 121 DISCUSSION. . ... .. 126 Mathematical and Physical Model. .. 126 Pi Versus P0o ...... ............... ... 126 Pi Versus Q ........ . 128 Animals. . ... . 132 SUMMARY AND CONCLUSIONS . . 140 ill APPENDIX 1. . .. .. ... 141 APPENDIX 2. .. ... ............. ....... 175 BIBLIOGRAPHY . . . 180 VITA .. . . . 186 LIST OF TABLES Table Page P02, PC02 and pH in left pulmonary arterial blood in fetal animals in which both lungs were unventilated, ventilated with fetal gas and ventilated with air. 96 2. P021 PC02 and pH in left pulmonary arterial and venous blood in fetal animals in which both lungs were unventilated, right lung only ventilated with fetal gas and right lung only ventilated with air. .. 109 3. P02* PCO2 and pH in left pulmonary arterial and venous blood of fetal animals before, during and after infusion of bradykinin . . 117 4. P02, PCO2 and pH in left pulmonary arterial and venous blood of newly ventilated animals before, during and after infusion of bradykinin . .. 120 5. P02, PC02 and pH in left pulmonary arterial blood of newborn animals in which both lungs were ventilated with air, 10% 02 and 5% 02 . 124 6. Data from fetuses in the unventilated fetal state (F), during ventilation of both lungs with fetal gas (VFG) and with air (VA) . 176 7. Data from animal 15 from table 6. . .. 177 8. Data from ventilated animals before (B), during (D) and after (A) infusion of bradykinin .. 178 9. Data from animal 5 from table 8. . .179 LIST OF FIGURES Figure Page 1. Diagram of a one tube model containing a Starling resis tor arranged to provide a constant inflow pressure 8 2. Diagram of a one tube model containing a Starling resis tor arranged to provide a constant flow. .. 10 3. Recording from program 1 of the relation betweenPT and Po in a one tube model . .. 14 4. Diagram of a four tube model containing a Starling res istor in each tube ... ...... 17 5. Diagram of surgical preparation of animals. .. 30 6. Recording of the relation between pulmonary artery pressure (PAP) and pulmonary venous pressure (PVP) in an unventilated fetal animal. . ... 33 7. Recording from program I of the relation between Pi and Po in a one tube model: effect of increasing PS. 38 8. Recording from program 1 of the relation between Pi and Po in a one tube model: effect of increasing RP. 40 9. Recording from program 2 of the relation between Pi and Po in a four tube model: flow occurring in all tubes . . 43 10. Recording from program 3 of the relation between Pi and Po in a four tube model: flow occurring in a partial number of tubes. . ... 46 11. Recording from program 4 of the relation between Q and Pi in a one tube model: effect of decreasing Rp and PS. .................. .. 49 12. Recording from program 5 of the relation between Q and Pi in a four tube model. . ... 52 13. Recording from program 5 of the relation between Q and Pi in a four tube model: effect of decreasing Rp . . . 54 14. Recording from program 5 of the relation between Q and Pi in a four tube model: effect of decreasing PS.. . .. .. .56 15. Recording from program 5 of the relation between Q and Pi in a four tube model: crossing of the intercept. . .... ..... 59 16. Recording from the one tube physical model of the relation between Pi and Po . .... .62 17. Recording from the one tube physical model of the relation between Pi and Po: effect of increasing PS . . . .. 64 18. Recording from the one tube physical model of the relation between Pi and Po: effect of increasing Rp . . . 66 19. Comparison of calibrated resistances of glass tubes used in the physical model to the resistances calculated while the tubes were in the proximal or distal position . ... .69 20. Recording from the three tube physical model of the relation between Pi and Po . .. 71 21. Recording from the two tube physical model of the relation between Pi and Po: flow occurring in all tubes. . ... ..... 74 22. Recording from the three tube physical model of the relation between Pi and Po: flow occurring in a partial number of tubes. . ... 76 23. Recording from the one tube physical model of the relation between and Pi. . .... 79 24. Recording from the one tube physical model of the relation between Q and Pi: effect of increasing Rp 81 25. Recording from the one tube physical model of the relation between Q and Pi: effect of increasing PS 84 26. Recording from the three tube physical model of the relation between and Pi: effect of increasing Rp 86 27. Recording from the three tube physical model of the relation between Q and Pi: effect of increasing PS .. 89 28. Recording of the relation between PAP and PVP in a ventilated animal . .. .92 vii 29. Comparison of proximal and distal resistance and surrounding pressure in the left lung during the unventilated fetal state (F), during vent ilation of both lungs with fetal gas (VFG) and during ventilation of both lungs with air (VA) . 30. Relation between proximal resistance and pulmonary arterial P02 in ventilated animals . 31. Relation between log proximal resistance and log pulmonary arterial P02 in ventilated animals . 32. Relation between distal resistance and pulmonary venous P02 in ventilated animals . 33. Comparison of total resistance (T), calculated in condition 3, to the sum of proximal and distatl resistance (P + D), calculated in condition 2, in unventilated fetal animals, animals venti lated with fetal gas and ventilated with air . 34. Comparison of proximal and distal resistance and surrounding pressure in the left lung during the unventilated fetal state (F), during venti lation of the right lung with fetal gas (VFG) and during ventilation of the right lung with air (VA) . . . 35. Relation between proximal resistance and pulmonary arterial P02 in unventilated animals . 36. Relation between distal resistance and pulmonary venous P02 in unventilated animals .. . 37. Comparison of proximal and distal resistance and surrounding pressure in the left lung of unventi lated animals before (B), during (D) and after (A) infusion of bradykinin into the pulmonary artery . . . 38. Comparison of proximal and distal resistance and surrounding pressure in the left lung of newly ventilated animals before (B), during (D) and after (A) infusion of bradykinin into the pulmonary artery . . . 39. Comparison ofproximal and distal resistance and surrounding pressure in the left lung of newborn animals during ventilation with air (A), 10% 02 in N2 (10) and 5% 02 in N2 (5) . . vii . 105 . 116 . 119 . 123 Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PULMONARY VASCULAR RESISTANCE IN FETAL AND NEONATAL GOATS By Raymond Dwight Gilbert June, 1971 S. Cassin, Chairman Department of Physiology Flow through a system of parallel tubes, each containing a Starling resistor, was considered both theoretically and experimentally. A method was proposed to calculate resistance proximal and distal to the Starling resistors by observing the relation between inflow pressure and outflow pressure. Proximal resistance (Rp) was calculated as inflow pressure minus the pressure surrounding the Starling resistor (Ps) divided by flow~ Distal resistance (RD) was calculated as surrounding pressure minus out flow pressure divided by flow. This method was used to analyze changes in pulmonary vascular resistance after ventilation or infusion of brady kinin in mature fetal goats and after hypoxia in newborn goats. Deter minations of proximal and distal resistances were made from measurements of pulmonary artery pressure and pulmonary venous pressure while pulmonary artery pressure was kept constant and pulmonary venous pressure varied. In mature goats ventilation of both lungs with a gas that did not change blood gases (fetal gas) resulted in a decrease in Rp and PS. Further ventilation of both lungs with air caused Rp, RD and PS to decrease. Ventilation of only the right lung with fetal gas did not result in any changes in Rp, RD or PS in the left lung; however, ventilation of the right lung with air was followed by decreases in Rp, RD and PS in the ix left lung. In newborn goats Rp, RD and PS increased in response to ventilation hypoxia (5% 02 in N2). Rp and PS decreased in unventilated fetuses after infusion of bradykinin into the pulmonary artery. After the fetuses were ventilated with air, bradykinin infusion still caused a decrease in Rp, but not in PS. INTRODUCTION The pulmonary circulation was shown to respond to changes in blood gases first in 1946 when von Euler and Liljestrand (1) demonstrated that hypoxia caused a rise in pulmonary artery pressure in the adult cat. Subsequently it has been well confirmed that the pulmonary vasculature of adult lungs constricts in response to decreased P02 (25). The action of the decreased P02 has been shown to be a local one, in isolated lung preparations (25), as well as being mediated through peripheral chemoreceptors (67). The response of fetal pulmonary vasculature to hypoxia and ventilation is very similar to that of adult lungs and has been reviewed extensively by several authors (810). Ventilation of fetal lungs with any gas causes a decrease in pul monary artery pressure and an increase in pulmonary artery flow (1116). Inflation of fetal lungs with saline or dextran containing a low P02 does not cause the same decrease in pressure and increase in flow but rather results in no change or a decrease in flow (12, 17). The reduction of fetal pulmonary vascular resistance (PVRY upon ventitatton with a gas has been shown to be the result of two separate causes: (1) the mechanical events which accompany expansion of the lungs with a gas and (2) the local effect on the pulmonary vasculature of an increase in P02, or decrease in PCO2 (13, 1516, 18). Campbell et al. (19) have shown also that changes in the gas composition of blood per fusing unventilated fetal lungs will elicit changes in PVR. To date, no one has reported in the literature any attempt to isolate the site of these changes in PVR in fetal lungs in response to ventilation and I 2 to changes in P02 and PC02. Determinations of the distribution of vascular resistance and of the sites sensitive to hypoxia and hyper capnia have been made for adult lungs (20, 21). However, similar determinations have not been made for fetal or newborn lungs. The effect of drugs on the pulmonary circulation and their relation ship to the pulmonary vascular response to hypoxia have been studied in both fetal and adult animals (2259). The catecholamines have been reported to constrict the pulmonary vasculature of fetal lambs even when given in small doses (0.10.5 mg/kg) (15, 55). Epinephrine also causes vascular constriction in adult lungs that has been localized, using pulmonary artery and vein wedge pressures, to the venous segment of the vasculature (22, 23). Norepinephrine increases pulmonary vascular resistance in both neonatal and adult animals (2427). Barer (28) demonstrated that norepinephrine increased PVR even in collapsed adult lungs. Hyman (27) concluded that the effect of norepinephrine in dog lungs was exerted on all vessels and not localized to one segment. The effect of the catecholamines on PVR has been blocked with phenoxybenzamine, phentolamine and propranolol (25, 26, 29). The response of the pulmonary vasculature to hypoxia has been shown by some (26, 28) to be abolished by phenoxybenzamine or phentolamine; however, others (25, 30, 31) have indicated these agents have no effect on the response to hypoxia. Depletion of catecholamine reserves with reserpine or by adrenalectomy does not decrease the hypoxic res ponse of either adult or neonatal lungs (25, 29). Cassin (15) showed that adrenalectomy did not alter the pulmonary circulatory response to asphyxia in immature fetal lambs. 3 Acetylcholine initiates a large increase in blood flow in the unexpanded lungs of the fetal lamb, but has little effect on pulmonary circulation after ventilation has begun (14). Shepard et al. (32) showed that acetylcholine decreased pulmonary vascular resistance in the hypoxic neonatal lamb, but had no effect on nonhypoxic neonates. In contrast, in the intact adult dog lung acetylcholine has been demon strated to constrict the vasculature (33). However, Chu et al. (34) has observed that acetylcholine dilates the pulmonary vasculature of newborn human infants. Others (35, 36) have shown that acetylcholine decreases pulmonary vascular resistance of normal men and women and in individuals with primary pulmonary hypertension. Histamine has been shown to increase PVR in normal adult lungs (22, 23) and in collapsed lungs (28). Some evidence suggests this response is larger in the venous segment of the vasculature than in the arterial segment (22, 23). Bjure et al. (35) has indicated that histamine injection results in a large increase in pulmonary blood flow (14). Histamine releasers and antihistamine drugs have been demon strated to abolish the pulmonary vascular pressor response to venti lation hypoxia in both isolated and intact adult lungs (27, 37, 38, 39). Bradykinin produces a decrease in PVR in isolated and intact dog lungs (40, 56, 57), in normal adult human lungs (58, 59), in lungs of humans with arterial hypertension, pulmonary arterial hypertension, and emphysema (58, 59), as well as in unventilated fetal lungs of the lamb (43). However, Hyman (42) suggested that bradykinin actually caused an active constriction of pulmonary veins, which was masked by a passive dilatation of the arterial segment in response to the increased cardiac output caused by the bradykinin. Bradykinin is also thought by some 4 (43) to be the mediator of the decrease in PVR upon ventilation of fetal animals. No one has attempted to demonstrate the sites of action of these drugs in the fetal or newborn pulmonary vasculature. Therefore, the purpose of the experiments to be presented here was to determine the sites of change in pulmonary vasculature resistance in response to: (1) changes in the PO2 and PC02 of the blood perfusing unventilated fetal lungs, (2) the mechanical events that accompany ventilation of fetal lungs, (3) ventilation of fetal lungs with air, (4) hypoxia in newborn lungs and (5) an infusion of bradykinin in fetal and newly ventilated lungs. It was impossible to investigate the sites of action of all the drugs mentioned above at the present time. Therefore, bradykinin was chosen to be studied because it has been suggested as a possible mediator in the events accompanying ventilation of fetal lung. In order to analyze segmentally the resistance in the pulmonary vasculature it was necessary to employ a model of the pulmonary circu lation as described by various workers (4454). This model is based on the tenet that the pulmonary circulation behaves in a manner similar to a system of parallel tubes containing Starling resistors. A Starling resistor was first described as a thin walled collapsible tube traversing a chamber in which the pressure surrounding the tube can be controlled. Evidence to support this model was first presented by Banister and Torrance in 1960 (44). They showed in isolated adult cat lungs that at a constant inflow, pulmonary artery pressure was independent of pul monary venous pressure if pulmonary venous pressure was below tracheal pressure. This work has been confirmed by others (45, 46). Permutt et al. (47) demonstrated that at a constant pulmonary arterial pressure, 5 flow is not influenced by changes in left atrial pressure if left atrial pressure is below tracheal pressure. Pulmonary arterial pressure, at a constant flow, is linearly related to tracheal pressure with a slope of one if tracheal pressure is above left atrial pressure (44). When left atrial pressure is zero, the pressure to which pulmonary arterial pressure falls when flow is stopped is equal to tracheal pressure, if tracheal pressure is above 5 mmHg. If tracheal pressure is less than 5 mmHg, the pulmonary arterial pressure at zero flow remains 5 mmHg, rather than falling to zero (46). Recently Permutt et al. (48) has given evidence that pulmonary capillaries are indistensible. Also, Abraham and Caldini have found that the pulmonary blood volume is linearly related to the slope of the pressure:flow curve, suggesting to him that resistance is constant along the straight line portion of the pressure:flow curve (49). A new method will be presented in this present study utilizing this concept of the pulmonary varculature containing Starling resistors, that allowed resistance to be calculated in two segments of the pul monary vasculature. Resistance was calculated in that segment proximal to the Starling resistors and also in the segment distal to the Starling resistors. The resistance in these two segments was used then to deter mine the sites of change in pulmonary vascular resistance in each of the conditions mentioned previously. MATERIALS AND METHODS Figure 1 is a diagrammatic representation of the basic model used in these experiments. This model has been described by others previously (45, 46). A constant inflow pressure is maintained in this model by means of a reservoir which can be raised or lowered. Inflow pressure (Pi), flow (Q) and outflow pressure (Po) can be measured at the points indicated in the figure. The Starling resistor is diagrammed as a collapsible tube traversing a plexiglas chamber filled with water. The pressure tending to close the Starling resistor (PS) is the hydrostatic pressure of the water surrounding the Starling resistor. The resistance from the point at which Pi is measured to the end of the Starling resistor is designated Rp or proximal resistance. The resistance from the end of the Starling resistor to the point at which Po is measured is denoted by RD or distal resistance. Po' is the pressure just distal to the Starling resistor. Outflow pressure can be raised or lowered by means of a pulley attached to the outflowtube. Outflow from the system is collected in areservoir and returned to the TnfTow reservoir by means of a Sigmamotor finger pump. In order to maintain a constant inflow rate it was necessary to modify this model as indicated in figure 2. The inflow reservoir was deleted so that the tube from the finger pump could be attached directly to the inflow tube. All other aspects of this model are identical to those in figure 1. Flow through a system as indicated in figure 1 is characterized by 6 cU 01 (a CLQ C U)U 41L c a 0 tn. cn L mP cc 1 0 E C C CI L 0 u 0 I CI)U C 04d) a 04 M 4u 0 41 Ecma) .0 > 4 0) 04 C 0. 4) E0 03 CD L L W X.. o.' 4'0 '4 4 0 0. to W4J ( ) E 0uE CC tot a) ~ L in co tc n I 1; V). E~ O & 4) I (UCI L.L *EU 0.. 0 1 8e C, i I E, Li. L.O'CL O C 4 J 4a) L) C (a 4 a.. CM I Q 4J 01 *c1 U lL C Cm) C . 0L 0 4 tn o oi 4I 1 c 0 41 (a >: 0 (n 4J ' E Cm 0* 1 1 0 Ow U 0 (D n t 4 (u cLo c (n 0 0 J 4 L. 4J. (n 4.' E = O MUoi 0 (U L00 4 ~c, cm I (A M . 41 01LI LW 415 a.: E * I In X ( 4f 00 ) 01 L. U> L CCaL C  I 11 the following sets of conditions: Condition I: if Pi < PS Q = 0 Condition 2: if Pi > PS > Po' = i P Rp Condition 3: if Pi > PS < Po' Q Pi Po Rp + RD Throughout the section on methodology the above conditions or equivalent conditions will always be referred to by the numbers indicated. In condition 3 the total resistance (RT = Rp + RD) of the system can be calculated by the equation RT =  In condition 2, Rp can be calculated from the equation Rp = Pi PS RD may be obtained in sev eral ways. Rp can be subtracted from RT to obtain a value for RD; or it P P may be calculated from the equation RD = o In order to calculate Rp and RD in vivo it is necessary to obtain values for Pi, PS, Po, Po' and Q. Measures of PI, Po and Q are easily obtainable; however, methods had to be devised to obtain values for PS and Po'. These methods were derived through further mathematical consid erations of the characteristics of a system such as that presented in figures I and 2. For purposes of clarity the section on methodology will be divided into three parts. The first part will deal with the theoreti cal and mathematical aspects of this system. Secondly, the application of these mathematical aspects to a physical model will be considered. Lastly, the use of these concepts in vivo to analyze segmentally pulmonary vascular resistance will be covered. Mathematical Model Pi Versus Po Initially it was necessary to observe the relationship between Pi and Po in a system such as that indicated in figure 2. Equations des cribing this system were programmed into a Hewlett Packard model 9100A calculator and desired relationships were recorded on a Hewlett Packard model HR98 XY plotter. A program was written to evaluate this relation ship based on the following reasoning. The actual program is given in Appendix 1 as program I. Given: Q is constant Qin = out Po' = QRD + Po Condition 1: if Q = 0 then Pi = PS in condition 2, or Pi = Po' in condition 3 Condition 2: if PS > Po' then Pi = Q.Rp + PS Condition 3: if PS < Po' then Pi = Q.Rp + Po' The program was given an initial Po. The calculator was programmed to calculate Po' according to the equation given. It next compared Po' to the given PS, calculated the appropriate Pi and plotted Pi against Po on the XY recorder. The calculator was programmed to increase Po by a given interval and execute the same procedure just described. This cycle was repeated automatically until the desired curve was obtained and the program manually stopped. Typical curves obtained from this program for several different flows are shown in figure 3. These curves are traced from the original curves obtained from the XY plotter. 4J5 0= E E0 0 L 4 4p Uc) 1I 0 n 00U 0 0 o '40 CD 0 U OU 3 4m cn C: 'p . W)0 cr L C 0 OU cle  c U. L .0 o m 0? 0 .o 0 C8 o E E I 15 According to this model when Q is zero, Pi = PS in condition 2, but Pi = Po' in condition 3. At any constant flow (or zero flow) Pi is inde pendent of Po as long as Po' is less than PS. Whenever Po' becomes greater than PS, Po will influence Pi in a one to one relationship. In other words Po' = PS is the boundary between condition 2 and condition 3. At zero flow the Po which begins to influence Pi (point A on figure 3) is equal to PS, since Po' = Po at zero flow. Therefore, the Po at point A may be taken as a measure of PS. At any constant flow Po' is greater than Po due to the resistance along the distal segment. When Po just begins to influence Pi (point B on figure 3) Po' is equal to PS. There fore, at point B the pressure drop along the distal segment is PS minus the outflow pressure at point B (PoB). Distal resistance may be calcu lated as this pressure drop divided by flow (RD = PS PB ). The PS used for this calculation is the value of Po at point A (PoA) on the zero flow curve described above. The correct equation for calculating RD is PoA PoB then: RD = This same value for PS may be used to calculate Rp. If a constant flow is maintained such that the system is in conditTon 2 (PS > Po') then Rp = P S. Again, the correct equation is actually Pi PoA Rp = . It was necessary to observe the relationship between Pi and Po in a model consisting of more than one tube. Figure 4 is a diagrammatic repre sentation of a system containing four tubes in parallel. The tubes were not stacked vertically but were all in the same horizontal plane. Each tube has a Starling resistor traversing a separate plexiglas box. Each 0) C C  L. 4J 0 .  00 00 0 I (U U in C E.  X 3 in  0~ z 0. , C .) (U 0 W00 C 1 0 *  C Q. 0(0C  4E o. S m 0 m 4I OXI I . 4) i0 0 E & c . *o' Om a( 0 E . 0 (U 4 Q. a 0 3 an 3 (0 * I ( n C Q in * 0 b.  L. t c w in L O r m n tn  ) Q ) O La. o L. Q. Q. 18 box may be filled with different amounts of water and in this manner PS for each Starling resistor can be varied independently. RPl designates the resistance from the point at which Pi is measured to the end of the Starling resistor in tube 1. The same description applies to RP2., Rp3 and RP4. The remainder of the symbols used for this model are equivalent to those described for figure 2. A program was written for this model according to the following equa tions. The actual program is given in Appendix 1 as program 2. Given: Q is constant Qin = Ql + Q2 + Q3 + Q4 = Qout Po' = Q'RD + Po PSI < PS2 < PS3 < PS4 and all are constant RPl = R2 = RP3 = RP4 and are represented by R Condition 2: State 1: if Po' < PSI < PS2 < PS3 < PS4 then: Ql = RPSI R Pi PS4 Qq = R andP PS Pi P PS2 Pi PS + Pi PS4 and: Q= R R R + R solving for Pi: Pi Q.R + PSI + PS2 + PS3 + PS4 4 19 This equation is valid only if the Pi obtained from it is greater than PS4; that is, if flow is occurring through all four tubes. For simplicity in this program it was assumed that the only time Pi < PS4 was when Q = 0. Therefore,in this state and the following states if the calculated Pi was less than PS4, flow was assumed to be zero. In this state Pi = PSI when Q = 0. if PSI < Po' < PS2 < PS3 < PS4 then: Q = Pi Po' Pi PS2 P PS + Pi PS4 te:Q =  + + + R R R R Solving for Pi: pi = Q.R + Po' + PS2 + PS3 + PS4 4 Again, if the calculated Pi is less than PS4 this equa tion is not valid. In this state Pi = Po' when Q = 0. if PSI < PS2 < Po' < PS3 < PS4 then: = P P' + Pi Po' + P PS3 + Pi PS4 R R R R Solving for Pi: SQ.R + 2Po' + PS3 + PS4 Pi = 4 In this state if = 0, then Pi = Po' State 4: if PSI < PS2 < PS3 < Po' < PS4 then: =i Po' + Pi Po' + Pi Po' + Pi PS4 R R R R Solving for Pi: State 2: State 3: p= R + 3Po' + PS4 P4 = In this state if Q = 0, then P.i = Po'. Condition 3: if PSI < PS2 < PS3 < PS4 < Po' then: Pi Po' Pi Po' Pi Po' Pi PO' then: Q = + + ++ L~1^SL~ R R R R Solving for Pi: SQ*R + 4Po' This equation is always valid. As in program 1 the calculator was given an initial Po with which it calculated Po' according to the given equation. It then made the appropriate comparisons and calculated the correct Pi which it plotted against the original Po. The program was set up so that the calculator increased Po by a given interval and calculated a new Pi which was pl tted against the second Po. This cycle was repeated until the program wai manually stopped. Leading from program 2 it was necessary to investigate the relation sthit between Pi and Po in condition 2, states 1 and 2, when Q > 0 yet te resultant Pi < PS4; that is, when flow was occurring through only a iarttial number of the tubes. The following program was written to inves tigate this relationship. Refer to figure 4 for nomenclature. In this program the calculator was also given an initial Po with which it calcu lated the correct Pi and plotted it against Po. It then raised Po by a gi've increment and calculated a new Pi. This cycle was repeated until theprogram was manually stopped. This program is given in Appendix 1 as program 3. Given: Q is constant Qin = Ql + Q2 + Q3 + Q4 = Qout Po' = Q'RD + Po PS1 < PS2 < PS3 < PS4 Condition 2: State 1: if Po' < PSI < PS2 < PS3 < Q'R + PS1 + PS4, then: PS2 + PS3 + PS4 4 if Pil < PS4, then: Pi2 QR + PSI + PS2 + PS3 if Pi2 < PS3, then: p QR + PSI + PS2 i3 2 if Pi3 < PS2, then: Pi4 = *R + PSI Pil is valid only if flow is occurring through allfour tubes. If the given flow does not generate a Pi high e than PS4 then the Starling resistor in tube four will be closed. If no flow is occurring through tube 4, then Pi2 will be valid if flow is occurring through the re maining three tubes. If the given flow does not generate a Pi higher than PS3, then the Starling resistor in tube 3 will be closed. In this case Pi3 will be valid if flow is occurring through the remaining two tubes. Again, if the given flow does not generate a Pi higher than PS2, 22 then no flow will occur through tube 2, 3 or 4. Pi4 will then be valid for any flow which generates a Pi less than PS2. The same reasoning applies to state 2. State 2: if PSI < Po' < PS2 < PS3 < PS4, then: QR + PS2 + PS3 + PS4 + Po' if Pil < PS4, then: P2 = QR + PS2 + PS3 + Po' Pi2 3 if Pi2 < PS3, then: QR + PS2 + Po' Pi3 = 2 if Pi3 < PS2, then: Pi4 = Q'R + Po' Pi Versus Q It was also interesting to me to study the relationship between and Pi in a model similar to the one presented in figure 1. Therefore, a program was written to describe this relationship. In this program PT was the controlled variable and Q was the dependent variable. The pro gram was designed to utilize an initial given Pi to calculate the appro priate Q and plot Pi as a function Q. The computer was programmed to increase Pi by a given interval and repeat the initial process. This could be repeated until the desired curve was obtained. The program to calculate Q was based on the following relationships. The actual program is given in Appendix 1 as program 4. Given: Po is constant Po' = QR + Po Condition 1: if Pi < PS then: Q= 0 Condition 2: if Pi > PS > Po' then: Q P PS then: Q= p Rp Condition 3: if Pi > PS < Po' then: Pi Po' then: Q = Rp + RD The relationship between flow and inflow pressure was also studied in a model containing four tubes such as that presented in figure 4. As in the one tube model the program was designed to calculate Q from a given Pi and plot Pi against Q. The Pi was then increased a given incre ment and Q again calculated and plotted against Pj. This cycle was re peated until the desired curve was obtained. The calculation of was carried out according to the following relationships. This program is given in Appendix 1 as program 5. Given: Po is constant Po' < PSI < PS2 < PS3 < PS4 . Condition 1: if Pi < PSI < PS2 < PS3 < PS4 then: Q = 0 Condition.2: State 1: if PSi < Pi < PS2 < PS3 < PS4 then: Pi PSi Rpi State 2: if PSI < PS2 < Pi < PS3 < PS4 e Pi PSI Pi PS? then: Q = PS + RPI RP2 State 3: if PSI < PS2 < PS3 < Pi < PS4 Pi PSI Pi PS2 Pi PS3 then: Q = P + + R RPI RP2 RP3 State 4: if PSI < PS2 < PS3 < PS4 < Pi then: Q = Pi PS + P P PSS Pi PPS4 then: Q = + + +=~ RPI RP2 RP3 RP4 Condition 3 was not included in this program for the sake of sim plicity. Therefore, care was taken so that Po' never became greater than PSI during the construction of the curves from this program. This pro gram was used to study the effects of changing PS values while holding Rp values constant and vice versa. The result of changing both PS and Rp values simultaneously was also studied. Physical Model Pi Versus P. In order to test the mathematical model presented above and also to determine if values for the desired parameters could be obtained accurately a physical model was built. To obtain pressure:flow curves from the phys ical model an inflow reservoir, as diagrammed in figure 1, was utilized to maintain a constant inflow pressure. However, in order to obtain the relationship between inflow pressure and outflow pressure the model was constructed as in figure 2 in order to maintain a constant inflow rate. As in the mathematical model, the initial measurements were made in a one tube system in the physical model. In order to determine the rela tionship between Pi and Po, the physical model was arranged as indicated in figure 2. Rp and RD were simulated by small bore glass tubes of var ious lengths. The diameter of the Starling resistor was of such magni tude that its contribution to total resistance was negligible. The 25 Starling resistor was made by placing two polyethylene sheets together and heat sealing two strips 1.2 cm apart. The tube thus obtained was trimmed and cut to the desired length (6.5 cm).. During this procedure inflow pressure and outflow pressure were measured with Statham model 23 PC pressure transducers. Flow was measured utilizing a Statham model FTQC cannulating flow probe and a Statham model M4001 electromagnetic flowmeter. Pressures and flows were recorded on a Grass model 5C poly graph. In addition Pi was plotted against Po during the procedure by means of a Houston model HR98 XY plotter; Saline was used as the per fusing fluid. The relationship between Pi and Po at any constant flow was obtained in the following manner: (1) the outflow tube was lowered so that Po' was less than PS, (2) a constant flow was maintained by the finger pump, (3) the outflow tube was then raised slowly while Pi was being plotted against Po on the XY recorder. This same procedure was. carried out to obtain the relationship between Pi and Po at zero flow. During this condition flow in the reverse direction was prevented by the finger pump which occluded the inflow tube. According to the mathematical model presented previously, the Poat the breakpoint of the curve drawn during zero flow may be taken as a measure of PS (point A on figure 3). This was done for the physical model and the values obtained were used to calculate both Rp and RD. Rp was calculated as previously described according to the equation SPi Pg Rp = P The Pi used was that pressure which resulted from a constant flow while the system was in condition 2 (Ps > Po'). RD was  also calculated as described in the mathematical model. The Po at the breakpoint of a curve drawn at constant flow (point B on figure 3) sub 26 tracted from PS was used as the pressure drop along the distal segment. RD was then calculated as RD = P P The Rp and RD calculated by this method were compared to the known resistances of the small bore glass tubes which simulated Rp and RD. The resistances of the glass tubes had been calibrated previously by measuring the pressure drop across each tube at several measured flow rates. In order to test if the relationship between Pi and Po in the phys ical model followed that predicted by the mathematical model in a system which contained more than one tube, a physical model was built which con tained three tubes in parallel. This system is analagous to the one pre sented in figure 4 with the exception that only three tubes were used. The Starling resistor in each tube traversed a separate plexiglas box in order that the pressure surrounding each Starling resistor could be varied independently. Rpl, Rp2 and Rp3 were simulated with separate small bore glass tubes so that each could be varied independently of the others. A constant inflow was provided by means of a finger pump. In this model the relationship between Pi and Po was obtained in exactly the same manner as described for the onetube model. Pi Versus Q In order to determine pressure:flow characteristics of a onetube model, the model was arranged as in figure 1. Inflow pressure, outflow pressure and flow were measured and recorded as described previously. Flow was also measured by collecting the outflow for a timed period. Saline was used as the perfusing fluid. Rp and RD were again simulated in the model by small bore glass tubes of various lengths. The diameter of the tube in the Starling resistor was of such magnitude that its con tribution to total resistance was negligible. 27 During the construction of a pressure:flow relationship, outflow pressure was held constant at some value below the hydrostatic pressure of the water surrounding the Starling resistor. The inflow reservoir was initially placed below the level of the Starling resistor. It was then raised a given distance, usually 1 cm, and held there until a stable flow was attained. The resulting flow and pressures were recorded and and inflow pressure was plotted against flow. The reservoir was again raised and the resulting flow measured and plotted against inflow pressure. This procedure was repeated until the desired pressure:flow curve was obtained. The effects on the pressure:flow curve of changing Rp and RD, by substituting various lengths of the small bore glass tubing, and of changing PS, by varying the level of water in the plexiglas box, were all studied in this model. The relation between pressure and flow in a model containing three tubes in parallel was also studied. The model was set up in the same man ner as it was for obtaining the relation between Pi and Po. The only modification was that a constant inflow pressure was provided by means of an inflow reservoir. Pressure:flow curves were obtained from this model in exactly the same manner as that just described for the onetube model. Animals Fetuses Pregnant goats were anesthetized with chloralose (50 mg/Kg I.V.) and sustaining doses (10 mg/Kg I.V.) given hourly. Fetuses (135145 days gestational age) were delivered by caesarean section onto a warmed table adjacent to the mother. Care was taken to prevent the fetuses from breath ing by placing a bag filled with saline over their heads. Colonic temp erature was monitored and maintained between 3739C. Caution was taken 28 not to disturb the umbilical circulation. A tracheotomy was performed and tracheal fluid allowed to drain at atmospheric pressure through a one way valve into a beaker. The left carotid artery was isolated and loose ligatures placed around it. Both femoral arteries were isolated and can nulated. A thoracotomy was performed on the left side, removing the 3rd 5th ribs. The left pulmonary artery and the vein draining the lower lobe of the left lung were dissected free and loose ligatures placed around them. The blood supply to and from the middle and upper lobes of the left lung was isolated and ligated. Fetuses were anticoagulated with heparin (2400 U/Kg I.V.). A cannula was introduced into the vein of the lower left lung lobe via the left atrium and blood directed into a reservoir as indicated in figure 5. Pulmonary venous pressure (PVP) was varied by raising or low ering this reservoir. Blood was pumped from the reservoir through a heat exchanger into the left femoral artery. The heat exchanger consisted of a siliconized glass condensing coil over which warm water, regulated at 41"C, was circulated. A cannula was placed in the left carotid artery and led through a finger pump into the distal end of the left pulmonary artery, which now perfused only the left lower lobe of the lung. Pulmon ary artery pressure (PAP) and pulmonary venous pressure were measured with Statham model 23 PC pressure transducers. PAP and PVP were corrected for the pressure drop due to the resistance of the cannulas. Pulmonary arterial and pulmonary venous blood flows were measured with Statham model FTQC cannulating flow probes and a Statham model M4001 electro magnetic flowmeter. Systemic blood pressure was monitored by means of the cannula in the right femoral artery. Pressures and flows were recorded on a Grass model 5C polygraph. L. o0 4.. 0 0 O .I  0 U ... 0 4 4J M M 0 &L= U> 4 M tn . M 4 C U .0 0 (0 U I 0  E 0 " C C > 0 0 10 0 .0 0 0 n 0 0 C U 04 0 U0 Cu  C0 3 C . * 4J I+ > C  0 C 0 0 4 > . j 4 > 4  E 0 L 4 30 Cu 0 0 I 0 L  > C D I I I 0 0 00 Cu .. UC I Cu u 6 u 0 cc U . c U 0 U. L.) > >  xz w 31 The relationship between PAP and PVP was obtained in exactly the same manner as in the physical model: (1) the outflow reservoir was initially lowered below the level of the lung, (2) a constant inflow was maintained, and (3) the outflow reservoir was slowly raised while PAP and PVP were being recorded on the Grass polygraph. Simultaneously PAP was plotted against PVP on a Houston model HR98 XY plotter. Curves for zero flow were obtained simply by stopping the inflow pump, which occluded the inflow cannula, and following the same procedure just des cribed. Normally four curves were drawn; one at zero flow and three curves at three different constant flow rates. Rp and RD were calculated in exactly the same manner described for the onetube physical model. The curves obtained from the animals did not exhibit a sharply defined breakpoint as did the curves from the model. Figure 6 presents representative curves obtained from an unventilated fetal animal. The breakpoint for each of the curves obtained from the animals was arbitrarily defined as the point on each curve which was raised one mmHg above the baseline for that curve. In order to determine the effects of ventilation on Rp and RD, the following procedure was carried out on one group of fetuses. A set of curves was drawn first for the unventilated fetal lung. The animal was then ventilated with a gas mixture intended not to change the blood gas values of the fetus. This gas mixture contained 4% 02 and 6% C02 in N2 and was termed the fetal gas mixture. Animals were ventilated with posi tive pressure with a peak inspi ratory pressure of 30 cmH20. This was accomplished by placing a tube, attached to a side arm of the tracheal cannula, under a 30cm column of water. Expiratory pressure was kept equal to atmospheric pressure. Ventilation in each group of experimental 4 LC m a > c OA E0 L.O 0 Q QC L. C 0)I J C 0 uE E c S , C G i 0  L 4 o( 0 U .. L L C ~. I I it1 F~C CJ LIL1 4:::::4 _L~~ i' F * . .j r 4  L 1L I I r lt I 1 I 4 l+ 4  L  S+ + L J.. L JL' IL1L~ 'J.JfLliW I p L I i  I , ~ ~ I ~c T I IAuii\ ww,. dVd S"n I"" 7E +HtSi ; T F I I I I I I '' ' S4H+0 c 34 animals was carried out by this method. Another set of curves was ob tained while the animal was being ventilated with this fetal gas mixture. The animal was then ventilated with air and another set of curves drawn. During the construction of each set of curves, pulmonary arterial and pulmonary venous blood samples were drawn and analyzed for P02, PC02 and pH on a Radiometer blood gas analyzer. Resistances were calculated from the curves obtained according to the method previously described. In another group of fetuses the effects on Rp and RD of changing blood gases alone was investigated in the following manner. The bronchus to the left lung was ligated and cut distal to the tie to allow fluid from the left lung to drain at atmospheric pressure. This allowed venti lation of the right lung while the left lung remained unventilated. A set of curves was obtained from the left lower lobe while both lungs were in the unventilated fetal state. The right lung was then ventilated with the fetal gas mixture and a set of curves for the lower left lobe obtained The right lung was then ventilated with air and another set of curves drawn for the left lower lobe. Pulmonary arterial and pulmonary venous blood samples were drawn during the construction of each set of curves and again analyzed for P02, PC02 and pH. Resistances were calculated as previously described. The effects of bradykinin on pulmonary vascular resistance were studied on a final group of fetuses. A set of curves was obtained while the lungs of the animals were in the unventilated state. Bradykinin was then infused into the left pulmonary artery (60240 ng/min) and a set of curves acquired. The infusion was then stopped and the animals allowed to stabilize;.after which another set of curves was drawn. The animals were then ventilated with air. The effects of bradykinin during venti 35 lation with air were studied in the same manner as in the unventilated state ;that is, sets of curves were collected before, during and after the infusion of bradykinin. Pulmonary arterial and pulmonary venous P02, PC02 and pH were monitored during the construction of each set of curves. Resistances were calculated as previously.described. Neonates The effects of hypoxia on the pulmonary circulation of neonatal kids was investigated in the following manner. Kids were anesthetized with chloralose (50 mg/Kg I.V.) and placed on a warmed table. Sustaining doses of chloralose were given hourly. The neonatal animals were pre pared surgically in exactly the same manner as the fetal animals as indicated in figure 5. After the chest was opened the kids were main tained on positive pressure ventilation with air. The relationship between PAP and PVP was obtained in the kids in the same manner as in the fetal animals. Rp and RD were calculated from this relationship as previously described. After surgery was completed a set of curves was obtained while the kids were being ventilated with air. The animals were then ventilated with a mixture of 10% 02 in N2 and another set of curves obtained. The ventilating gas was then changed to 5% 02 in N2 and another set of curves drawn. Pulmonary arterial and pulmonary venous blood samples were drawn during the construction of each set of curves and analyzed for PO2, PC02 and pH. RESULTS Mathematical Model Pi Versus Po Figure 3 shows a plot, traced from the original, of the relation between Pi and Po in a onetube mathematical model obtained from program 1 when Rp = 1.0 mmHgmin/ml, RD = 0.5 mmHg.min/ml and PS= 5.0 mmHg. Three curves were drawn at flows of 0, 20 and 40 ml/min. For the curve drawn at 20 ml/min the pressure drop across the distal resistance (PoA PoB) is 10 mmHg. The pressure drop across the proximal resistance (Pi PoA) is 20 mmHg. Increasing the PS to 10 mmHg, while holding Rp = 1.0 mmHgmin/ml and RD = 0.5 mmHg.min/ml (figure 7), merely increases Pi; the pressure drops across the proxi mal and distal resistances remain the same. For the curve drawn at 20 ml/min the pressure drop across the distal resistance (PoA PoB) is still 10 mmHg. Also, the pressure drop across the proximal resistance is still 20mmHg, although Pi is 5 mmHg higher. The only other difference noted from increasing PS from 5 to 10 mmHg was that the breakpoint for each curve shifted to the right. Figure 8 represents the effects of increasing Rp from 1.0 to 2.0 mmHg.min/ml. RD was held at 0.5 mmHgmin/ml and PS was held at 10 mmHg. In this situation the pressure drop across the proximal resistance, at a flow of 20 ml/min, doubled from 20 mmHg to 40 mmHg in contrast to that in figure 7. However, the pressure drop across the distal resis tance remained 10 mmHg. The breakpoint for each curve remained the same for the curves of equal flows in figure 7. In figures 3, 7 and 8 36 44 0 0 S4 C L * 0. I (U E . I a) E s  E L" 4 0 C 4 0P 0 C C a L. e 0 C O*" u: cc 00 UC0 a 0 cm 41 CE COD * +3 . 0 0) ,, L 0 c c a. o 0i E E' z LL 4 2 do A 0Y Q o 0 0 uE E W U 4 C L 4 . g) E Q. 3 0 L.. 0)  3 II C Q 0E C L  0(06  o Ec O E U5Ce 0 0  L. 5 4 o . 0 4 J . Q: C H' 0) 0 fl 0)C co ( * O Cn O 1 Qo   U i 0  .C C ) Lz J . n. O O 0 0 0Q( o ao 0 CM a o E2 41 the Po at the breakpoint for each of the curves drawn during zero flow (PoA) is equal to PS. The relationship between Pi and Po in a system containing four tubes in parallel (program 2) is shown in figure 9. Program 2 was written (assuming that RPl = RP2 = RP3 = Rp4) to investigate the characteristics of the system when flow was occurring through all four tubes simultaneously, or when no flow was occurring at all. The program was written in this manner for the sake of simplicity. The characteristics of this system when flow was occurring through a partial number of the tubes were investigated in the subsequent program (program 3). In figure 9, RPI = Rp2 = Rp3 = Rp4 = 1.0 mmHgmin/ml, RD = 0.2 mmHgmin/ml and PS1 = 5, PS2 = 10, PS3 = 15, PS4 = 20 mmHg. Curves were drawn at 0, 40, 70 and 100 ml/min. On the curve drawn at zero flow, there is one breakpoint (point A on figure 9). The value for Po at this point is equal to the lowest PS. On each of the other curves, however, there are four distinct break points. In the curve obtained at a flow of 40 ml/min in figure 9, these breakpoints are marked by the letters B, C, D and E. The portion of this curve up to point B indicates the system is in condition 2: state 1 (Po' < PSI < PS2 < PS3 < PS4). From point B to point C the system is in condition 2: state 2 (PSI < Po' < PS2 < PS3 < PS4); from point C to point D it is in condition 2: state 3 (PSI < PS2 < Po' < PS3 < PS4); and from point D to point E the system is operating in accordance with condition 2: state 4 (PSI < PS2 < PS3 < Po' < PS4). Beyond point E the system is in condition 3 (Ps1 < PS2 < PS3 < PS4 < Po') Up to point B in figure 9flow through each of the tubes is occurring in accordance with condition 2, or the waterfall condition (the PS of each E 4 CLU O .o  E L Ui 4 0 C im 0 II 4  O II cCOE E L CL L II 0 CCth L 0 0 ,A u  Ic O II Io CC L m n 0 C3 E IU 4 . E o 0 2 U.0 CU o o c c .0 .O 01 (A C 4o La a c0)U u  4C 0 Li. 4'Oo 2 .0 o 2 0 I I I I 0u Ni 0 44 tube is greater than Po'). From point B to point C (condition 2: state 2) tubes 2, 3 and 4 are still in the waterfall condition, but .flow through tube 1 has changed to condition 3 (PSI'< Po'). From C to D (condition 2: state 3) tubes 3 and 4 are in condition 2, but tube 2 has joined tube 1 in condition 3. From point D to point E (condition 2: state 4) only tube 4 is still in the waterfall condition; flow through the remaining three tubes is occurring in accordance with condition 3. From point E on, flow in all four tubes is in condition 3. As shown by the dashed line in figure 9, the first breakpoint for each curve that has a positive flow may be connected by a straight line. However, this line does not intersect the breakpoint for the curve drawn at zero flow. Program 2, by means of which figure 9 was obtained, assumed either that flow was occurring through all four tubes simul taneously or that flow was zero. Therefore,the condition when flow was occurring through only one, two or three of the tubes was not considered. Program 3 was written to observe the relation between Pi and Po when flow was occurring through less than four tubes. Figure 10 illustrates the results of plotting program 3. For simplicity this program was written to study the characteristics of the system only in condition 2: states 1 and 2. In figure 10, Rp = 1.0 mmHg.min/ml, RD = 0.2 mmHg.min/ml and PSI = 5, PS2 = 10, PS3 = 15, PS4 = 20 mmHg. As in figure 9, the first breakpoints on the curves drawn at 40, 80 and 120 ml/min can be connected by a straight line. However, the first breakpoints for the curves drawn at 20, 10, 1 and 0 ml/min cannot be connected by a straight line. For all curves the first breakpoint occurred when Po' became greater than PSI1 4 O 0 II U 4 CL0 04 CC o L ** IC L4  E E t0 3 II 40 C C C 4 0 CL 0. 4) (U 0m U .o II r 4, c e . 0 3.Q Q. * S1 (0  cc * e  0 4  1 C W O 41 0E 0 O (U 11 O . .o0 c,, L U  U.. , 0 .r 0 u Oa / / / 0 II 46 0 0 o E Q:o 0 I 0 I / / / / / / / I 0E 2P ~ Pi Versus Q The relationship between Pi and Q for a onetube mathematical model as described in figure 1 is displayed in figure 11. The curves in this figure were obtained from program four. For curve 1, Rp = 1.0 mmHg.min/ ml, RD = 0.2 mmHg.min/ml and PS = 10 mmHg. For curve 2, Rp = 1.0 mmHg. min/ml, RD = 0.2 mmHg.min/ml and PS = 15 mmHg. For curve 3, Rp = 0.5 mmHgmin/ml, RD = 0.2 mmHg.min/ml and PS = 10 mmHg. In curve 1, no flow occurred until Pi became greater than PS, which was equal to 10 mmHg. Up to this point the Starling resistor Is closed and the system is in condition 1. When Pi is higher than PS flow occurred in accordance with condition 2 (Q = Pi PS). Point A Rp marks the point on curve 1 that Po' became greater than PS. Beyond this point condition 3 governed flow through the system (Q = Pi Po). Rp + RD Curve 2 demonstrates the effect of increasing PS from 10 to 15 mmHg. On curve 2, no flow occurs until a Pi of 15 mmHg is reached. Also, the flow at which the system changes from condition 2 to condition 3 (point B) has increased, because Po' must now increase to 15 mmHg rather than 10 mmHg for the change to occur. The slope of curve 2 during conditions 2 and 3 is the same as the slope of curve 1 during conditions 2 and 3. Curve 3 presents the effects of changing only Rp. Neither the pressure at which flow begins to occur nor the flow at which the system changes from condition 2 to condition 3 (point C) is different from curve 1. However, the slope of curve 3 during conditions 2 and 3 is greater than the slope of curve 1 during conditions 2 and 3. The relationship between Pi and Q in a model containing four tubes EE 4 EE 0 4 Tr 0 EE E 4, EE q4UU LQ) 0 LA 4 0 4 o LG)EE L 3 E CL L 4 0 0)I EE] cu .r 0 0 C 3 C > > L. L 00 a. E ID cr o uo c 0 = LCI EEE 4 EEE o > IDVp LB II It I LC 41J m L) vCALn V ca a a r C) 0)a_ E E 00)0 m.2.m L C tc C; C EE Onf r ao co CD 0 U 4w' W 0) (000 a3 L 0) III LL4JraCncrcZ n Ct 0 0 0 OD .0 .0 E *oO 1*u C 50 in parallel is shown in figure 12. In this figure tube 1 has an Rpl of 4.0 mmHg.min/ml and a PSI of 10 mmHg; tube 2 has an RP2 of 4.0 mmHg.min/ml and a PS2 of 15 mmHg; tube 3 has an Rp3 of 4.0 mmHg.min/ml and a PS3 of 20 mmHg; and tube 4 has an Rp4 of 4.0 mmHg.min/ml and a PS4 of 25 mmHg. There are four distinct breaks (points A, B, C and D) on this curve. Up to point A, Pi has not exceeded the lowest PS and no flow takes place because all the Starling resistors are closed. Between points A and B, Pi is greater than PS] but less than PS2; therefore,flow is occurring through tube one only. Between points B and C, Pi is greater than PS2 but less than PS3. In this region flow Is occurring through tubes 1 and 2. Between points C and D, flow is occurring through tubes 1, 2 and 3 because Pi is greater than PS3 but less than PS4. Beyond point D, Pi is greater than PS4 and flow is taking place in all four tubes. Figure 13 points out the effects of decreasing proximal resistance without changing PS values. In this figure curve I is the same as in figure 12. For curve 2, Rp] = 1.0, Rp2 = 2.0, Rp3 = 3.0, RP4 = 4.0 mmHg.min/ml and PSI = 10, PS2 = 15, PS3 = 20, PS4 = 25 mmHg. On curve 2 there are again four distinct breaks as in curve 1, but the slope of the linear portion of curve 2 has increased in comparison to the slope of the same portion of curve I. Of interest is the fact that the inter cept of the straight line portion (beyond the last break) of the two curves is different. Therefore, in this model changing only resistance changes both the slope and the intercept of the straight line portion of the pressure:flow curve. Figure 14 demonstrates the effects of decreasing PS while holding Rp constant. Curve I in this figure is the same as the curve presented 4 0 E tL n O I 0 r L E m. E EO 0 0 4 E II 0 4 I C 4^ E O) L  fu E U 0 4 C E 0 r 0 E *~CVC rQ c cI 0 40e 0.0 C.  C  0 ii E *'U E W 0 4) C14 L II I  4 &WnCL . 1 II II  uC Q < 0 0 (U!W/ll) 0 E E 0r 0 3.. F' E C 4 E 04 O0 SJ E I EU E L Y I O il 0 0) CM4 M 0I . 0. ** 0 11 a0 > r E 0 L ME 0"O E L 0 .. cc 4 E LA o C( E II ) L L E ".  :O3 " L 0 0) 0)  0 4. 0n 4 E = E m EE O t E L C ( 0 4 * 0 E S0 (U II II U Ln fU0 O  L C 1 0.. ( 0) a  cr >E E . ... E 0 4 E E E 00U * Cc E E O E E II , t ,, L II II  =3 L 0 ) 0u * ra C a) a. 0 E LL 4j 0 W W E O 0 CP E E 0 (UIu/IW) 4 o04 0 Lf% 4, EU 10 0 L 4 00 L EO 00 LO 1 0 4E Q)L LcO) 0 ECu 0 4f Oc 0 fu CU o LC cn cU 0 Lv0 0 41 0 0 o 0 C LL 41 04NE E >0 L II N1 (n )c E 0 E SEQ 4 II E Ul T Ln E CU 0 (nf 0DE E E CU 0 I E > ~1 II 3Q CLL 0I o~a I1 E mn E C N1 00 CU 1 C ( U ~ Ni ) flC/) 0 (U:W/IW) 0 57 in figure 12. For curve 2, Rp, = RP2 = RP3 = Rp4 = 4.0 mmHgmin/ml. PSI, PS2, PS3 and PS4 have values of 5, 10, 15 and 20 mmHg respectively. In figure 14 the slope of the straight line portion of curve 2 is the same as that of curve 1; however, the intercept has decreased. Therefore, changing the PS values alone changes only the intercept of the straight line portion of the pressure:flow curve and not the slope. The question has sometimes arisen as to whether a pressure:flow curve may have less of a slope (increased resistance) than another in a family of curves and simultaneously have a lower intercept than the curve with a lower resistance. Figure 15 shows that this situation is indeed possible from program 5. For curve I in this figure, RpI = RP2 = Rp3 = Rp4 = 1.0 mmHg.min/ml and PSI = 5, PS2 = 10, PS3 = 15, PS4 = 20 mmHg. Curve 2 has the same values for PS as curve 1, but in curve 2, RpI = 1.0, Rp2 = 2.0, RP3 = 3.0 and RP4 = 4.0 mmHgmin/ml. In this instance curve 2, which has a higher resistance than curve 1, has an intercept which is less than curve 1. Physical Model Pi Versus Po Figure 16 illustrates an XY recording of the relationship between Pi and Po in a one tube physical model set up as indicated in figure 2. In figure 16 the glass tubes simulating both Rp and RD had a resistance of 0.110 mmHgmin/ml. The depth of water in the box produced a pressure surrounding the Starling resistor of 10 mmHg. The three curves in figure 16 were drawn on the XY recorder at constant flow rates of 0, 74 and 111 ml/min. The Po at the breakpoint on the curve drawn at 0 ml/min (PoA) should be a measure of PS, and as can be seen in the figure, is very close to 10 mmHg, which was the pressure produced by the depth of E 4 , Wn O * 4 0 toC 0 in C 0) E E wr E M o E E L. OE in ai S 0 4 On O a) 0 U0 C J E 3 CL *II  E a) II 'E O t/ o)  E E. ) cn E   D. II Z" E c03 E O\ C .J iE c N. . Cn uLL\ E LOll 04 II e O II 4 N N 0 E E Cuo aC. cc E O oL 0 1 C 0 *o "   11 4 E 0 o 0 r" C II S c EE  f u EE T L C I . 4. C0 0 D 0C E o' E " Cen ) II E cc> E L ) t C   U3 1 C O0 E U) 0 II m 0 .0 01 C1 OC 4' = C CL E o E 0 0Q E c E . o * Uf 4J LO I 0 4L1 A1 mJ SQ) C Z: L . II a) II a) . > > o a) a) L (r>L LLU 4 41 Q. 0) : U 0 (U! W/iUw) s I E 60 water in the plexiglas box. As in the mathematical model the pressure drop across the distal resistance is given by POA POB (or PS POB) for each flow rate. The pressure drop across the proximal resistance is given by Pi PoA Cor Pi PS), where Pi is the inflow pressure in the system when the system is in condition 2. Therefore,in figure 16 the pressure drop across the distal resistance at a flow of 74 ml/min is 6.6 mmHg. The pressure drop across the proximal resistance is 7.4 mmHg. The effects of increasing PS upon this relationship are shown in figure 17. To increase PS more water was added to the plexiglas chamber until a depth producing a PS of 15 mmHg was achieved. Rp and RD were kept the same as in the previous figure. As noted in the figure, the pressure drop across the distal resistance at a flow of 74 ml/min is still 6.7 mmHg and the pressure drop across the proximal resistance is still 7.3 mmHg. However, the breakpoint for each curve has been shifted to the right by 5 mmHg when compared to figure 16. Also the Pi during condition 2 for each curve has increased 5 mmHg. By increasing Rp and maintaining PS at 10 mmHg the curves pre sented in figure 18 were obtained. In this figure RD was equal to 0.216 mmHgmin/ml and PS was held at 10 mmHg as in figure 16. In figure 18 the breakpoint for each curve occurs at the same point as in figure 16 and the pressure drop across the distal resistance at a flow of 74 ml/min is still 6.6 mmHg as in figure 16. However, the Pi during condition 2 for the curve drawn at a flow of 74 ml/min has increased by 9.6 mmHg and the pressure drop across the proximal resis tance has increased to 16.8 mmHg. The pressure drops across the proximal and distal resistances FIGURE 16. Recording from the one tube physical model of the relation between Pi and Po. Rp = 0.110 mmHgmin/ml, RD = 0.110 mmHgmin/ml, PS = 10 mmHg 50 40 I E E 30 III ml/min S20 74 ml/m'n t *0 ml/min 20 o * 20 I0 Pn 0 (mm.Hg.) 10 2 FIGURE 17. Recording from the one tube physical model of the relation between Pi and Po: effect of increasing PS. Rp = 0.110 mmHgmin/ml, RD = 0.110 mmHgmin/ml, PS = 15 mmHg l III ml/min Q = 74 ml/min rninwr n .. d 4 0 ml/mmn oA (mm.Hg.) FIGURE 18. Recording from the one tube physical model of the relation between Pi and Po: effect of increasing Rp. Rp = 0.216 mmHgmin/ml, RD = 0.110 mmHg'min/ml, PS = 10 mmHg Q iII rnVitn 6 = 74 ml/min 0 o mI/mn 0 / / 20 Po 6 (mm.H9.) 11 1 . ~UI ~I~ ~  20 67 obtained from these curves can be used to calculate proximal and distal resistance simply by dividing them by the flow rate for each curve. This was done and the values obtained were compared to the previously calibrated resistance values fQr the glass tubes used to simulate proximal and distal resistance. The results of this comparison are displayed in figure 19. The bars labelled C in this figure depict the calibrated resistances for the three small bore glass tubes used in this study. The bars labelled P for tubes 1, 2 and 3 indicate the resistance of these tubes calculated according to the method just described when each of these tubes was placed in the proximal position in the model. The bars labelled D are the resistances calculated for these tubes when they were placed in the distal position. These data show that there is no significant difference between the known resis tances of tubes 1, 2 and 3 and the resistances calculated according to the method just described when the tubes were placed in either the proximal or distal position in the model. The relationship between Pi and Po in a physical model with three tubes in parallel is exhibited in figure 20. In these curves RpI = RP2 = Rp3 = .162 mmHg.min/ml, RD = .110 mmHg.min/ml and PSI = 6.5, PS2 = 15.0 mmHg. One curve was drawn at zero flow and another curve was drawn at a flow rate of 112 ml/min. As shown in the figure there is only one breakpoint on the curve drawn at zero flow. For the curve drawn at 112 ml/min there are three breakpoints as indicated by the arrows. \ However, the small difference in the slopes of the portions of the curve between the breaks makes it difficult to visualize the precise breakpoints. Therefore, a physical model with only two parallel tubes was used to observe this relationship. The results of this system are (A CU W 3 ~4J 4 00u cr 0 U u 4P u 0 ro 'U t6. 4i In4Jl (a Vc = 0 4j oc fOL M4' E u x 4 0 00 L 00. CE 0 0 In  (U 4.' LU Er 0 i L.) CLL _0 ul Q) 4 0,3  0 C.0 w .Q ' 4 z,0C FE  i l Mw 0.  0  a  m mm m m m m m ii a (U  mmm   T 0 c a I Si O (. O      H a 'HI (U I (jW/ulw. ECH W) AP 0; A 0I N 0) l ij _ __I~_~   ~~  1 1 I FIGURE 20. Recording from the three tube physical model of the relation between Pi and Po. Rp1 = R P2 = Rp = 0.162 mmHgmin/ml, RD = 0.110 mmHggmin/ml, PS 6.5 mmHg, PS = 10 mmHg, PS 15 mmHg 6 a 112 mI/min S 0 ml/min _ __ 72 shown in figure 21. For this figure Rpl = RP2 = 0.162 mmHgmin/ml, RD = 0.110 mmHg.min/ml, PSI = 10 mmHg and PS2 = 15 mmHg. Curves were drawn at flows of 0, 40, 110 and 142 ml/min. These flow rates were high enough so that flow was occurring through both tubes at all times. For the curve drawn at zero flow there is only one breakpoint as pre dicted by the mathematical model. For each of the other curves there are two distinct breakpoints, indicated on the curve drawn at 40 ml/min by the arrows labelled A and B. According to the mathematical model flow, up to point A, is occurring according to condition 2 in both tubes. Between point A and point B flow is occurring according to condition 3 (Pi > PSi < Po') in tube 1, but still according to condition 2 in tube 2 (Pi > PS2 > Po'). Beyond point B flow is occurring according to condi tion 3 in both tubes. Also, as predicted by the mathematical model (figure 9) a line drawn through the first breakpoint of each curve (indicated by the dashed line on figure 21) does not intersect the breakpoint of the curve drawn at zero flow. To investigate the relation between Pi and Po in a multitube model when flow was taking place through only a partial number of tubes, the threetube physical model was again employed. As in the mathematical model this relation was studied only in condition 2: states 1 (Po' PSI < PS2 < PS3 < PS4) and 2 (PSI < Po' < PS2 < PS3 < PS4) in order to determine the position of the first breakpoint for each curve. Figure 22 demonstrates this relationship. In this figure Rpl = RP2 = Rp3 = 0.216 mmHgmin/ml and RD = 0.110 mmHgmin/ml. The depth of water in each box simulated surrounding pressures of PSI = 6 mmHg, PS2 = 10 mmHg and PS3 = 14.2 mmHg. Curves were drawn at 0, 15, 52, 105, 118 and 133 ml/min. As indicated by the dashed line, the breakpoint for the curves FIGURE 21. Recording from the two tube physical model of the relation between Pi and Po: flow occurring in all tubes. RpI = RP2 = 0.162 mmHg'min/ml, RD = 0.110 mmHgmin/ml, PSI = 10 mmHg, PS2 = 15 mmHg = 40 ml/min B A Iy  0Q 0 mt/min u J 20i 0 imm. i 50 40 I E E 30 rrr.rsr+nr~Praraa~"ldlDDU"l"~ i~142 mi/min ~ i~110 ml/min~~`~, " 10 io 20 Po 0 (mm.Hg.) FIGURE 22. Recording from the three tube physical model of the relation between Pi and Po: flow occurring in a partial number of tubes. RpI = Rp = Rp3 = 0.216 mmHgmin/ml, RD = 0.110 mmHg.min/ml, PSI = 6.0 mmRg, PS2 = 10 mmHg, PS3 = 14.2 mmHg A e Q= 133 ml/min Q 118 mVmin , 6105 l ml/nin 6=105011/^10~U = 52 mVmin 0 15 ml V \/min \E /min \ .o m\1 0*0 mimn 1 Io po 6 (mm.Hg.) o1 25 20 I E E 15 r  20 20 77 drawn at 105, 118 and 133 ml/min (points A, B and C) can be connected by a straight line. However, this line does not intersect the break point of any of the remaining three curves. Neither can a straight line be drawn through points D, E and F. Ti. is exactly what was predicted by the mathematical model in figure 10. Pi Versus Q The relationship between Q and Pi in a one tube physical model is shown on figure 23. In this instance Rp = 0.110 mmHg.min/ml and RD = 0.216 mmHg.min/ml. The water depth in the box simulated a PS of 10.3 mmHg. Throughout the drawing of the curve Po was held at 0 mmHg. As the curve indicates there is no flow until Pi becomes greater than PS, after which flow occurs in a linear relationship with Pi up to point A. On this portion of the curve, the reciprocal of the slope of the line is 0.111 mmHgmin/ml, which corresponds very well to the resistance of the glass tube used in the proximal position. This indicates that flow is occurring in accordance with condition 2 as predicted by the mathematical model. Beyond point A the reciprocal of the slope of the line is 0.308 mmHgmin/ml, which agrees well with the sum of Rp and RD, or total resistance. This indicates that point A is the flow at which Po' becomes greater than PS and that beyond point A flow occurs according to condition 3 as predicted by the mathematical model. In the following figures the relation between Pi and Q will be studied only in conditions 1 and 2. Figure 24 illustrates the effect on the pressure:flow curve of increasing Rp. In curve 1, Rp = 0.110 mmHg.min/ml, RD = 0.110 mmHgmin/ ml and PS = 10.3 mmHg. In curve 2, Rp = 0.216 mmHgmin/ml and RD and PS were the same as in curve 1. The Pi at which flow begins to occur FIGURE 23. Recording from the one tube physical model of the relation between Q and Pi. Rp = 0.110 mmHgmin/ml, RD = 0.216 mmHg'min/ml, PS = 10.3 mmHg 0 5 1o pi (mm.Hg.) FIGURE 24. Recording from the one tube physical model of the relation between Q and Pi: effect of increasing Rp. Curve 1 Rp = 0.110 mmHgmin/ml, RD = o.110 mmHgmin/ml, PS = 10.3 mmHg. Curve 2 Rp = 0.216 mmHgmin/ml, RD = 0.110 mmHgmin/ml, PS = 10.3 mmHg CURVE I CURVE 2 (mm.Hg.) 82 is the same for both curves; however, the slope for curve 2 is less than the slope of curve 1 as predicted by the mathematical model. Figure 25 presents the effects on the pressure:flow relationship of increasing only PS. For both curves 1 and 2, Rp = 0.110 mmHgmin/ml and RD = 0.110 mmHgmin/ml. In curve 1, PS = 10.3 mmHg, but in curve 2 PS = 15.4 mmHg. Po was held at 0 mmHg for both curves. As shown by the figure, no flow occurred in curve 1 until Pi became greater than 10.3 mmHg. In curve 2 no flow occurred until Pi became greater than 15.4 mmHg. However, the slope of both curves is the same after flow has begun to take place. The behavior of the physical model in this case is again in accordance with that predicted by the mathematical model. The threetube physical model was used to investigate the relation ship between Q and Pi in a multiple tube system. This relationship is illustrated in figure 26. For curve 1, the model was arranged so that Rpl = 0.436 mmHg.min/ml, Rp2 = 0.162 mmHg.min/ml and RP3 = 0.110 mmHg. min/ml. The water level in each box was adjusted so that PSI = 7.8 mmHg, PS2 = 10.0 mmHg and PS3 = 12.9 mmHg. RD was 0.110 mmHg.min/ml and Po was held at 5 mmHg throughout the construction of the curve. Curve 1 exhibits three definite breakpoints as indicated by the arrows labelled A, B and C. Up to point A no flow occurred. As Pi increased beyond point A flow began to occur through tube 1 and between points A and B flow occurred only through tube 1. At point B flow began to occur through tube 2 and between points B and C flow was occurring through tubes I and 2. Beyond point C flow was taking place through all three tubes. As can be seen, the Pi at which flow begins to occur in each tube corresponds very well with the PS for each tube. FIGURE 25. Recording from the one tube physical model of the relation between Q and Pi: effect of increasing PS. Curve 1 Rp = 0.110 mmHgmin/ml, RD = 0.110 mmHgmin/ml, PS = 10.3 mmHg. Curve 2 Rp = 0.110 mmHgmin/ml, RD = 0.110 mmHgmin/ml, Ps = 15.4 mmHg CURVE I 0 5 10 P. 15 (mm.Hg.) 20 FIGURE 26. Recording from the three tube physical model of the relation between Q and Pi: effect of increasing Rp. Curve 1 RpI = 0.436 mmHgmin/ml, Rp2 = 0.162 mmHgmin/ml, Rp3 = 0.110 mmHgmin/ml, RD = 0.110 mmHgmin/ml, PS = 7.8 mmHg, PS2 = 10 mmHg, PS3 = 12.9 mmHg. Curve 2 RPl = 0.436 mmHg.min/ml, RP2 = 0.324 mmHgmin/ml, Rp3 = 0.272 mmHg.min/ml, RD = 0.110 mmHgmin/ml, PSI = 7.8 mmHg, PS2 = 10 mmHg, PS3 = 12.9 mmHg CURVE CURVE 2 87 Also shown in this figure is the intercept of that portion of curve 1 beyond point C (the straight line portion), indicated by the dashed line. Curve 2 in figure 26 indicates the effects of increasing Rp on the relation between Q and Pi. For curve 2 the values for PS and RD were the same as for curve 1. Po was held constant at 5 mmHg during the construction of curve 2. However, for curve 2, Rpl = 0.436 mmHg. min/ml, Rp2 = 0.324 mmHgmin/ml and Rp3 = 0.272 mmHgmin/ml. There are three distinct breaks on curve 2, each of which occurs at the same value of Pi as on curve 1. However, the slope of the straight line portion of curve 2 is less than that of curve 1. Also the intercept of curve 2, indicated by the dotted line, is different from that of curve 1. This figure also affords an example of the phenomenon shown in figure 15. That is, curve 2 has a greater Rp than curve 1, but also has a lower intercept. Figure 27 points out the results of increasing PS on the pressure: flow curve. For both curve 1 and 2, Rpl = 0.436 mmHg.min/ml, RP2 = 0.324 mmHg.min/ml and RP3 = 0.272 mmHg.min/ml. In each case RD = 0.110 mmHgmin/ml and Po was held constant at 5 mmHg throughout the procedure. For curve 1, the model was arranged so that PSI = 7.8 mmHg, PS2 = 10.0 mmHg and PS3 = 12.9 mmHg. For curve 2, PSI = 10.0 mmHg, PS2 = 12.9 mmHg and PS3 = 15.0 mmHg. As indicated by the arrows there are three breakpoints on each curve which correspond to the three PS values for each curve. The intercept of the straight line portion (indicated by the dashed line for both curves) of curve 2 is higher than the intercept of curve 1, but the slope of both curves is the same. Thus the physical model behaves in the manner predicted by the FIGURE 27. Recording from the three tube physical model of the relation between 0 and P.:, effect of increasing PS. Curve 1 same as curve 2 in figure 26. Curve 2  Rpl = 0.436 mmHg'min/ml, Rp2 = 0.324 mmHgmin/ml, Rp3 = 0.272 mmHgmin/ml, RD = 0.110 mmHgmin/ml, PSI = 10 mmHg, PS2 = 12.9 mmHg, PS3 = 15 mmHg CURVE 'CURVE 2 (mm.Hg.) mathematical model. Animals Fetuses The relationship between pulmonary artery pressure (PAP) and pulmonary venous pressure (PVP) in an unventilated fetal lung has already been shown in figure 6. This same relationship in a fetus ventilated with air is presented in figure 28. The intermittent loops in each curve demonstrate the effect of positive pressure inflation on PAP and PVP. These loops were disregarded in obtaining the values necessary to calculate Rp and RD. Only the portions of each curve during end expiration were used to obtain these values. In the unventilated lung the trachea was open to atmospheric pressure. There fore, in the ventilated animals end expiratory pressure was held at atmospheric pressure so that a comparison could be made at the same alyeolar pressure. Changes in Rp, RD and PS when the fetal animals were ventilated with a fetal gas mixture and then with air are depicted in figure 29. The bars labelled F indicate values for the unventilated animals; the bars labelled VFG represent those animals ventilated with the fetal gas mixture; and the bars labelled VA represent animals ventilated with air. Upon ventilation with the fetal gas mixture Rp fell significantly from 3.78 to 2.95 mmHg.Kg.min/ml. Distal resistance decreased, but not significantly, from 0.714 to 0.569 mmHg.Kgmin/ml. Upon substituting air for the fetal gas mixture, both proximal and distal fell signifi cantly to 1.57 and 0.262 mmHg.Kg.min/ml respectively. In the unventi lated lung PS averaged 21.6 mmHg. Upon ventilation with the fetal gas mixture PS fell significantly to 16.7 mmHg. Further ventilation with 