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Indicator Methods for Measurement of Organ and Tissue Blood Flow

Niels A. Lassen, Ole Henriksen, Per Sejrsen

10.1002/cphy.cp020302

Source: Supplement 8: Handbook of Physiology, The Cardiovascular System, Peripheral Circulation and Organ Blood Flow

Originally published: 1983

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Basic Concepts
1.1 Systemic Steady State
1.2 Indicators
2 Indicator‐Dilution Methods
2.1 Constant Infusion (Stewart Principle)
2.2 Constant Infusion with Constant Recirculation (Fick Principle)
2.3 Bolus Injection (Henriques‐Hamilton‐Bergner Principle)
2.4 Flow by Indicator Fractionation (Sapirstein Principle)
3 Flow Measurement by Indicator Mean Transit Time
3.1 Noncompartmental Analysis
3.2 Compartmental Analysis
4 Practical Applications of Indicator Methods for Blood Flow Measurements in Individual Tissues
4.1 Cutaneous Tissue
4.2 Subcutaneous Tissue
4.3 Myocardium
4.4 Skeletal Muscle
4.5 Myometrium
4.6 Brain
4.7 Kidney
4.8 Lungs
4.9 Liver
4.10 Cardiac Output
Figure 1. Figure 1.

Fluid flowing through tube at constant rate (F; ml/s). At certain site cross‐stream mixing can be induced. Graph (below) shows outlet concentration (Cout) of indicator infused at constant rate of influx (Jin) upstream to mixing site. F is calculated as Jin divided by Cout (∞) during indicator steady state, plateau level of curve (Stewart principle, see Eq. 5).

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY
Figure 2. Figure 2.

Correction for recirculation in continuous‐infusion experiment by sampling from outlet of organ studied [Cinj (t)] and from symmetrical organ [Cnoninj(t)], e.g., kidneys, forearms, legs. Steady‐state Cout used in Eq. 5 is maximal difference between these 2 concentrations.

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY
Figure 3. Figure 3.

Outflow concentrations of indicator after bolus injection with recirculation seen by increase in concentration after peak. Broken line, curve after correction for recirculation (see RECIRCULATION, p. 26, and CORRECTION FOR RECIRCULATION, p. 37). F then calculated as injected dose divided by area under outflow curve corrected for recirculation (see Eq. 21).

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY
Figure 4. Figure 4.

Equal‐area rule, as described by Bergner 8. Outlet curves from different outlets of system with a single well‐mixed inlet have different shapes but same area. Thus total inflow (F) can be calculated as dose injected divided by area applied to any outlet.

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY
Figure 5. Figure 5.

Fractional rate of indicator ([dQ(t)/dt]/Qo), which leaves single‐inlet‐single‐outlet system after injection of amount Qo as ideally brief bolus (impulse). This normalized outflow curve represents frequency distribution of transit times within system h(t). Mean transit time () is calculated as time‐weighted area under h(t) curve, that is = · h(t) dt (see Eq. 38).
Figure 6. Figure 6.

Curves, cumulative fraction of ideally brief bolus that has left system H(t) and fraction remaining in the system (residue) [1 − H(t)] (see Eqs. 39,40); equals area between horizontal line 1 and H(t) curve, which is similar to area under residue curve, dt (see Eq. 46).
Figure 7. Figure 7.

Outflow curve during continuous‐infusion experiment. Step‐input function apparently is a series of small, ideally brief impulses (upper panel), each with response curve h(t) (middle panel). Outflow curve (lower panel) is built up as sum of contributions to outflow from each of these brief impulses (see Eq. 41).
Figure 8. Figure 8.

Constant infusion, inlet‐outlet detection: Kety‐Schmidt method 45. Upper curve shows inlet concentration [Cin(t)] and lower curve shows outlet concentration [Cout(t)]. Perfusion coefficient is calculated as tissue‐to‐blood partition coefficient (λ) times concentration at infinity (C∞) divided by area between curves (see Eq. 45).
Figure 9. Figure 9.

Figure showing that area between inlet‐outlet curves divided by height (A/H) during constant infusion [Kety and Schmidt (45)] equals area/height ratio of residue curve in bolus experiment, namely, mean transit time of system.

Lassen et al. 52
Figure 10. Figure 10.

Constant‐infusion experiment with residue detection. Top: input [Jin(t)] starts instantaneously (step) at time zero at left and stops instantaneously at time zero at right. Bottom: residue curve initially linear in time interval corresponding to shortest transit time in system. During indicator steady‐state curve reaches plateau level. After input dropped to zero (desaturation), curve changes are symmetrical. According to Eq. 42 the plateau level (Q∞) equals influx rate (jin,∞) times . Thus equals relative reciprocal initial slope, that is, = Q∞/(dQ/dt) for t → 0 (see Eq. 49).
Figure 11. Figure 11.

Bolus experiment with inlet‐outlet detection. Function hin(t), normalized to unit area, is frequency function of transit times for input system after ideally brief bolus input (impulse). Thus time‐weighted area of this curve to time infinity gives of input system (in). Function hout(t) is frequency distribution of t values for input plus system studied. Time‐weighted area of this curve gives for input plus system (out). For system studied is calculated out − in (see Eqs. 59,60).
Figure 12. Figure 12.

Summary of black‐box analysis for determining mean t. From top to bottom, input, residue, outflow, and cumulative outflow curves in saturation‐desaturation experiment (left) and bolus experiment (right). For details see SUMMARY OP NONCOMPARTMENTAL ANALYSIS FOR DETERMINATION OF , p. 35.
Figure 13. Figure 13.

Correction for recirculation in bolus experiment with residue detection in open system according to Larson and Snyder 49. gA(t), Normalized residue curve including recirculation after injecting amount Qo of indicator at inlet; gV(t), normalized recirculatory function after injecting indicator in outlet as bolus. Mean transit time equals area between these 2 curves divided by height (hatched area) (see Eq. 68). Difference between gA(t) and gV(t) does not equal 1 − H(t) function of system because here input to recirculatory system is brief bolus, whereas input to recirculatory system in first case equals h(t) function for system studied.
Figure 14. Figure 14.

Correction for recirculation in bolus experiment with residue detection in closed system. Both curves gA(t) and gV(t) approach same value as t →, namely g∞. Area between normalized curves (hatched area) divided by 1 − g∞ (height) calculates (see Eq. 69).
Figure 15. Figure 15.

Washout of indicator from single‐compartment system with varying blood flow, seen as nonlinear washout function in semilogarithmic plot. Average blood flow () from t1 to t2 can be calculated as shown: = 102 · λ · ln [Q(t1)/Q(t2)]/(t2 − t1) ml · h−1 · 100 g−1. Tissue‐to‐blood partition coefficient (λ) is in ml/g; Q(t1) and Q(t2) are recorded activities with identical detection efficiency at time t1 and t2, respectively. This method makes it possible to calculate average blood flow in, e.g., subcutaneous tissue during 24 h using 133Xe as indicator, which might have important clinical implications in patients with various vascular diseases.
Figure 16. Figure 16.

Experiment on isolated cat gastrocnemius muscle: 51Cr‐ethylenediaminetetraacetic acid injected intra‐arterially as bolus. Upper curve, normalized residue curve (ext.); lower curve, normalized outflow curve to unit area (vein) plotted in senulogarithmic diagram. After about 90 min curves become parallel, indicating that slowest washout rate (final slope) has practically been reached. Thus at this time monoexponential extrapolation can be used for calculating area or time‐weighted area from this time to time infinity.

From Lassen and Sejrsen 58, by permission of the American Heart Association, Inc
Figure 17. Figure 17.

A 133Xe‐washout curve in semilogarithmic diagram after atraumatic epicutaneous labeling over lateral surface of crus. Dots indicate recorded washout curve. The curve can be expressed by 2 monoexponential functions after curve resolution: the fast one is indicated by open circles; washout curve for cutaneous tissue alone is obtained by drawing line parallel to line through circles and passing through top point of measured curve. Subtracting values given by this line from measured values gives washout curve for subcutaneous tissue alone, indicated by crosses. Perfusion coefficient in cutaneous tissue equals washout rate constant obtained from fast component times λ for cutaneous tissue. Subcutaneous blood flow similarly calculated as washout rate constant of slow component times λ for subcutaneous tissue. This interpretation is based on monoexponential washout function from cutaneous as well as subcutaneous tissue, as shown in Figs. 18,19.

From Sejrsen 91, by permission of the American Heart Association, Inc
Figure 18. Figure 18.

A 133Xe‐washout curve measured over distal 2 mm of skin fold between thumb and forefinger after epicutaneous labeling. Remainder of hand covered by lead shield. In this set‐up, recorded washout curve can be regarded as washout from cutaneous tissue alone. Washout curve follows a monoexponential course to background values. Proposed model for this observation supports interpretation of 133Xe‐washout curves from skin by Sejrsen 92.

From Sejrsen 91, by permission of the American Heart Association, Inc
Figure 19. Figure 19.

A 133Xe‐washout curve from abdominal subcutaneous fatty tissue of cat after introduction of indicator atraumatically by diffusion from exposed tissue surface. Washout curve is monoexponential, supporting proposed model for interpretation of 133Xe‐washout curve from skin.

From Sejrsen 91, by permission of the American Heart Association, Inc
Figure 20. Figure 20.

Two simultaneously recorded 133Xe‐washout curves. Upper curve obtained after intradermal microinjection on lateral surface of crus on 1 side and lower curve after atraumatic epicutaneous labeling of symmetrical area on other leg. Initial part of upper curve is steeper than after epicutaneous labeling. Hyperemia caused by injection trauma can explain this. However, after about 15 min, 2 curve shapes are virtually identical, indicating that injection technique can be used when influence of injection trauma has become insignificant.

From Sejrsen 91, by permission of the American Heart Association, Inc
Figure 21. Figure 21.

Several 133Xe‐washout curves from skin fold between thumb and forefinger after epicutaneous labeling. Curves from study of influence of postural changes on cutaneous blood flow. Elevating hand 30 cm above heart level did not change 133Xe‐washout rate, indicating that blood flow remained constant. Elevating hand decreases local arterial mean pressure while venous pressure remains constant. Thus elevation of hand causes compensatory decrease in vascular resistance (autoregulation). Lowering hand 40 cm decreases cutaneous blood flow, indicating increase in vascular resistance because driving pressure remains constant during lowering. Arteriolar constriction underlying increase in vascular resistance during lowering is probably due to local venoarteriolar reflex mechanism 29. T½, half‐time; k, rate constant; f, cutaneous blood flow.

Data from Henriksen, Sejrsen, et al. 31
Figure 22. Figure 22.

Example of effect of venous stasis (40 mmHg) on 133Xe‐washout curves from skin fold between thumb and forefinger measured simultaneously on both sides. Patient sympathectomized (cervicodorsal) unilaterally 9 yr previously; no sweat secretion from hand on operated side, but excessive sweating (hyperhidrosis) on nonoperated side. Venous stasis caused normal decrease in blood flow on control side (upper curves), whereas blood flow remained constant on sympathectomized side (lower curves). Thus normal arteriolar constriction induced by venous stasis is abolished after chronic sympathetic denervation. Because normal vasoconstriction is seen 1st day after sympathectomy 28, arteriolar constriction induced by venous stasis is due to local sympathetic reflex mechanism (venoarteriolar reflex).

From Henriksen and Sejrsen 32
Figure 23. Figure 23.

A 133Xe‐washout curve from rabbit inguinal fat‐pad after atraumatic labeling. Washout curve is strictly monoexponential. r, Coefficient of correlation; p, probability.

From Nielsen 75
Figure 24. Figure 24.

Indirectly determined perfusion coefficient in rabbit inguinal fat‐pad based on 133Xe‐washout curve in Fig. 23 plotted vs. directly measured venous outflow; λ determined in each single case. Calculated and directly recorded blood flow in adipose tissue agreed well. byx, Linear regression coefficient.

From Nielsen 75
Figure 25. Figure 25.

Several 133Xe‐washout curves recorded after injection of 0.1 ml 133Xe dissolved in isotonic saline. Upper curve, from subcutaneous inguinal tissue in an unanesthetized rabbit; lower curve, from same tissue after surgical isolation of fat‐pad. In both situations initial phase of fast washout lasted about 30 min (trauma phase) and was followed by monoexponential washout during which calculated blood flow agreed with directly measured venous outflow (see Fig. 26).

From Nielsen 74
Figure 26. Figure 26.

Comparison between directly recorded blood flow values of isolated inguinal fat‐pad of rabbit and those calculated from monoexponential part of 133Xe‐washout curves 30 min after local injection of 133Xe dissolved in saline. In each case λ values calculated from determination of composition of blood and adipose tissue. Directly recorded perfusion coefficient values and those calculated from 133Xe‐washout curves agree well.

From Nielsen 74
Figure 27. Figure 27.

Several 133Xe‐washout curves from subcutaneous adipose tissue of distal part of forearm. Measurements performed with depot area on test arm (upper curves) placed at heart level (ref1); depot area lowered 40 cm and again placed at heart level (ref2); depot area on control arm remained at heart level. Log activity given against time in min. Figures denote calculated 133Xe‐washout rate constants · 103 ± 1 SE. Since λ was not determined, relative blood flow can be calculated only as ratio between washout rate constant during lowering and average value of washout rate constant at heart level. Lowering area 40 cm below heart level reduces blood flow by about 50% in that area, whereas blood flow remains almost constant on control side. Thus arteriolar constriction underlying decrease in blood flow during lowering seems caused by local mechanism (vasoconstrictor response).

Data from Henriksen 29
Figure 28. Figure 28.

Effect of 30‐mmHg venous stasis on 133Xe‐washout curves from subcutaneous tissue on distal part of forearm and at lateral maleolus. Patient sympathectomized (cervicodorsal) on both sides 2 yr previously due to manual hyperhidrosis. On leg 30‐mmHg venous stasis reduces subcutaneous blood flow 50%, corresponding to increase in total vascular resistance of about 35%. On sympathetically denervated forearm, however, venous stasis does not alter subcutaneous blood flow. Venous stasis of 30 mmHg induces decrease in total vascular resistance, indicating that arteriolar constriction induced by venous stasis is due to local sympathetic reflex mechanism because arteriolar constriction can be demonstrated 1 day after operation.

From Henriksen 28
Figure 29. Figure 29.

Two 133Xe‐washout curves recorded over exposed heart in dogs. A: curve immediately after intramyocardial injection of 5 μl indicator solution. B: curve immediately after atraumatic labeling by applying 4 μl indicator solution under a Mylar membrane covering epicardium. Detector collimated to record only from site of indicator application. Shapes of curves are virtually similar, indicating insignificant injection trauma in myocardium. After brief acceleration phase, curves are practically monoexponential for more than 1 decade. Thus perfusion coefficient in myocardial tissue can be calculated as λ · k · 100 (ml · min−1 · 100 g−1) according to Kety 44, where λ is myocardial tissue‐to‐blood partition coefficient (0.7 ml/g) and k is 133Xe‐washout rate constant obtained from monoexponential portion of washout curve.

From Haunso et al. 27
Figure 30. Figure 30.

Calculated perfusion coefficients in myocardium based on 133Xe‐washout curves after local intramyocardial injection compared to those calculated from 133Xe‐washout curves after atraumatic epicardial application. Calculated perfusion coefficients based on washout curves after local intramyocardial injection of indicator agree well with those after atraumatic epicardial labeling, indicating that injection trauma is insignificant in myocardium, contrary to that seen in skeletal muscle.

From Haunsø et al. 27
Figure 31. Figure 31.

Role of collimation on 133Xe‐washout curves from myocardium. Upper curve (solid circles) is obtained by registration from whole heart; lower curve (open circles) obtained with detector collimated to record only from site of indicator application. Curve obtained with narrow collimation is monoexponential for more than 2 decades, whereas other curve obtained with broad collimation is bent. This bent shape can be explained by recording 133Xe accumulated in fat tissue around great vessels, which is not detected with narrow collimation. Slope of nearly monoexponential part of curve obtained with broad collimation is less than that obtained from other curve, indicating that perfusion coefficient calculated from upper curve is underestimated [Masari (66)].

From Haunsø et al. 27
Figure 32. Figure 32.

Use of local 133Xe‐wahsout technique to study reactive hyperemia in myocardial tissue after circulatory arrest. Maximum blood flow can be calculated from steepest part of washout curve after release of circulatory arrest. Also excess cumulative blood flow (integrated total blood flow during hyperemic period minus integrated control blood flow for same period can be calculated as indicated. k(po), Washout rate constant before occlusion; q(t1)ph, activity obtained by retropolation of monoexponential washout curve recorded after end of reactive hyperemia to time t = t1; a/b, cumulative excess blood flow divided by cumulative blood flow deficit.

From Haunsø and Amtorp 26
Figure 33. Figure 33.

Two 133Xe‐washout curves from experiments on the isolated cat gastrocnemius muscle during exercise induced by electrical stimulation of sciatic nerve. All visible fat carefully removed. Crosses, curve after arterial step input (desaturation); dots, curve after local saturation by applying indicator by diffusion into muscle from surface. Total blood flow measured by venous outflow rate was identical in the 2 experiments. Shapes of 2 curves are virtually similar. Furthermore they are bent in a semilogarithmic plot, indicating that skeletal muscle is not a single well‐mixed compartment with regard to 133Xe washout. Here blood flow can be calculated from initial slope (see Eq. 49).

From Sejrsen and Tønnesen 93, by permission of the American Heart Association, Inc
Figure 34. Figure 34.

Comparison of perfusion coefficient in isolated cat gastrocnemius muscle calculated from 133Xe‐desaturation curves after intra‐arterial step input with those obtained by direct recording of venous outflow rate. Perfusion coefficient calculated as λ times washout rate constant of initial steepest part of washout curve (see Eq. 49). Indirectly calculated and directly recorded perfusion coefficients agreed well. b′, Linear regression coefficient.

From Sejrsen and Tønnesen 93, by permission of the American Heart Association, Inc
Figure 35. Figure 35.

Comparison between directly measured blood flow as venous outflow rate in isolated cat gastrocnemius muscle and blood flow as calculated from 133Xe‐washout rate of initial steepest part of desaturation curve after local gas labeling by allowing 133Xe to diffuse into muscle from surface. Reasonable agreement was found between sets of blood flow values. Because only minor part of muscle is labeled with indicator, distribution of blood flow in tissue as measured by local saturation technique is fairly uniform. This is also supported by identical shapes of 133Xe‐washout curves shown in Fig. 33.

From Sejrsen and Tønnensen 93, by permission of the American Heart Association, Inc
Figure 36. Figure 36.

A 133Xe‐washout curve from isolated cat gastrocnemius muscle after intramuscular injection of 0.1 ml of 133Xe dissolved in saline. Blood flow calculated from initial steepest part of curve and from final monoexponential tail part as compared to directly measured venous outflow rate. Blood flow value from the initial part of curve was 26.9 ml · min−1 · 100 g−1, whereas recorded venous outflow was only 6.4 ml · min−1 · 100 g−1. Thus injection procedure causes local hyperemia due to trauma, but because labeled area is too small to affect total muscle blood flow, this is hardly seen by recording venous outflow rate. Using tail part of curve gave values about 50% of those obtained by recording venous outflow rate. This can be explained by fact that 133Xe recirculates due to venoarterial shunting by diffusion 94 and by fact that some 133Xe may be trapped in remaining fat tissue, although all visible fat was removed in this preparation. Thus correct values for resting blood flow in skeletal muscle cannot be obtained by local 133Xe‐washout technique, but it may still be possible to calculate relative resting blood flow during various experimental conditions, as discussed in MUSCLE BLOOD FLOW DURING RESTING CONDITIONS IN HUMAN BEINGS, p. 52. , Average flow.

From Tønnesen and Sejrsen 102
Figure 37. Figure 37.

Comparison of calculated blood flow in isolated cat gastrocnemius muscle based on initial part of 133Xe‐washout curve after intramuscular injection of 0.1 ml 133Xe mixed with saline (see Fig. 36) and blood flow recorded as venous outflow rate. Results show considerable scatter. For flow rates less than 10 ml · min−1 · 100 g−1 the 133Xe method gave values too high in all cases, indicating that significance of injection trauma is most pronounced at low flow rates.

From Tønnesen and Sejrsen 102
Figure 38. Figure 38.

A 133Xe‐washout curve from isolated cat gastrocnemius muscle after intramuscular injection of 0.1 ml 133Xe mixed with saline. Motor nerve stimulated after slow monoexponential part of 133Xe‐washout curve was reached. This increased 133Xe‐washout rate, second slope. Blood flow calculated from second slope agree favorably with directly measured venous outflow (see Fig. 39). MBF, muscle blood flow.

From Tønnesen and Sejrsen 102
Figure 39. Figure 39.

Comparison between blood flow calculated from second slope of 133Xe‐washout curves (see Fig. 38) and that measured directly as venous outflow rate. There is good agreement between values obtained by second‐slope technique and directly recorded blood flow, whereas this was not seen using initial part of 133Xe‐washout curve (see Fig. 37). Thus using second‐slope technique avoids injection trauma influence.

From Tønnesen and Sejrsen 102
Figure 40. Figure 40.

Several 133Xe‐washout curves during resting conditions from anterior tibial muscle (upper curves) and from brachioradial muscle (lower curves). Subject had undergone cervicodorsal sympathectomy 2 yr previously. Measurements performed about 20 min after injection; 133Xe washout followed monoexponential course (see Fig. 36). Although impossible to obtain correct value for resting blood flow in muscle, relative blood flow for same depot can be calculated during different experimental conditions because sources of error such as venoarterial shunting by diffusion and accumulation of 133Xe in fat tissue tend to be ruled out when reference curve before and after test situation (in this case venous stasis) is used. Venous stasis decreases blood flow in anterior tibial muscle 50%, corresponding to increase in total vascular resistance of about 33%. In chronically sympathectomized forearm, venous stasis did not change blood flow in brachioradial muscle, indicating that total vascular resistance had decreased. Thus, as in subcutaneous and cutaneous tissues, arteriolar constriction during venous stasis can be ascribed to a local sympathetic reflex mechanism, venoarteriolar reflex.

From Henriksen and Sejrsen 33
Figure 41. Figure 41.

A 133Xe‐washout curve from a uterine horn of nonpregnant rabbit after atraumatic labeling and covering with Mylar membrane. No collimation limitation. Curve is bent in semilogarithmic diagram. Slow part of curve may be due to accumulation of 133Xe in perivascular fat tissue, as in skeletal muscle. This component can be avoided by shielding off all tissues except uterine horn by lead (see Fig. 42).

From Ottesen 77
Figure 42. Figure 42.

Same type experiment as in Fig. 41. All tissues except uterine horn covered with lead shield. After atraumatic labeling 133Xe‐washout curve follows monoexponential course for more than 2 decades, indicating that monocompartmental model applies to washout of inert gas from myometrial tissue.

From Ottesen 77
Figure 43. Figure 43.

A 133Xe‐washout curve from myometrial tissue in nonpregnant rabbits after local injection of 5 μl 133Xe. All adjacent tissue except uterine horn covered by lead shield, as in Fig. 42. As is true with atraumatic labeling (Fig. 42), curve follows monoexponential course. Thus, similar to myocardium, injection trauma is not significant in this tissue, contrary to that seen in, e.g., skeletal muscle.

From Ottesen 77
Figure 44. Figure 44.

Application of Kety‐Schmidt method 45 for determining cerebral blood flow in human beings. Subject inhaled 85Kr from closed respiratory system with circulating air for 14 min. Catheters placed in superior bulb of left internal jugular vein and in left femoral artery. Upper curve, arterial concentrations; lower curve, venous concentrations vs time. Arterial and venous concentration 14 min after start of experiment differ a little, indicating that full saturation of cerebral tissue has not been obtained at this time. Extrapolation for time above 14 min performed to obtain area between 2 curves to time infinity. Mean perfusion coefficient then calculated as = λ 85Kr · C∞/ dt.

From Lassen and Munck 56
Figure 45. Figure 45.

Biexponential 133Xe‐washout curve from human brain recorded externally after bolus injection in internal carotid artery. Average perfusion coefficient can be calculated as λ times height divided by area. Using 2‐compartment, in‐parallel model, fast component can be ascribed to 133Xe washout from gray matter and slow component to washout from white matter. Initial slope is dominated by washout of 133Xe from gray matter. Thus a good approximation in calculating perfusion coefficient can be obtained in gray matter by using initial monoexponential part of 133Xe‐washout curve.
Figure 46. Figure 46.

Comparison between perfusion coefficient in dog kidney based on initial slope of 133Xe‐washout curve after step input of 133Xe in renal artery and those measured with electromagnetic flowmeter. There is good agreement between the 2 methods. In humans also there is similarity between blood flow calculated from 133Xe‐desaturation curves and that calculated by PAH‐clearance method.

From Ladefoged 48


Figure 1.

Fluid flowing through tube at constant rate (F; ml/s). At certain site cross‐stream mixing can be induced. Graph (below) shows outlet concentration (Cout) of indicator infused at constant rate of influx (Jin) upstream to mixing site. F is calculated as Jin divided by Cout (∞) during indicator steady state, plateau level of curve (Stewart principle, see Eq. 5).

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY


Figure 2.

Correction for recirculation in continuous‐infusion experiment by sampling from outlet of organ studied [Cinj (t)] and from symmetrical organ [Cnoninj(t)], e.g., kidneys, forearms, legs. Steady‐state Cout used in Eq. 5 is maximal difference between these 2 concentrations.

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY


Figure 3.

Outflow concentrations of indicator after bolus injection with recirculation seen by increase in concentration after peak. Broken line, curve after correction for recirculation (see RECIRCULATION, p. 26, and CORRECTION FOR RECIRCULATION, p. 37). F then calculated as injected dose divided by area under outflow curve corrected for recirculation (see Eq. 21).

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY


Figure 4.

Equal‐area rule, as described by Bergner 8. Outlet curves from different outlets of system with a single well‐mixed inlet have different shapes but same area. Thus total inflow (F) can be calculated as dose injected divided by area applied to any outlet.

From Tracer Kinetic Methods in Medical Physiology, by N. A. Lassen and W. Perl 57. © 1979, with permission of Raven Press, NY


Figure 5.

Fractional rate of indicator ([dQ(t)/dt]/Qo), which leaves single‐inlet‐single‐outlet system after injection of amount Qo as ideally brief bolus (impulse). This normalized outflow curve represents frequency distribution of transit times within system h(t). Mean transit time () is calculated as time‐weighted area under h(t) curve, that is = · h(t) dt (see Eq. 38).



Figure 6.

Curves, cumulative fraction of ideally brief bolus that has left system H(t) and fraction remaining in the system (residue) [1 − H(t)] (see Eqs. 39,40); equals area between horizontal line 1 and H(t) curve, which is similar to area under residue curve, dt (see Eq. 46).



Figure 7.

Outflow curve during continuous‐infusion experiment. Step‐input function apparently is a series of small, ideally brief impulses (upper panel), each with response curve h(t) (middle panel). Outflow curve (lower panel) is built up as sum of contributions to outflow from each of these brief impulses (see Eq. 41).



Figure 8.

Constant infusion, inlet‐outlet detection: Kety‐Schmidt method 45. Upper curve shows inlet concentration [Cin(t)] and lower curve shows outlet concentration [Cout(t)]. Perfusion coefficient is calculated as tissue‐to‐blood partition coefficient (λ) times concentration at infinity (C∞) divided by area between curves (see Eq. 45).



Figure 9.

Figure showing that area between inlet‐outlet curves divided by height (A/H) during constant infusion [Kety and Schmidt (45)] equals area/height ratio of residue curve in bolus experiment, namely, mean transit time of system.

Lassen et al. 52


Figure 10.

Constant‐infusion experiment with residue detection. Top: input [Jin(t)] starts instantaneously (step) at time zero at left and stops instantaneously at time zero at right. Bottom: residue curve initially linear in time interval corresponding to shortest transit time in system. During indicator steady‐state curve reaches plateau level. After input dropped to zero (desaturation), curve changes are symmetrical. According to Eq. 42 the plateau level (Q∞) equals influx rate (jin,∞) times . Thus equals relative reciprocal initial slope, that is, = Q∞/(dQ/dt) for t → 0 (see Eq. 49).



Figure 11.

Bolus experiment with inlet‐outlet detection. Function hin(t), normalized to unit area, is frequency function of transit times for input system after ideally brief bolus input (impulse). Thus time‐weighted area of this curve to time infinity gives of input system (in). Function hout(t) is frequency distribution of t values for input plus system studied. Time‐weighted area of this curve gives for input plus system (out). For system studied is calculated out − in (see Eqs. 59,60).



Figure 12.

Summary of black‐box analysis for determining mean t. From top to bottom, input, residue, outflow, and cumulative outflow curves in saturation‐desaturation experiment (left) and bolus experiment (right). For details see SUMMARY OP NONCOMPARTMENTAL ANALYSIS FOR DETERMINATION OF , p. 35.



Figure 13.

Correction for recirculation in bolus experiment with residue detection in open system according to Larson and Snyder 49. gA(t), Normalized residue curve including recirculation after injecting amount Qo of indicator at inlet; gV(t), normalized recirculatory function after injecting indicator in outlet as bolus. Mean transit time equals area between these 2 curves divided by height (hatched area) (see Eq. 68). Difference between gA(t) and gV(t) does not equal 1 − H(t) function of system because here input to recirculatory system is brief bolus, whereas input to recirculatory system in first case equals h(t) function for system studied.



Figure 14.

Correction for recirculation in bolus experiment with residue detection in closed system. Both curves gA(t) and gV(t) approach same value as t →, namely g∞. Area between normalized curves (hatched area) divided by 1 − g∞ (height) calculates (see Eq. 69).



Figure 15.

Washout of indicator from single‐compartment system with varying blood flow, seen as nonlinear washout function in semilogarithmic plot. Average blood flow () from t1 to t2 can be calculated as shown: = 102 · λ · ln [Q(t1)/Q(t2)]/(t2 − t1) ml · h−1 · 100 g−1. Tissue‐to‐blood partition coefficient (λ) is in ml/g; Q(t1) and Q(t2) are recorded activities with identical detection efficiency at time t1 and t2, respectively. This method makes it possible to calculate average blood flow in, e.g., subcutaneous tissue during 24 h using 133Xe as indicator, which might have important clinical implications in patients with various vascular diseases.



Figure 16.

Experiment on isolated cat gastrocnemius muscle: 51Cr‐ethylenediaminetetraacetic acid injected intra‐arterially as bolus. Upper curve, normalized residue curve (ext.); lower curve, normalized outflow curve to unit area (vein) plotted in senulogarithmic diagram. After about 90 min curves become parallel, indicating that slowest washout rate (final slope) has practically been reached. Thus at this time monoexponential extrapolation can be used for calculating area or time‐weighted area from this time to time infinity.

From Lassen and Sejrsen 58, by permission of the American Heart Association, Inc


Figure 17.

A 133Xe‐washout curve in semilogarithmic diagram after atraumatic epicutaneous labeling over lateral surface of crus. Dots indicate recorded washout curve. The curve can be expressed by 2 monoexponential functions after curve resolution: the fast one is indicated by open circles; washout curve for cutaneous tissue alone is obtained by drawing line parallel to line through circles and passing through top point of measured curve. Subtracting values given by this line from measured values gives washout curve for subcutaneous tissue alone, indicated by crosses. Perfusion coefficient in cutaneous tissue equals washout rate constant obtained from fast component times λ for cutaneous tissue. Subcutaneous blood flow similarly calculated as washout rate constant of slow component times λ for subcutaneous tissue. This interpretation is based on monoexponential washout function from cutaneous as well as subcutaneous tissue, as shown in Figs. 18,19.

From Sejrsen 91, by permission of the American Heart Association, Inc


Figure 18.

A 133Xe‐washout curve measured over distal 2 mm of skin fold between thumb and forefinger after epicutaneous labeling. Remainder of hand covered by lead shield. In this set‐up, recorded washout curve can be regarded as washout from cutaneous tissue alone. Washout curve follows a monoexponential course to background values. Proposed model for this observation supports interpretation of 133Xe‐washout curves from skin by Sejrsen 92.

From Sejrsen 91, by permission of the American Heart Association, Inc


Figure 19.

A 133Xe‐washout curve from abdominal subcutaneous fatty tissue of cat after introduction of indicator atraumatically by diffusion from exposed tissue surface. Washout curve is monoexponential, supporting proposed model for interpretation of 133Xe‐washout curve from skin.

From Sejrsen 91, by permission of the American Heart Association, Inc


Figure 20.

Two simultaneously recorded 133Xe‐washout curves. Upper curve obtained after intradermal microinjection on lateral surface of crus on 1 side and lower curve after atraumatic epicutaneous labeling of symmetrical area on other leg. Initial part of upper curve is steeper than after epicutaneous labeling. Hyperemia caused by injection trauma can explain this. However, after about 15 min, 2 curve shapes are virtually identical, indicating that injection technique can be used when influence of injection trauma has become insignificant.

From Sejrsen 91, by permission of the American Heart Association, Inc


Figure 21.

Several 133Xe‐washout curves from skin fold between thumb and forefinger after epicutaneous labeling. Curves from study of influence of postural changes on cutaneous blood flow. Elevating hand 30 cm above heart level did not change 133Xe‐washout rate, indicating that blood flow remained constant. Elevating hand decreases local arterial mean pressure while venous pressure remains constant. Thus elevation of hand causes compensatory decrease in vascular resistance (autoregulation). Lowering hand 40 cm decreases cutaneous blood flow, indicating increase in vascular resistance because driving pressure remains constant during lowering. Arteriolar constriction underlying increase in vascular resistance during lowering is probably due to local venoarteriolar reflex mechanism 29. T½, half‐time; k, rate constant; f, cutaneous blood flow.

Data from Henriksen, Sejrsen, et al. 31


Figure 22.

Example of effect of venous stasis (40 mmHg) on 133Xe‐washout curves from skin fold between thumb and forefinger measured simultaneously on both sides. Patient sympathectomized (cervicodorsal) unilaterally 9 yr previously; no sweat secretion from hand on operated side, but excessive sweating (hyperhidrosis) on nonoperated side. Venous stasis caused normal decrease in blood flow on control side (upper curves), whereas blood flow remained constant on sympathectomized side (lower curves). Thus normal arteriolar constriction induced by venous stasis is abolished after chronic sympathetic denervation. Because normal vasoconstriction is seen 1st day after sympathectomy 28, arteriolar constriction induced by venous stasis is due to local sympathetic reflex mechanism (venoarteriolar reflex).

From Henriksen and Sejrsen 32


Figure 23.

A 133Xe‐washout curve from rabbit inguinal fat‐pad after atraumatic labeling. Washout curve is strictly monoexponential. r, Coefficient of correlation; p, probability.

From Nielsen 75


Figure 24.

Indirectly determined perfusion coefficient in rabbit inguinal fat‐pad based on 133Xe‐washout curve in Fig. 23 plotted vs. directly measured venous outflow; λ determined in each single case. Calculated and directly recorded blood flow in adipose tissue agreed well. byx, Linear regression coefficient.

From Nielsen 75


Figure 25.

Several 133Xe‐washout curves recorded after injection of 0.1 ml 133Xe dissolved in isotonic saline. Upper curve, from subcutaneous inguinal tissue in an unanesthetized rabbit; lower curve, from same tissue after surgical isolation of fat‐pad. In both situations initial phase of fast washout lasted about 30 min (trauma phase) and was followed by monoexponential washout during which calculated blood flow agreed with directly measured venous outflow (see Fig. 26).

From Nielsen 74


Figure 26.

Comparison between directly recorded blood flow values of isolated inguinal fat‐pad of rabbit and those calculated from monoexponential part of 133Xe‐washout curves 30 min after local injection of 133Xe dissolved in saline. In each case λ values calculated from determination of composition of blood and adipose tissue. Directly recorded perfusion coefficient values and those calculated from 133Xe‐washout curves agree well.

From Nielsen 74


Figure 27.

Several 133Xe‐washout curves from subcutaneous adipose tissue of distal part of forearm. Measurements performed with depot area on test arm (upper curves) placed at heart level (ref1); depot area lowered 40 cm and again placed at heart level (ref2); depot area on control arm remained at heart level. Log activity given against time in min. Figures denote calculated 133Xe‐washout rate constants · 103 ± 1 SE. Since λ was not determined, relative blood flow can be calculated only as ratio between washout rate constant during lowering and average value of washout rate constant at heart level. Lowering area 40 cm below heart level reduces blood flow by about 50% in that area, whereas blood flow remains almost constant on control side. Thus arteriolar constriction underlying decrease in blood flow during lowering seems caused by local mechanism (vasoconstrictor response).

Data from Henriksen 29


Figure 28.

Effect of 30‐mmHg venous stasis on 133Xe‐washout curves from subcutaneous tissue on distal part of forearm and at lateral maleolus. Patient sympathectomized (cervicodorsal) on both sides 2 yr previously due to manual hyperhidrosis. On leg 30‐mmHg venous stasis reduces subcutaneous blood flow 50%, corresponding to increase in total vascular resistance of about 35%. On sympathetically denervated forearm, however, venous stasis does not alter subcutaneous blood flow. Venous stasis of 30 mmHg induces decrease in total vascular resistance, indicating that arteriolar constriction induced by venous stasis is due to local sympathetic reflex mechanism because arteriolar constriction can be demonstrated 1 day after operation.

From Henriksen 28


Figure 29.

Two 133Xe‐washout curves recorded over exposed heart in dogs. A: curve immediately after intramyocardial injection of 5 μl indicator solution. B: curve immediately after atraumatic labeling by applying 4 μl indicator solution under a Mylar membrane covering epicardium. Detector collimated to record only from site of indicator application. Shapes of curves are virtually similar, indicating insignificant injection trauma in myocardium. After brief acceleration phase, curves are practically monoexponential for more than 1 decade. Thus perfusion coefficient in myocardial tissue can be calculated as λ · k · 100 (ml · min−1 · 100 g−1) according to Kety 44, where λ is myocardial tissue‐to‐blood partition coefficient (0.7 ml/g) and k is 133Xe‐washout rate constant obtained from monoexponential portion of washout curve.

From Haunso et al. 27


Figure 30.

Calculated perfusion coefficients in myocardium based on 133Xe‐washout curves after local intramyocardial injection compared to those calculated from 133Xe‐washout curves after atraumatic epicardial application. Calculated perfusion coefficients based on washout curves after local intramyocardial injection of indicator agree well with those after atraumatic epicardial labeling, indicating that injection trauma is insignificant in myocardium, contrary to that seen in skeletal muscle.

From Haunsø et al. 27


Figure 31.

Role of collimation on 133Xe‐washout curves from myocardium. Upper curve (solid circles) is obtained by registration from whole heart; lower curve (open circles) obtained with detector collimated to record only from site of indicator application. Curve obtained with narrow collimation is monoexponential for more than 2 decades, whereas other curve obtained with broad collimation is bent. This bent shape can be explained by recording 133Xe accumulated in fat tissue around great vessels, which is not detected with narrow collimation. Slope of nearly monoexponential part of curve obtained with broad collimation is less than that obtained from other curve, indicating that perfusion coefficient calculated from upper curve is underestimated [Masari (66)].

From Haunsø et al. 27


Figure 32.

Use of local 133Xe‐wahsout technique to study reactive hyperemia in myocardial tissue after circulatory arrest. Maximum blood flow can be calculated from steepest part of washout curve after release of circulatory arrest. Also excess cumulative blood flow (integrated total blood flow during hyperemic period minus integrated control blood flow for same period can be calculated as indicated. k(po), Washout rate constant before occlusion; q(t1)ph, activity obtained by retropolation of monoexponential washout curve recorded after end of reactive hyperemia to time t = t1; a/b, cumulative excess blood flow divided by cumulative blood flow deficit.

From Haunsø and Amtorp 26


Figure 33.

Two 133Xe‐washout curves from experiments on the isolated cat gastrocnemius muscle during exercise induced by electrical stimulation of sciatic nerve. All visible fat carefully removed. Crosses, curve after arterial step input (desaturation); dots, curve after local saturation by applying indicator by diffusion into muscle from surface. Total blood flow measured by venous outflow rate was identical in the 2 experiments. Shapes of 2 curves are virtually similar. Furthermore they are bent in a semilogarithmic plot, indicating that skeletal muscle is not a single well‐mixed compartment with regard to 133Xe washout. Here blood flow can be calculated from initial slope (see Eq. 49).

From Sejrsen and Tønnesen 93, by permission of the American Heart Association, Inc


Figure 34.

Comparison of perfusion coefficient in isolated cat gastrocnemius muscle calculated from 133Xe‐desaturation curves after intra‐arterial step input with those obtained by direct recording of venous outflow rate. Perfusion coefficient calculated as λ times washout rate constant of initial steepest part of washout curve (see Eq. 49). Indirectly calculated and directly recorded perfusion coefficients agreed well. b′, Linear regression coefficient.

From Sejrsen and Tønnesen 93, by permission of the American Heart Association, Inc


Figure 35.

Comparison between directly measured blood flow as venous outflow rate in isolated cat gastrocnemius muscle and blood flow as calculated from 133Xe‐washout rate of initial steepest part of desaturation curve after local gas labeling by allowing 133Xe to diffuse into muscle from surface. Reasonable agreement was found between sets of blood flow values. Because only minor part of muscle is labeled with indicator, distribution of blood flow in tissue as measured by local saturation technique is fairly uniform. This is also supported by identical shapes of 133Xe‐washout curves shown in Fig. 33.

From Sejrsen and Tønnensen 93, by permission of the American Heart Association, Inc


Figure 36.

A 133Xe‐washout curve from isolated cat gastrocnemius muscle after intramuscular injection of 0.1 ml of 133Xe dissolved in saline. Blood flow calculated from initial steepest part of curve and from final monoexponential tail part as compared to directly measured venous outflow rate. Blood flow value from the initial part of curve was 26.9 ml · min−1 · 100 g−1, whereas recorded venous outflow was only 6.4 ml · min−1 · 100 g−1. Thus injection procedure causes local hyperemia due to trauma, but because labeled area is too small to affect total muscle blood flow, this is hardly seen by recording venous outflow rate. Using tail part of curve gave values about 50% of those obtained by recording venous outflow rate. This can be explained by fact that 133Xe recirculates due to venoarterial shunting by diffusion 94 and by fact that some 133Xe may be trapped in remaining fat tissue, although all visible fat was removed in this preparation. Thus correct values for resting blood flow in skeletal muscle cannot be obtained by local 133Xe‐washout technique, but it may still be possible to calculate relative resting blood flow during various experimental conditions, as discussed in MUSCLE BLOOD FLOW DURING RESTING CONDITIONS IN HUMAN BEINGS, p. 52. , Average flow.

From Tønnesen and Sejrsen 102


Figure 37.

Comparison of calculated blood flow in isolated cat gastrocnemius muscle based on initial part of 133Xe‐washout curve after intramuscular injection of 0.1 ml 133Xe mixed with saline (see Fig. 36) and blood flow recorded as venous outflow rate. Results show considerable scatter. For flow rates less than 10 ml · min−1 · 100 g−1 the 133Xe method gave values too high in all cases, indicating that significance of injection trauma is most pronounced at low flow rates.

From Tønnesen and Sejrsen 102


Figure 38.

A 133Xe‐washout curve from isolated cat gastrocnemius muscle after intramuscular injection of 0.1 ml 133Xe mixed with saline. Motor nerve stimulated after slow monoexponential part of 133Xe‐washout curve was reached. This increased 133Xe‐washout rate, second slope. Blood flow calculated from second slope agree favorably with directly measured venous outflow (see Fig. 39). MBF, muscle blood flow.

From Tønnesen and Sejrsen 102


Figure 39.

Comparison between blood flow calculated from second slope of 133Xe‐washout curves (see Fig. 38) and that measured directly as venous outflow rate. There is good agreement between values obtained by second‐slope technique and directly recorded blood flow, whereas this was not seen using initial part of 133Xe‐washout curve (see Fig. 37). Thus using second‐slope technique avoids injection trauma influence.

From Tønnesen and Sejrsen 102


Figure 40.

Several 133Xe‐washout curves during resting conditions from anterior tibial muscle (upper curves) and from brachioradial muscle (lower curves). Subject had undergone cervicodorsal sympathectomy 2 yr previously. Measurements performed about 20 min after injection; 133Xe washout followed monoexponential course (see Fig. 36). Although impossible to obtain correct value for resting blood flow in muscle, relative blood flow for same depot can be calculated during different experimental conditions because sources of error such as venoarterial shunting by diffusion and accumulation of 133Xe in fat tissue tend to be ruled out when reference curve before and after test situation (in this case venous stasis) is used. Venous stasis decreases blood flow in anterior tibial muscle 50%, corresponding to increase in total vascular resistance of about 33%. In chronically sympathectomized forearm, venous stasis did not change blood flow in brachioradial muscle, indicating that total vascular resistance had decreased. Thus, as in subcutaneous and cutaneous tissues, arteriolar constriction during venous stasis can be ascribed to a local sympathetic reflex mechanism, venoarteriolar reflex.

From Henriksen and Sejrsen 33


Figure 41.

A 133Xe‐washout curve from a uterine horn of nonpregnant rabbit after atraumatic labeling and covering with Mylar membrane. No collimation limitation. Curve is bent in semilogarithmic diagram. Slow part of curve may be due to accumulation of 133Xe in perivascular fat tissue, as in skeletal muscle. This component can be avoided by shielding off all tissues except uterine horn by lead (see Fig. 42).

From Ottesen 77


Figure 42.

Same type experiment as in Fig. 41. All tissues except uterine horn covered with lead shield. After atraumatic labeling 133Xe‐washout curve follows monoexponential course for more than 2 decades, indicating that monocompartmental model applies to washout of inert gas from myometrial tissue.

From Ottesen 77


Figure 43.

A 133Xe‐washout curve from myometrial tissue in nonpregnant rabbits after local injection of 5 μl 133Xe. All adjacent tissue except uterine horn covered by lead shield, as in Fig. 42. As is true with atraumatic labeling (Fig. 42), curve follows monoexponential course. Thus, similar to myocardium, injection trauma is not significant in this tissue, contrary to that seen in, e.g., skeletal muscle.

From Ottesen 77


Figure 44.

Application of Kety‐Schmidt method 45 for determining cerebral blood flow in human beings. Subject inhaled 85Kr from closed respiratory system with circulating air for 14 min. Catheters placed in superior bulb of left internal jugular vein and in left femoral artery. Upper curve, arterial concentrations; lower curve, venous concentrations vs time. Arterial and venous concentration 14 min after start of experiment differ a little, indicating that full saturation of cerebral tissue has not been obtained at this time. Extrapolation for time above 14 min performed to obtain area between 2 curves to time infinity. Mean perfusion coefficient then calculated as = λ 85Kr · C∞/ dt.

From Lassen and Munck 56


Figure 45.

Biexponential 133Xe‐washout curve from human brain recorded externally after bolus injection in internal carotid artery. Average perfusion coefficient can be calculated as λ times height divided by area. Using 2‐compartment, in‐parallel model, fast component can be ascribed to 133Xe washout from gray matter and slow component to washout from white matter. Initial slope is dominated by washout of 133Xe from gray matter. Thus a good approximation in calculating perfusion coefficient can be obtained in gray matter by using initial monoexponential part of 133Xe‐washout curve.



Figure 46.

Comparison between perfusion coefficient in dog kidney based on initial slope of 133Xe‐washout curve after step input of 133Xe in renal artery and those measured with electromagnetic flowmeter. There is good agreement between the 2 methods. In humans also there is similarity between blood flow calculated from 133Xe‐desaturation curves and that calculated by PAH‐clearance method.

From Ladefoged 48
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Article Title: Indicator Methods for Measurement of Organ and Tissue Blood Flow
 

How to Cite

Niels A. Lassen, Ole Henriksen, Per Sejrsen. Indicator Methods for Measurement of Organ and Tissue Blood Flow. Compr Physiol 2011, Supplement 8: Handbook of Physiology, The Cardiovascular System, Peripheral Circulation and Organ Blood Flow: 21-63. First published in print 1983. doi: 10.1002/cphy.cp020302