## Abstract

In an attempt to identify and quantify the sites of atrial natriuretic peptide (ANP) degradation, a new tracer experiment has been developed.^{125}I-ANP was injected as a bolus just upstream from the right atrium, and blood was sampled from two different sites (pulmonary artery and aorta) in eight cardiac patients. Data were analyzed using a physiologically based circulatory model consisting of three blocks in series (right heart, lungs and left heart, and periphery) supplied by the same flow (cardiac output, measured by thermodilution); the extraction coefficients of the three blocks and of the whole body could be determined from the areas under tracer concentration curves in plasma (AUCs). The values for AUCs (means ± SD) were 64.8 ± 9.4 and 65.5 ± 10.7% dose ⋅ l^{−1} ⋅ min^{−1}for pulmonary artery and aorta curves, respectively; the area under the pulmonary artery curve could be subdivided into the area under the first-pass curve (30.6 ± 4.7% dose ⋅ l^{−1} ⋅ min^{−1}) and the area under the recirculating curve (34.0 ± 7.7% dose ⋅ l^{−1} ⋅ min^{−1}). The metabolic clearance rate of^{125}I-ANP, computed as dose divided by the area under the recirculating curve, was 3.1 ± 0.7 l/min, and the whole body extraction was 47.6 ± 6.6%. In our patients with myocardial dysfunction, neither right heart block nor lungs and left heart block significantly extracted ANP, and periphery block accounted for almost all removal of the hormone from the blood.

- atrial natriuretic factor
- tracer method
- metabolic clearance rate
- heart failure

atrial natriuretic peptide (ANP) is a hormone produced and secreted into the blood by the heart; it has several biological effects, such as natriuresis, vasorelaxation, hypotension, and neuromodulation (7, 20). This hormone seems to play an important role in the natural history of heart failure, mainly by counteracting the detrimental effects of activation of the vasoconstrictor sodium-retaining system (3, 7, 17, 20).

Extensive studies in animals and humans have documented that ANP is secreted into the circulatory system via the coronary sinus into the right atrium and then rapidly degraded and removed from the blood (7,20). Although the kidney and lungs have been considered to be major sites of ANP removal, little is known about the contributions of the various organs or tissues to ANP clearance from the blood in vivo in humans.

Studies of ANP kinetics (as well as the kinetics of other rapidly degraded, biologically active molecules) have been carried out by a standard experimental protocol in which labeled or unlabeled hormone is administered (by constant infusion or bolus injection) and the corresponding concentration of the hormone is measured in peripheral venous blood (10-13, 26).

Metabolic clearance rate (MCR), the sole parameter describing the rate of disposal at whole body level, is computed by the compartmental (or the so-called noncompartmental) approach (8); in any case, the measured plasma concentration of the substance from a single sampling site is considered to represent the whole intravascular compartment. A uniform plasma distribution is, however, approximately reached only for the slowly degrading system(s), in which the mixing process, ensured by blood flow, is rapid with respect to the degradation rate or, in other words, when MCR is very small relative to plasma cardiac output. However, in the case of rapidly degraded molecules (such as ANP), significant differences in plasma concentrations are measured upstream and downstream from various organs involved in hormone degradation. Indeed, arteriovenous differences have been reported and used to compute hormone extraction values from several circulatory districts (e.g, liver, kidney, lungs) (1, 9, 15, 16, 19, 21, 22). From this, it can be deduced that, after tracer bolus injection, different areas under concentration curves (AUCs) have to be measured upstream and downstream from circulatory ANP-degrading districts and that these different AUCs can be exploited to quantitate extraction values.

To verify this idea, a new experimental protocol has been developed and carried out in a group of cardiac patients undergoing a complete hemodynamic study to evaluate their cardiac disease. The tracer experiment necessitates a bolus injection of^{125}I-ANP into the right atrium and sampling of concentration curves in the pulmonary artery and aorta. The use of low-rate continuous (integrated) sampling during the first 130 s of the experiment makes it possible to define accurately the earliest part of the pulmonary arterial concentration curve and, thus, distinguish the first pass of the injected bolus from the recirculating curve. Independent measurement of cardiac output was simultaneously obtained by thermodilution.

Because the classical compartmental approach is not suitable for interpreting the extended set of experimental data, we used a more physiological circulatory model that does not assume a uniform intravascular distribution of the hormone. The new circulatory model for describing ANP disposal consists of three blocks connected in series: *1*) right heart block,*2*) lungs and left heart block, and*3*) periphery block. The model can be defined by the three experimentally determined curves:*1*) the first-pass curve sampled in the pulmonary artery, *2*) the recirculating curve sampled in the pulmonary artery, and*3*) the aorta curve.

We report a detailed description of the model, how it works, and the results from a preliminary application in a group of cardiac patients and compare the results with those of standard analysis.

## MATERIALS AND METHODS

### Experimental Subjects and Hemodynamics

#### Experimental subjects.

Eight normotensive cardiac patients were enrolled in the study. All the patients were subjected to a complete baseline cardiological evaluation, including physical and X-ray examination, two-dimensional echocardiography, and radionuclide angiography. The patients underwent the hemodynamic study because of their cardiac disease. Their main clinical parameters are reported in Table1. Because it was not possible to apply this experimental protocol to normal subjects for ethical reasons, we studied patients with a wide range of myocardial involvement (from mild to severe, i.e., left ventricular ejection fraction ranging from 30 to 15%) (Table 1).

The patients were hospitalized in the metabolic ward of the Consiglio Nazionale delle Ricerche Institute of Clinical Physiology for the time required to perform the kinetic and clinical studies. On admission, all the patients were maintained on a relatively restricted sodium diet (100–120 mmol/day). Body weight, plasma and urinary creatinine, and electrolytes were measured daily. To ensure that sodium balance was achieved, the kinetic study was performed only after three consecutive 24-h urinary collections demonstrating a steady-state sodium excretion, as previously reported (10-12).

All patients received a daily dose of 20 drops of saturated lugol solution from the day before until the day after the kinetic study. The study protocol was approved by the local Ethics Committee, and written consent was obtained from the patients before the study.

#### Hemodynamics.

The study was carried out in the hemodynamic ward of the Consiglio Nazionale delle Ricerche Institute of Clinical Physiology after selective left and right coronary angiograms were performed using the Judkins technique (*patients 1–5*). No premedication was given, and no heparin was used (catheters were regularly flushed with boluses of normal saline). At least 30 min were allowed between coronary angiography and the beginning of the study to minimize any possible interference of the contrast medium with the metabolic parameter.

In all patients a 7-Fr triple-lumen flow-directed balloon-tipped catheter was inserted transcutaneously through the right femoral vein and advanced to obtain right atrial, pulmonary arterial, and pulmonary capillary wedge pressures. Cardiac index was calculated as the ratio of the mean of at least five thermodilution cardiac output measurements to body surface area (m^{2}). After hemodynamic assessment, the flow-directed catheter was removed, and a 7-Fr multipurpose multiple-side-hole catheter was positioned in the pulmonary artery. A 5-Fr pig-tail multiple-side-hole catheter was advanced via the ascending aorta through the introducer positioned in the right femoral artery for diagnostic study in five patients (*patients 1–5*) submitted to right and left heart catheterization. A three-way stopcock was used to connect each catheter to the pressure transducer and to draw blood or fill the catheter with saline flush solution. Pulmonary arterial pressure, aortic pressure, and one electrocardiographic lead were continuously monitored. Blood samples were simultaneously drawn from the pulmonary artery and ascending aorta. In *patients 6–8* a simplified protocol was used consisting of right catheterization and pulmonary arterial blood sampling only.

### Preparation of the Tracer

Synthetic human α-ANP-(1—28) (Bachem Feinchemikalien, Bubendorf, Switzerland) was iodinated with Na^{125}I or Na^{131}I (both supplied by Sorin, Saluggia Vercelli, Italy), as previously described (5, 11). The labeling mixture was then purified using ion-exchange chromatography and high-performance liquid chromatography (HPLC) procedures. Because only the fraction containing the monoiodinated labeled peptide was used to prepare the tracer, the specific activity of^{125}I-ANP was 2,000–2,200 Ci/mmol (650–700 μCi/μg), which is very close to the theoretical maximum specific activity for the monoradioiodinated hormone (2,200 Ci/mmol) (5, 11).

### Experimental Protocols of Tracer Studies

During the hemodynamic study, two blood samples (4–5 ml) were collected from the pulmonary artery and the aorta for measuring baseline plasma concentrations of native ANP. A known amount (∼80 μCi, corresponding to 110 ng of^{125}I-ANP, i.e., ∼10–15% perturbation of the initial distribution pool of ANP) (11) of freshly prepared tracer (see above) was then intravenously injected as a bolus via a catheter for isotope injection inserted percutaneously from the antecubital vein to near the junction of the superior vena cava and the right atrium. After injection, blood samples were simultaneously collected from the aorta and the pulmonary artery. To make possible a reliable definition of the area under the concentration curve of the tracer during the first few minutes after injection, “integrated” samples were obtained by a continuous withdrawal of blood using a computerized and programmable automatic collector specifically developed for this purpose by the Electronics Unit of the Consiglio Nazionale delle Ricerche Institute of Clinical Physiology. The device consists of *1*) a peristaltic pump, *2*) a microcontroller, which operates two drivers for piloting two stepping motors,*3*) an electronic apparatus for piloting an electromagnet to change the row of tubes,*4*) an operating panel with display to program and visualize the work cycle, and*5*) an electronic apparatus with an emergency push button to stop the work cycle if necessary. Thirteen 10-s integrated blood samples (1.2 ml each) were simultaneously collected from the aorta and pulmonary artery throughout the first 130 s; the remaining part of the curve (from 130 s to 30 min) was described by at least five “discrete” blood samples of 5 ml, typically taken at 3.5, 8, 15, 20, and 30 min. The larger volume of the five discrete samples was necessary to allow a reliable measure of ANP concentration also through the final part of the curve, where ANP activity is extremely low.

A volume of 0.9% NaCl solution equal to the volume of blood withdrawn was infused. The blood samples were immediately put into ice-chilled disposable polypropylene tubes containing aprotinin (500 kallikrein-inactivating units/ml plasma) and EDTA (1 mg/ml plasma), and the plasma was rapidly separated in a refrigerated centrifuge at 4°C.

### Extraction, Purification, and Measurement of Labeled ANP in Plasma Samples Collected During the Kinetic Studies

#### Extraction and purification of labeled ANP from plasma by HPLC.

All plasma samples were loaded onto Bond Elut C_{18} cartridges (Analytical International, Harbor City, CA) activated with 2 ml of methanol and washed with 4 ml of 1% trifluoroacetic acid (TFA). After a 10-ml washout with 0.1% TFA, labeled peptides were eluted with 3 ml of a solution containing 99:1 methanol-TFA. The collected effluent was evaporated using a vacuum centrifuge, and the samples were successively reconstituted and subjected to HPLC, as previously described (5, 11). To measure the recovery of labeled ANP throughout the extraction and purification procedures and to take into account possible in vitro labeled ANP degradation in blood, after sample collection, a known amount of purified ^{131}I-ANP (∼3,000–4,000 cpm) was added as internal standard to each polypropylene tube before the start of blood collection (5, 11).

#### Gamma counting.

The ^{125}I and^{131}I activities were measured in a gamma counter (1282 CompuGamma CS, LKB Wallac, Turku, Finland) with an efficiency of 54 and 60%, respectively; the counting time was 20 min for each fraction, and the operating conditions were chosen so as to obtain a high sample-to-background ratio. After background subtraction, the measured ^{125}I counts were corrected for ^{131}I spillover into the ^{125}I channel (which was 6% under the chosen conditions) (5, 11).

### Computation of ^{125}I-ANP Blood-Plasma Partition Factor

Because labeled ANP concentrations were measured in plasma, directly measured blood flow (cardiac output) had to be corrected by multiplying it by the ANP blood-to-plasma ratio, as previously reported (13). The partition of a known amount of labeled ANP added to 3 ml of blood (drawn immediately before the tracer injection) between plasma and cells (e.g., erythrocytes, leukocytes, platelets) was measured in each patient after the common procedure of centrifugation and separation utilized for the kinetic study. On average, this factor was 0.65 ± 0.041.

### ANP Assay

Plasma samples, immediately separated by centrifugation, then frozen and stored in various aliquots at −20°C, were assayed for ANP (at least in duplicate) by immunoradiometric assay (IRMA), as previously described in detail (4). This method is a solid-phase sandwich IRMA, which uses two monoclonal antibodies prepared against two sterically remote epitopes of ANP molecule; the first antibody was coated on the bead’s solid phase and the second was radiolabeled with^{125}I. The sensitivity of this IRMA method was 2.13 ± 0.91 (SD) pg/ml, and the between-assay imprecision, evaluated throughout 1-yr experiments in two different plasma pools, was 11.4% (22.61 ± 2.57 pg/ml,*n* = 15) for one pool and 8.0% (178.6 ± 14.3 pg/ml, *n* = 15) for the other.

## DATA ANALYSIS

### Description of the Kinetic Model

The analysis is based on the circulatory model depicted in Fig.1. The ANP body system is schematized as three blocks: right heart, lungs + left heart, and periphery. In more detail, the periphery block can be considered as a parallel of various organs and/or circulatory districts. The same flow (F) circulates through the three blocks connected in series; because the concentration of tracer ANP is measured in plasma and not in blood, the conversion factor is indirectly included in F, which is computed by multiplying cardiac output by the blood-to-plasma concentration ratio and is referred to here as plasma cardiac output. The tracer injection point, the sampling points used in the actual protocol (pulmonary artery, aorta), and the sampling point of a standard protocol (peripheral vein) are indicated in the scheme.

Under the usual assumptions of linearity and stationarity, each block is characterized by its unitary impulse response [*f*(*t*); this function, also called transit time-density function (ttdf), is normalized, i.e.,
*f*(*t*)d*t*= 1] and by its extraction coefficient (E) or, alternatively, by its transmission coefficient (T). As usual, E is defined as the amount of substance degraded within the block and expressed as a fraction of the total amount that enters the block. T represents the remainder, which, not being extracted, escapes intact from the block and recirculates into the body. Because E + T = 1, E or T is used interchangeably, and one is preferred over the other, because the actual equation can be written in a simpler or more suggestive way. E and T are occasionally reported as a percentage, rather than a fraction.

We recall that when the substance is carried by a constant F and concentrations are constant in input (C_{i}) and output (C_{o}), then from the definition it follows that E = (C_{i} − C_{o})/C_{i}and T = C_{o}/C_{i}. If input is a bolus (corresponding experimentally to a concentration curve with a peak), the amount entering the system is AUC_{i}F (where AUC_{i} is the AUC in input). Moreover, the amount leaving is AUC_{o}F (where AUC_{o} is the AUC in output), and therefore E = (AUC_{i} − AUC_{o})/AUC_{i}and T = AUC_{o}/AUC_{i}.

Let us define*f*
_{rh}(*t*), T_{rh} and*f*
_{p}(*t*), T_{p} and*f*
_{l + lh}(*t*), T_{l + lh}, and the ttdf and transmissions of right heart, lungs + left heart, and periphery blocks, respectively. It is convenient to consider the whole body as a single perfused organ with “open-loop” extraction (E_{wb}) and flow equal to F. The situation can be easily imagined by cutting the circulation at some point, e.g., at the level of the pulmonary artery; E_{wb} is therefore the fraction of the substance entering the pulmonary artery that is degraded throughout the body system in one cycle (and that does not return to the pulmonary artery). Because the whole body block is made up of three blocks arranged in series, its transmission is the product of individual transmissions, i.e.
Equation 1and whole body single-pass (or open-loop) ttdf is the convolution product of the three individual ttdf
Equation 2

### Description of the Experimental Curves

After bolus injection of the tracer [dose (D)] upstream from the right heart block, concentration curves are measured in the pulmonary artery [c_{pulm}(*t*)] and aorta [c_{aorta}(*t*)]. The typical shape of the two curves is shown in Figs.2-4. According to the circulatory model, these curves are thought to be generated by the summation of a series of peaks
Equation 3
Equation 4with each peak corresponding to one passage [1st pass (1p), 2nd pass (2p), 3rd pass (3p)] at the sampling site of the bolus of the tracer that recirculates. At each successive passage the area under the peak is smaller, since only a fraction (T_{wb}) is transmitted (not extracted) after recycling through the whole body. In addition, after each passage the peak is delayed because of recycling time through the body and more dispersed because of distribution into body fluids. In practice, for ANP it is possible to experimentally resolve the first pass of the bolus; the second, third, and subsequent passes (recycles) together contribute to generate a smooth (recirculating) curve, which, as a whole, resembles an exponential (or multiexponential) decay curve (24). These observations are confirmed by the shapes of the curves depicted in Figs. 2-4; note the narrow peak in the very early part followed by the slower recirculating curve.

Because of frequent sampling, it was possible to split the whole concentration curve generated in the pulmonary artery into a first-pass curve [c_{pulm,1p}(*t*)] and a recirculating curve [c_{pulm,rc}(*t*) = c_{pulm,2p}(*t*) + c_{pulm,3p}(*t*) + ...]
Equation 5The areas under the pulmonary artery and aorta curves [AUC_{pulm} and AUC_{aorta}; the symbol AUC is used to indicate the integral
c(*t*)d*t*] were calculated; in addition, the whole area of the pulmonary artery was subdivided into two portions relative to the first-pass curve and the recirculating curve
Equation 6Note the close similarity of the recirculating curve in the pulmonary artery to the disappearance curve sampled in a peripheral vein in a standard bolus injection protocol (see Fig. 1 to compare the 2 different sampling points); the main difference is that sampling in the peripheral vein reflects the venous return from a peripheral district, whereas the recirculating curve in the pulmonary artery is the average of venous return from all peripheral districts (including 1 more pass through the right heart).

### Computation of the Extraction Coefficients of the Model

With regard to hormone disposal, the model is defined by three independent transmission coefficients: T_{rh}, T_{l + lh}, and T_{p} (plus T_{wb} = T_{rh}T_{l + lh}T_{p}).

The three transmissions (and hence the 3 extractions) are computed from AUC_{pulm}, AUC_{pulm,1p}, and AUC_{aorta} and plasma cardiac output (F) using the following equations.

#### Extraction of the right heart.

The first pass of tracer in the pulmonary artery [Fc_{pulm,1p}(*t*)] can be viewed as the output of the right heart block after bolus injection (upstream to right heart block) of the dose D; by definition it is
Equation 7and in terms of AUCs (i.e., integrating from 0 to infinity)
or
Equation 8where the product of AUC_{pulm,1p}(*t*) and F is the amount of tracer that escapes extraction of the right heart block and passes in the pulmonary artery. The relationship written in the form
Equation 9gives the transmission coefficient (and hence the extraction coefficient) of the right heart block.

#### Extraction of the whole body block.

The whole curve measured in the pulmonary artery is the sum of the individual passes of the bolus that recirculates (see*Eq. 3
*), and in terms of areas (i.e., integrating from 0 to infinity)
Equation 10The second pass of *Eq. 3
* is the output of the whole body block produced by the first pass in input, i.e.
Equation 11integrating from 0 to infinity [taking account that*f*
_{wb}(*t*) is normalized and the properties of the convolution product]
Equation 12following the same line of reasoning, it can be understood that
Equation 13and so on. Therefore, we can rewrite *Eq.10
* as
Equation 14from which it follows that
Equation 15or also taking into account *Eq. 6
*
Equation 16
*Equation15
* (or *Eq. 16
*) is used to obtain the whole body extraction (or transmission) coefficient.

#### Extraction of the lungs + left heart.

Let us consider the curves measured in the pulmonary artery and the aorta as the sum of the individual passes (see *Eqs.3
* and *
4
*). The first pass in the aorta curve can be written as the output of the lungs + left heart block produced by the first pass in the pulmonary artery as input; i.e.
Equation 17Similar relations can be written for all corresponding passes. In terms of areas, it is
Equation 18
Equation 19and so on; summing up term by term *Eqs. 18
* and *
19
* and so on for all passes, we obtain
Equation 20and therefore the transmission coefficient of the lungs + left heart block is computed as the ratio of the area under the aorta curve to the area under the whole pulmonary artery curve.

#### Extraction of the periphery block.

The transmission (T_{p}) and, hence, the extraction can be obtained from *Eq.1
*, once T_{rh}, T_{wb}, and T_{l + lh} have been computed (from *Eqs. 9, 16
*, and*
20
*).

Alternatively, the transmission coefficient of the periphery + right heart block (T_{p}T_{rh}, defined as the series of periphery and right heart) is computed as the ratio of the area under the recirculating curve in the pulmonary artery (output curve) to the area under the aorta curve (input curve); i.e.
Equation 21Once the product T_{p}T_{rh}has been computed, T_{p} can be separately calculated, because T_{rh}is known (from *Eq. 9
*).

#### Extraction coefficients computable by use of a simplified experimental protocol (right heart catheterization only).

By this simplified experiment, only the pulmonary curve is available; it can be split into first pass and recirculating curves, from which AUC_{pulm}, AUC_{pulm,1p}, and AUC_{pulm,rc} are computed. AUC_{aorta} is not available.

From the foregoing equations, the following parameters can be computed:*1*) transmission (extraction) of the right heart block (*Eq. 9
*) and*2*) transmission of the whole body block (*Eq. 15
*). T_{l + lh} and T_{p} cannot be further evaluated unless some assumption is made.

### Relationship Between E_{wb} and Metabolic Clearance Rate

According to the circulatory model, the overall degradative capability of the metabolic system is quantitated by the extraction coefficient E_{wb}. Because the whole body is viewed as a perfused organ with flow F, it is reasonable to expect that its metabolic clearance rate is obtained from extraction and flow according to the well-known relationship
Equation 22Note use of the symbol MCR*, which indicates the metabolic clearance rate defined according to *Eq. 22
*.

On the other hand, the MCR currently reported in the literature on hormone kinetics is obtained by dividing the bolus administered dose by the AUC sampled in a peripheral vein (AUC_{v})
Equation 23or, equivalently
Equation 24because in the experiments reported here, AUC_{v} is not measured and is replaced by AUC_{pulm,rc}, which is very similar.

It is therefore most interesting to derive the relationship between MCR and MCR*; to do this, we also express MCR* in terms of AUCs. We recall two equations already derived: *Eq. 8
*states that AUC_{pulm,1p} is equal to the dose that reaches the pulmonary artery (DT_{rh}) divided by F, and*Eq. 14
* states that the whole area AUC_{pulm} is equal to the AUC_{pulm,1p} divided by E_{wb}. Combining*Eqs. 8
* and *
14
*, we obtain
Equation 25Therefore, MCR* can also be calculated as the ratio of “corrected dose” to the area under the whole curve in the pulmonary artery; the dose is corrected by multiplying it by the transmission coefficient from the injection point to the sampling point (pulmonary artery) of the curve.

Multiplying the numerator and the denominator of*Eq. 25
* by T_{wb} and taking into account that AUC_{pulm}T_{wb}= AUC_{pulm,rc}(*Eq. 16
*), we obtain
Equation 26MCR* is computed as the ratio of the corrected dose to the area under the recirculating curve, where the correction factor T_{rh}T_{wb}is the transmission coefficient from the injection point to the sampling point (pulmonary artery) after a passage through the right heart block and again through the whole system.

When *Eq. 26
* is compared with*Eq. 24
*, it follows that
Equation 27which makes explicit the relationship between MCR, MCR*, and E_{wb}. In conclusion, the MCR values generally reported are larger than MCR* calculated as E_{wb} multiplied by F being the linking factor: 1/(T_{rh}T_{wb}).

### Generalized Relationship Between MCR* and AUC

MCR* can also be calculated from AUC_{v} (schematically represented in Fig. 1 as the effluent of the parallel subblock P_{1} perfused by flow F_{1}). At variance with central sampling sites (pulmonary artery and aorta), the peripheral sampling site is perfused by a fraction of the total plasma cardiac output. An equation analogous to *Eq. 8
* can be written for the area under first pass in the peripheral vein
Equation 28where D_{1}, the amount of injected dose that reaches the sampling point, can be written as D_{1} = DT_{rh}T_{l + lh}(F_{1}/F)
, which is the product of all the transmission coefficients of crossed blocks and the ratio F_{1}/F. With substitution of this expression for D_{1} in *Eq.28
*, it follows that
Equation 29where T_{v} = T_{rh}T_{l + lh}
is the transmission from the point of injection to the point of sampling (v). In addition, an equation analogous to*Eq. 14
* can be written; i.e.
Equation 30
*Equation 30
* is derived by considering that the curve is the superposition of all passes and that the area of each successive pass is linked to the area of the previous pass by a factor T_{wb} (see*Eq. 14
*); combining*Eqs. 29
* and *
30
*, we obtain
Equation 31Therefore, MCR* is expressed as the ratio of the corrected dose to the AUC_{v}; the correction factor is T_{v}, i.e., the transmission coefficient from the point of injection to the point of sampling of the curve (v).

In conclusion, *Eqs. 25, 26
*, and*
31
* are particular cases of a general relationship
Equation 32stating that MCR* can be calculated from the AUC_{x} measured at a generic sampling point, provided that the dose is corrected by the transmission coefficient T_{x} from the point of administration to the point of sampling.

### Simplified Relationships When Right Heart Block Does Not Extract

It is useful to consider the case in which the tracer is not extracted by right heart block; this case seems of practical relevance for the present studies, in which extraction by right heart block was virtually absent.

When T_{rh} = 1, *Eq.11
* becomes
Equation 33and MCR* is obtained simply by dividing D by the area under the whole curve sampled in the pulmonary artery.

Also *Eq. 27
* is simplified as follows
Equation 34and the relationship between MCR and MCR* becomes
Equation 35
*Equation34
* allows computation of MCR if one has already obtained F and E_{wb}. On the other hand, on many occasions we want to calculate E_{wb} from the measured values of MCR and from an estimate of plasma cardiac output (F); to do this,*Eq. 34
* is more conveniently written as
Equation 36

### Estimation of AUCs

Accurate determination of AUCs (of the pulmonary artery and aorta curves) during the earliest minutes of the study (including the 1st-pass peak) relies on continuous sampling technique. The AUC was computed by summing all concentrations of consecutive integrated samples (which are the average concentrations in each sampling interval) and multiplying by the length of the time interval. The area under the remaining portion (normal sampling) of the curve was analytically calculated from a function sum of two exponentials fitted on the experimental points (6–7 points), as previously described (11).

Because of frequent sampling in the first minutes, the onset of recirculation in the pulmonary artery could be detected as a change in the descending slope of the initial peak evident when data are plotted on a logarithmic scale. The area relative to the first pass (AUC_{pulm,1p}) was computed as previously described until the onset of recirculation; the area of the tail computed by monoexponential extrapolation of the descending branch of the peak was added.

## RESULTS

### Native ANP Plasma Levels

The ANP plasma concentrations determined in the pulmonary artery and aorta in all the patients are reported in Table 1. As expected, the highest values were observed in patients with more severe disease, as indicated by their lower ejection fraction and cardiac index associated with higher wedge pressure and New York Heart Association class (*patients 1, 4,* and*8*). If one takes into account the ratio of pairs of samples simultaneously drawn from the aorta and the pulmonary artery for each patient, extraction values range from 39 to −78%, thus indicating that computation of extraction based on the individual pairs of values is unreliable, owing to the fluctuations of measured ANP circulating levels during the study.

### Tracer Purity

A drop of the injected tracer remaining in the syringe after the injection was collected and tested for purity by HPLC; in all kinetic studies, impurity was <1%. As an example, a typical chromatogram of the dose injected (*patient 3*) is shown in Fig. 5; only one peak of radioactivity was found, corresponding to the elution pattern of monoradioiodinated ANP (^{125}I-ANP injected and ^{131}I-ANP added just before HPLC to monitor the possible in vitro degradation).

### Tracer Studies

The time courses of ^{125}I-ANP concentrations measured in the pulmonary artery and aorta from a typical study are reported in Figs. 2-4. The sampling protocol made it possible to obtain a good definition of the radioactivity time course at these two different sites of the circulation. Total AUCs could, therefore, be calculated accurately for both sites. Moreover, the curve sampled in the pulmonary artery could be split into first-pass and recirculating curves (as indicated in Fig. 4), and total area (AUC_{pulm}) could be divided into the respective components AUC_{pulm,1p} and AUC_{pulm,rc} (Table2).

In Fig. 3, ^{125}I-ANP activity sampled in the pulmonary artery is compared with total radioactivity in the corresponding samples. Total radioactivity and^{125}I-ANP activity during the first pass are practically superimposable (the ratio of^{125}I-ANP activity to total radioactivity is 99.5 ± 4.3%). A significant amount of degradative products from injected ^{125}I-ANP was found in plasma only after recycling of the labeled dose (Fig.5
*B*). If we start at the onset of recycling [at 2 min ^{125}I-ANP activity is 77 ± 7% (SD) of total radioactivity,*n* = 8], the difference between the two curves markedly increases (at 4.5 min^{125}I-ANP activity is 38 ± 4% of total radioactivity) because of the progressive accumulation of final metabolites (^{125}I-tyrosine,^{125}I, and/or other radiolabeled metabolites of^{125}I-ANP) with slower kinetics (5,11). At the end of the experiment (30 min after tracer injection)^{125}I-ANP activity was only 5.0 ± 2.1% of total radioactivity.

Total areas under the two curves (calculated from zero to infinity) sampled in the pulmonary artery and the aorta are reported in Table 2for each study; the area under the first-pass curve and the area under the recirculating curve in the pulmonary artery are also reported. These values, together with plasma cardiac output (Table3), allow extraction (or transmission) coefficients of the three blocks (right heart, lungs + left heart, and periphery) and of the whole body system (whole body block) to be computed and so to completely define the circulatory model (Table 3).

The product of AUC_{pulm,1p} (on average 30.6% dose/l) and plasma cardiac output [on average 3.31 l/min, determined as cardiac output (obtained by thermodilution) multiplied by the measured blood-plasma partition factor, seematerials and methods] allows the amount of ANP that passes through the pulmonary artery and enters the lungs to be computed (on average 99.2% of the injected dose as calculated by weighing the syringe). This value corresponds to the percentage of the dose that is recovered from the pulmonary artery and allows a direct measurement of the ANP transmission coefficient through the right heart block (see T_{rh} in Table 3). The computed mean value of 99.2% indicates that no measurable extraction of ANP took place during the transit through the right heart chambers.

The area under the first-pass peak measured in the pulmonary artery (AUC_{pulm,1p}) was about one-half of the total AUC_{pulm} in all patients (Table 2); as a consequence, E_{wb}, calculated as the ratio of first pass to total area, was 47.6% on average, with a relatively narrow range (39.9–60.0%).

The mean total curves (from the first 5 studies in Table 2) in the pulmonary artery and aorta are depicted in Fig. 4; the aorta curve is delayed relative to the pulmonary curve, and it can be appreciated at a glance that the two AUCs (AUC_{pulm}and AUC_{aorta}) are similar. This impression is confirmed by data in Table 2 (on average 64.8 vs. 65.5% dose ⋅ l^{−1} ⋅ min^{−1}for AUC_{pulm} vs. AUC_{aorta}), and so the transmission of the lungs + left heart block was ∼100%. Inasmuch as no measurable extraction was found for the lungs + left heart or the right heart block, whole body extraction could be entirely attributed to the periphery block.

The last three studies (*patients 6–8* in Tables 1-3) were carried out with a simplified experimental protocol that required right heart catheterization only; by this approach, extraction values of whole body and right heart block can be calculated, whereas no information on lungs + left heart block extraction can be obtained. With regard to whole body extraction and right heart transmission, the results we obtained (52.2 ± 8.8 and 99.7 ± 1.4%, respectively) were superimposable on those of the previous five studies (44.9 ± 3.7 and 98.9 ± 1.2%, respectively). The periphery block can then be considered responsible for the total hormone extraction; therefore, we conclude that, on average, extraction of the periphery block is 47.6% (i.e., equal to average whole body extraction observed in all 8 studies).

### MCR Values

Two different values for clearance rate (MCR and MCR*) are reported in Table 3 for each case; the first (MCR) was calculated as D/AUC_{pulm,rc} and is directly comparable (see data analysis) to previously reported values (6, 9-13, 26). All these values, reported by many authors and by us (6, 9-13, 26), were computed as the ratio of the entire dose to AUC_{v}; this area is very similar to AUC_{pulm,rc}, i.e., the area under the pulmonary curve after subtraction of the first-pass curve. In accordance with these considerations, the mean values of MCR (3.06 l/min) were similar to those previously reported (10, 11).

On the other hand, MCR* is the clearance rate defined as the perfused body extraction (E_{wb}) multiplied by the plasma cardiac output (F). The values of MCR* reported in Table3 have been computed as follows: MCR* = D/AUC_{pulm}, which is theoretically correct (see data analysis) when 100% of the injected dose reaches the pulmonary artery. In each case, the MCR* was similar to E_{wb} times F; on average, MCR* was 1.57 l/min, which coincides with the product of average values of F and E_{wb} (i.e., 3.31 × 47.6% = 1.57 l/min).

The MCR* was about one-half of MCR (on average 1.57 vs. 3.06 l/min, with MCR/MCR* = 1.57/3.06 = 51.3%). Indeed, from theory (seedata analysis) it can be derived that MCR*/MCR is equal to the perfused body transmission coefficient (T_{wb}), which was 52.4% on average.

## DISCUSSION

### Why Resort to the Circulatory Model, and How Does the Circulatory Model Work?

A very popular experimental protocol for describing the kinetics (renewal) of endogenously produced substances implies the bolus injection of tracer (generally in a peripheral vein) and the plasma sampling of only one disappearance concentration curve (generally from a different peripheral vein or more rarely from an artery district). On the basis of the compartmental model (or of the so-called noncompartmental approach) (8), a single parameter (MCR) is computed to quantitate the degradation rate at the whole body level; whatever the approach, MCR is calculated as the ratio of the injected dose to the area under the single disappearance curve (MCR = D/AUC_{v}).

This approach, which has the advantage of being very practicable, has been applied, essentially unmodified, to the study of numerous endogenously produced substances, despite their very different kinetic characteristics (8). Measured MCR values show extreme variations. For example, an MCR of 0.7 ml/min has been reported for thyroxine (T_{4}) (18), whereas the MCR of several produced hormones (e.g., all gonadal and adrenal sexual hormones and aldosterone) is 1,000–1,500 ml/min (i.e., on the same order as plasma cardiac output). Furthermore, MCR values as large as 3,000 ml/min or more have been found for ANP (7, 11, 20). It is, however, intuitive that the wide differences in metabolic behavior (e.g., slowly degraded T_{4} vs. rapidly degraded ANP) imply that experimental data produced by the bolus injection protocol should be interpreted in somewhat different ways.

Indeed, when labeled hormone is bolus injected (or alternatively when native hormone is secreted in a burst), it can be predicted that the AUC can be the same along the whole intravascular compartment (at least within the limits of precision of the measurement) when the degradation processes are relatively slow with respect to the mixing ensured by circulation (e.g., for T_{4}). However, for rapidly degrading systems (such as ANP) the AUCs, sampled at different circulatory districts, will be different. The different AUCs measured at different sampling sites in rapidly degrading systems, as opposed to the slowly degrading system in which only one AUC is measured, pose some problems in interpretation. In fact, one would be puzzled by the different MCR values produced by the simple formula D/AUC (8) when different values of AUC are introduced.

The experimental protocol of the present studies allows an extended set of data to be collected after the bolus injection of tracer ANP, i.e., AUCs measured at different sampling sites together with direct measurement of cardiac output. As expected for a substance with a very high clearance rate, large differences in the AUCs were observed in all studies (Table 2); in particular, AUC_{aorta} (65.5% dose ⋅ l^{−1} ⋅ min^{−1}), i.e., upstream from the periphery, was about twice that of AUC_{pulm,rc} (34% dose ⋅ l^{−1} ⋅ min^{−1}) measured downstream from the periphery.

Although these new experimental data give a more detailed description of the ANP system, they could not be analyzed using the compartmental model (or the so-called noncompartmental approach) used in previous works on ANP kinetics (6, 7, 26) and also adopted in our previous studies (10-13). These models of whole body ANP kinetics are extremely simplified and assume (more or less explicitly) that the intravascular space behaves as a single initial distribution compartment; therefore, they cannot account for different disappearance curves of tracer sampled in different sites of the intravascular space. Moreover, hemodynamic factors cannot be explicitly addressed by these approaches. For these reasons, we resort to the circulatory model previously developed and mostly used in different applications for exogenous substances (2, 14, 24, 25).

With respect to the compartmental approach, the circulatory model gives a more physiologically based description of the kinetics of rapidly degraded substances (such as ANP) directly secreted into the bloodstream. The parameters that describe the degradation of ANP are the extraction (or transmission) coefficients associated with the individual blocks and the cardiac output. At the whole body level, a single parameter, E_{wb}, extraction of open-loop “perfused body,” is defined. The analysis is based on the indicator-dilution principles, avoiding any assumption of instantaneous mixing into a central (plasma) compartment, which is clearly unrealistic for rapidly degraded substances. Transmission coefficients for the individual block (or for the whole body) are computed as the ratio of the AUC measured downstream to that measured upstream from the pertinent block (or the perfused body). An obvious advantage is that different AUCs measured in plasma at different sites can be interpreted, and these differences can be exploited to compute extraction coefficients of individual districts, provided that pertinent experimental data (upstream and downstream curves) are available.

An additional advantage of the circulatory model is that the effects of hemodynamics on the metabolism of the substance can be made evident. Although in a compartmental model the degradation is described by the single parameter MCR, in the circulatory model the degradation is associated with two parameters, E_{wb} and F, linked by the well-known relationship: MCR* = E_{wb}F. By this definition, MCR* depends on two factors: extraction, which represents an intrinsic characteristic of the body, and plasma cardiac output, which represents the contribution of hemodynamic factors. In fact, for hormones with very fast kinetics (such as ANP), changes in cardiac output can affect the rate of removal (flow-limited removal), a behavior that cannot be accounted for by compartmental analysis in which circulation is not considered.

More explanation is needed to describe why, in rapidly degrading systems, MCR*, defined as E_{wb}F, differs from the very popular and much referred to MCR = D/AUC_{v}, computed from a peripheral venous curve. In the presence of different plasma AUCs measured in different circulatory districts, the simple formula MCR = D/AUC cannot be used without more explanation, since confusingly different values of MCR are generated. It can be shown (see data analysis) that the general relationship to be used is MCR* = DT_{x}/AUC_{x}, in which the dose is corrected for the transmission coefficient T_{x} from the injection site to the generic (*x*) sampling site of the curve used to obtain AUC_{x}. Indeed, by introducing different AUC_{x} into this general formula, the same value of MCR* is calculated, since the corresponding transmission coefficient T_{x} takes into account the fraction of the dose extracted during the passage from the administration site to the sampling site.

As an example from the present experiment, the finding that MCR was about twice MCR* is a consequence of MCR being computed as the ratio of the entire dose to the AUC measured in the periphery. According to the circulatory model, this formula is not correct in the case of a rapidly degraded hormone, such as ANP; in this case, it should be taken into account that only 52.4% of the administered dose reaches the periphery because of rapid extraction in a single pass.

The relationship linking MCR* with MCR can also be written as follows: E_{wb} = MCR/(MCR + F) (seedata analysis); in this form the relationship allows E_{wb} to be derived from MCR when an estimate of F is available. It is easily seen that when we measure an MCR value (3.06 l/min on average) similar to plasma cardiac output F (3.31 l/min on average), as in the case of ANP, the E_{wb} approximates 50%. The above relationship is correct for rapidly and slowly renewed systems; however, when MCR ≪ F (i.e., in slowly renewed systems such as that of the thyroid hormone T_{4}) (18), the relationship is approximated by the simpler equation E_{wb} = MCR/F, so that MCR and MCR* practically coincide. It is also important to emphasize that the complete relationship always gives a correct value of extraction, even when MCR is larger than F; however, in this case, the simplified relationship E_{wb} = MCR/F would produce a puzzling value of extraction >1.

### Circulatory Model and Constant-Infusion Protocol

The use of the circulatory model can easily be extended to the protocol in which tracer is administered by constant infusion (13). The main difference is that, after a proper equilibration period, different steady-state tracer concentrations (instead of different AUCs, as in the case of bolus administration) are measured upstream and downstream from various extracting circulatory districts. The equations are very similar to those derived here, where the corresponding steady-state levels substitute for AUCs. In particular, transmission coefficients are computed as the ratio of tracer levels measured downstream to those measured upstream from the district. A relationship was derived previously (13) to convert from peripherally measured MCR [computed as the ratio of infusion rate (IR) to steady-state concentration in peripheral vein (C_{v}), i.e., MCR = IR/C_{v}] to E_{wb}, if a value for F is available. We previously reported values for MCR and E_{wb} of labeled ANP determined by means of a relatively simplified constant-infusion protocol (13); these values are similar to those reported in the present study by using the bolus injection protocol and sampling in the pulmonary artery.

Indeed, one important limitation of the approach presented previously (13) is that it was based on a direct measurement of only C_{v} (where steady-state concentration in peripheral vein was considered to be the output of the perfused body). The concentration of tracer ANP in pulmonary artery, input of the perfused body, has been reconstructed as peripheral venous concentration added to the ratio of infusion rate (experimentally controlled) to measured plasma cardiac output (i.e., C_{v} + IR/F) under the assumption of negligible right heart extraction (13). It should be emphasized that by using the bolus protocol the input and the output from the perfused body are accurately and directly measured by the curve sampled in the pulmonary artery and separated as first-pass and recirculating curves. This is not possible, even if pulmonary samples were available, for infusion studies, since output steady-state concentration of perfused body (steady-state concentration at the pulmonary artery level) cannot be experimentally resolved from input function.

A major advantage of the experimental protocol in which tracer is infused at a constant controlled rate is that it simulates the endogenous condition in which the native substance is secreted at a constant rate. It seems more useful to continuously monitor the degradation rate and extraction during stimulatory tests that produce, for instance, variation in the endogenous secretion of the hormone (13).

### Accuracy in the Computation of AUC_{v}

In rapidly degrading systems the accurate estimate of AUC_{v} from the concentration curve measured in a peripheral vein after bolus injection is not a simple task and requires the adoption of a suitable sampling protocol. Generally speaking, the higher the degradation rate, the more frequent should be the sampling of the earliest part of the concentration curve. In fact, when MCR is of the same order as plasma cardiac output, ∼50% of the tracer is extracted in every single pass through the whole body (which requires a mean recycling time of ∼1 min). It is therefore intuitive that if the first sample is taken starting from 3–5 min after injection, a considerable amount of tracer is already degraded, and therefore an accurate estimate of AUC is unlikely to be reconstructed regardless of the mathematical approach.

From our “recirculating” curves of ANP, we observed that a large fraction (40–50%) of the area is relative to the first 5 min (Fig. 5), and so an insufficient sampling in this early period could produce large errors in AUC_{v}. On the other hand, the area extrapolated from 30 min to infinity represents only a minor contribution to the total area (<5% of total area on average in the present studies), and therefore the sampling protocol is less critical.

According to these considerations, it is advisable when quantifying ANP (or similar substances) to obtain at least four or five samples in the first 5 min, thus avoiding the integral of the sharp peak of the initial part of the curve being inaccurately computed due to insufficient sampling. In any case, it is not advisable to use exponentials with nonzero intercepts to fit the experimental points as is currently done in compartmental analysis; the use of a function with nonzero intercept derives from the assumption of instantaneous mixing of the tracer dose before an appreciable degradation takes place, and this assumption is untenable for rapidly degraded hormones. Clearly, the backextrapolation to zero of the early experimental points, in contrast to any experimental evidence reported here, induces overestimation of AUC_{v}, in our experience a 20% overestimation of multiexponential fit in respect to trapezoidal integration. In addition, the overestimation can be particularly large when cardiac output is slow and the peak of recirculation is delayed (up to 40% overestimation in our studies).

A better strategy would be to use an integrated sampling (as reported here for the curves sampled in pulmonary artery and aorta), which ensures against loss of accuracy due to insufficient sampling and, at the same time, does not require any interpolating procedure.

### Pathophysiological Implications of Kinetic Results

The results obtained with the newly developed kinetic approach applied in the present study provide new information on ANP degradation in humans and, at the same time, could help clarify previous, often contradictory, data. Our data confirm that whole body extraction of the hormone is very high (∼50%), as previously reported by others (6, 7,20) or by us (13) using a different experimental approach (infusion instead of bolus injection). An important finding is that in our patients no measurable extraction of^{125}I-ANP was found for lungs and heart, so all the hormone-extracting processes take place downstream from the aorta district. Our results seem to be in contrast with previous reports on the role of the lungs in ANP extraction in normal and heart failure states (9, 22, 23). These data, however, need further confirmation in a larger sample of patients with a study design specific for this purpose. A major limitation of this approach is that it is feasible only in patients undergoing a complete hemodynamic study because of their cardiac disease, including a direct measurement of cardiac output (by thermodilution).

Finally, an interesting finding is that whole body extraction of ANP could be a relatively stable parameter (47.6 ± 6.6%), even in the presence of large fluctuations of plasma flow (2.7–4.3 l/min) and MCR (2–4 l/min), thus confirming the intrinsic, organ-specific nature of this parameter independent of changes in hemodynamic factors. However, to improve our knowledge of the action and the pathophysiological role of ANP, future studies using this model should be planned to identify sites and mechanisms of ANP clearance from the circulation.

## Acknowledgments

We thank Stefano Turchi and Franco Cazzuola for technical assistance, Marisa Corfini for dietetic assistance, and Roberta Bertolini for secretarial assistance. In addition, we thank Alessandro Riva and Marco Paterni for setting up the automatic sampling device.

## Footnotes

Address for reprint requests: A. Pilo, C. N. R. Institute of Clinical Physiology, Via Savi 8, 56100 Pisa, Italy.

- Copyright © 1998 the American Physiological Society