## Abstract

The aim of the present study was to describe a method combining easy implementation in a clinical setting with accuracy and precision in quantification of ^{123}I-labeled *N-*(3-iodoprop-(2E)-enyl)-2β-carboxymethoxy-3β-(4′-methylphenyl)nortropane (PE2I) binding to brain dopamine transporter. **Methods:** Five healthy subjects (mean age, 50 y; range, 40–68 y) were studied twice. In the first experiment, dynamic SPECT data and arterial plasma input curves obtained after ^{123}I-PE2I bolus injection were assessed using Logan, kinetic, transient equilibrium, and peak equilibrium analyses. Accurate and precise determination of BP_{1} (binding potential times the free fraction in the metabolite-corrected plasma compartment) and BP_{2} (binding potential times the free fraction in the intracerebral nonspecifically bound compartment) was achieved using Logan analysis and kinetic analysis, with a total study time of 90 min. In the second experiment, ^{123}I-PE2I was administrated as a combined bolus and constant infusion. The bolus was equivalent to 2.7 h of constant infusion. **Results:** The bolus-to-infusion ratio of 2.7 h was based on the average terminal clearance rate from plasma in the bolus experiments. Steady state was attained in brain and plasma within 2 h, and time-activity curves remained constant for another 2 h. Even when an average bolus-to-infusion ratio was used, the striatal BP_{1} and BP_{2} values calculated with kinetic analysis (BP_{1} = 21.1 ± 1.1; BP_{2} = 4.1 ± 0.4) did not significantly differ from those calculated with bolus/infusion analysis (BP_{1} = 21.0 ± 1.2; BP_{2} = 4.3 ± 0.3). Computer simulations confirmed that a 2-fold difference in terminal clearance rate from plasma translates into only a 10% difference in BP_{1} and BP_{2} calculated from 120 to 180 min after tracer administration. **Conclusion:** The bolus/infusion approach allows accurate and precise quantification of ^{123}I-PE2I binding to dopamine transporter and is easily implemented in a clinical setting.

The tropane analog *N-*(3-iodoprop-(2E)-enyl)-2β-carboxymethoxy-3β-(4′-methylphenyl)nortropane (PE2I) binds with high affinity to the neuronal dopamine transporter (DAT) (inhibition constant [K_{i}] = 17 nmol/L) and with much lower affinity to the serotonin transporter (29-fold) and the noradrenaline transporter (>58-fold) (1). In vivo, PET and SPECT studies on healthy subjects have demonstrated excellent kinetic properties for ^{11}C-PE2I (2) and ^{123}I-PE2I (3–5). Time-activity curves showed that striatum-specific binding peaked approximately 60 min after bolus injection and that, for PET, the striatum-to-cerebellum ratio was approximately 10 at peak time (2). The usefulness of the cerebellum and neocortex as reference regions has been demonstrated in monkeys, in which the striatal time-activity curves after ^{11}C-PE2I injection reached the level of the cerebellum and neocortex after injection of unlabeled 2β-carbomethoxy-3β-(4-iodophenyl)tropane (β-CIT). In addition, the cerebellar and neocortical time-activity curves were unchanged after injection of unlabeled β-CIT (2). This finding agrees with the very low ^{125}I-PE2I binding seen in the neocortex and cerebellum on human whole-hemisphere autoradiography (6). Only polar plasma metabolites of ^{11}C-PE2 (2) and ^{123}I-PE2I (7), unlikely to cross the blood-brain barrier to any significant extent, have been demonstrated. In baboons, in vivo striatal ^{11}C-PE2I B′_{max} values correlated with in vivo striatal 6-^{18}F-fluoro-l-dopa K_{i} values, with in vitro striatal ^{125}I-PE2I B_{max} values, and with the number of tyrosine hydroxylase-immunoreactive neurons in the substantia nigra (8). ^{123}I-PE2I has proven useful for preclinical and early diagnosis of Parkinson’s disease in humans (5) and experimental Parkinson’s disease in monkeys (5,9).

The aim of this study was to describe a method that provides a reliable quantitative estimate of receptor parameters and is easy to implement in a clinical setting. We present results from 5 healthy subjects who underwent SPECT twice: first after a bolus injection of ^{123}I-PE2I and then, days or weeks later, after a bolus injection plus a constant infusion of ^{123}I-PE2I. The ratio of the bolus size (MBq) to the infusion velocity (MBq/h) is defined as the bolus-to-infusion ratio (h). The bolus-to-infusion ratio used in all bolus/infusion studies was determined from the average kinetic parameters of the initial bolus studies. The design of the study allowed direct comparison of binding potential (BP) after bolus and BP after bolus/infusion in each individual. The design also allowed comparison of use of the average bolus-to-infusion ratio and use of the theoretic optimal bolus-to-infusion ratio calculated from an individual’s terminal clearance rate of ^{123}I-PE2I from plasma.

## MATERIALS AND METHODS

### Subjects

Five healthy subjects (mean age, 50 y; range, 40–68 y) were included in the study. All claimed to be alcohol and drug free, had no history of neurologic or psychiatric disorders, had normal results on physical examination and routine blood tests, and gave written informed consent. The study was performed in accordance with the ethical standards of the Declaration of Helsinki and was approved by the ethical committee of Copenhagen and Frederiksberg (KF 02-150/98).

### Regions of Interest (ROIs)

The individual bolus SPECT images and bolus/infusion SPECT images were manually aligned using software supplied with the scanner. Subsequently, the individual SPECT images were aligned on a voxel-by-voxel basis using a 3-dimensional automated 6-parameter rigid-body transformation (10). ROIs were drawn on the first frame of the bolus study and applied to all other frames, including the frames of the bolus/infusion study, thus generating time-activity curves for striatum and occipital cortex. ROIs were defined according to a standard anatomic atlas. To maximize the statistical quality of the SPECT data, we did not divide the striatum into smaller anatomic regions. The use of whole-striatum ROIs is not applicable in the study of Parkinson’s disease and related disorders because of the possibility of left/right and caudate/putamen asymmetry. In pathologic conditions, coregistration with MR images is beneficial for ROI delineation.

### Derivation of Outcome Parameters

Derivation of outcome parameters was based on the 2-tissue-compartment model, which includes the metabolite-corrected plasma compartment (C_{1}, Bq/mL), the intracerebral nonspecifically bound compartment (C_{2}, Bq/mL), and the intracerebral specifically bound compartment (C_{3}, Bq/mL). K_{1} (mL/mL/min) and k_{2} (/min) denote the rate constants for transfer between C_{1} and C_{2}; k_{3} (/min) and k_{4} (/min) denote the rate constants for transfer between C_{2} and C_{3}; f_{1} (unitless) is the fraction of C_{1} free to transfer between C_{1} and C_{2}; and f_{2} (unitless) is the fraction of C_{2} free to transfer between C_{2} and C_{1} or C_{2} and C_{3}. Because of the overall physicochemical constancy of brain tissue, the concentration of tracer in C_{2} is often assumed to equal the concentration of tracer in an ROI devoid of receptors (C_{ref}).

We defined 2 outcome parameters, BP_{1} and BP_{2}. The transfer of tracer between compartments can be described by a set of 1-order differential equations. A similar set of equations can be written for the simple bimolecular association of a ligand with its receptor. Combining these sets of equations defines BP_{1} (unitless) and BP_{2} (unitless) in terms of steady-state concentrations of tracer in compartments, rate constants, and binding parameters:
Eq. 1

C_{1}(∞), C_{2}(∞), and C_{3}(∞) denote the steady-state radiotracer concentration in compartments. SPECT measures the total concentration of radiotracer in the brain (C_{tot}). Because of the overall physicochemical constancy of brain tissue, C_{2}(∞) is assumed to equal the concentration of tracer in an ROI devoid of receptors (C_{ref}(∞)), and C_{3}(∞) is calculated as C_{tot}(∞) − C_{ref}(∞).

The terms BP_{1} and BP_{2} are the BP of Mintun et al. (1984) (11) containing f_{1} and f_{2}, respectively. Those authors used the non-protein-bound fraction of C_{1} as a representation of f_{1} and calculated f_{2} from cerebellar data (assuming C_{ref} = C_{2}) and the measured value of f_{1}. BP is equal to the ratio of B′_{max} to K_{d}. B′_{max} (mmol/L) is the concentration of sites available for binding, and K_{d} (mmol/L) is the affinity constant of the tracer.

Bolus data were analyzed using graphical analysis (12,13), kinetic analysis (14) with the simplified reference tissue model (15,16), peak equilibrium analysis (17), and transient equilibrium analysis (18). Graphical analysis and kinetic analysis were performed using PMOD version 2.5 (PMOD Technologies). Striatal Logan plots were linear starting at 44 min (range, 30–60 min), and striatal Logan plots using occipital cortex as a representation of the input function were linear starting at 42 min (range, 40–50 min). The 2-tissue-compartment model (mean Akaike information criterion = 57 [range, 46–70]) gave better fits than did the 1-tissue-compartment model (mean Akaike information criterion = 86 [range, 77–96]). The full reference tissue model (16) and the simplified reference tissue model (15) provided practically identical Akaike information criterion values (*P* > 0.12, paired Student *t* test) and BP_{2} values (*P* > 0.26, paired Student *t* test). Peak equilibrium analysis was done from 40 to 80 min. This period was based on the range of individual peak times for striatum-specific binding. For calculation of BP_{1}, the average ^{123}I-PE2I plasma concentration from 40 to 80 min was used. The transient equilibrium analysis was done from 90 to 180 min. The terminal elimination rate constant (a_{3}) associated with the slowest component of the bolus arterial input curve was determined for each subject. Linear regression analyses were done on logarithmic metabolite-corrected arterial input data from 105 to 175 min. Individual bolus-to-infusion ratios were calculated as −1/a_{3} (in hours) as previously described (19).

## RESULTS

### Bolus Studies

Figure 2A shows the average time-activity curve for parent compound in arterial plasma. The individual bolus-to-infusion ratios ranged from 1.8 to 3.7 h (Table 1). The 95% confidence intervals for the individual a_{3} values were large, and in subject 4 the SE of a_{3} was comparable in size to a_{3}. The 95% confidence intervals of the individual bolus-to-infusion ratios (Table 1) were calculated from the 95% confidence intervals of a_{3}. An average bolus-to-infusion ratio of 2.5 h was calculated from average a_{3} values. This bolus-to-infusion ratio is ideal for attaining a sustained steady state in plasma. We chose to increase the bolus-to-infusion ratio slightly—to 2.7 h—for faster steady-state attainment in the DAT-rich striatal ROI.

Figure 2B shows the average time-activity curves from striatum and occipital cortex. Striatal time-activity curves peaked between 15 and 21 min, and occipital cortex time-activity curves peaked between 3 and 9 min. Striatum-specific binding (striatum - occipital cortex) peaked between 45 and 75 min.

Figure 3 shows the mean normalized BP_{1} and BP_{2} values as a function of time after bolus injection of tracer. For each subject, BP_{1}(t) and BP_{2}(t) were calculated by deleting a progressive number of frames from the end of the study. For each subject, BP_{1}(t) and BP_{2}(t) were normalized to the individual outcome measure calculated at 180 min (using the maximal number of data points). Except for the BP_{1} value at 90 min, normalized BPs using kinetic analysis were greater than 90% of the final values from 65 min after ^{123}I-PE2I bolus injection. With the kinetic analysis, the SDs of normalized BP_{1} were, however, larger than those obtained with the Logan analysis. The SDs of normalized BP_{2}, conversely, were comparable to those obtained with the Logan analysis except for the value at 65 min. In contrast to kinetic analysis, with Logan analysis the SDs of the average normalized BPs were less than 10% of the average normalized BP. However, for the Logan approach to be accurate, the acquisition time must be extended beyond 90 min for normalized BPs to be larger than 90% of the final values.

The individual and average outcome parameters are listed in Tables 2 and 3. Average striatal BP_{1} and BP_{2} values as calculated with kinetic analysis were 21.1 ± 1.1 and 4.1 ± 0.4, respectively. Compared with kinetic analyses, Logan analysis underestimated BP_{1} by 11% ± 5% (*P* < 0.02, paired Student *t* test) and BP_{2} by 3% ± 4% (*P* < 0.18, paired Student *t* test). Compared with kinetic analyses, transient equilibrium analyses overestimated BP_{1} by 170% ± 20% (*P* < 0.002, paired Student *t* test) and BP_{2} by 136% ± 8% (*P* < 0.0002, paired Student *t* test). Compared with kinetic analyses, peak equilibrium analyses overestimated BP_{1} by 133% ± 21% (*P* < 0.025, paired Student *t* test) and BP_{2} by 102% ± 7% (*P* < 0.5, paired Student *t* test). The distribution volume equaled the steady-state ratio of tissue to plasma parent activity and was calculated as K_{1}/k_{2}(1 + k_{3}/k_{4}) using kinetic analysis. The average striatal distribution volume was 25.9 ± 1.4 mL/mL, and the average occipital cortex distribution volume was 5.0 ± 0.5 mL/mL. In subjects 1–5, the transfer rates from the tissue compartment to plasma (/min) were 0.016 ± 0.001, 0.009 ± 0.001, 0.014 ± 0.001, 0.009 ± 0.001, and 0.011 ± 0.001.

### Bolus/Infusion Studies

In Figure 4, each data point represents the mean value of the 5 subjects studied with the average bolus-to-infusion ratio of 2.7 h (Table 1). The average time-activity curves (Figs. 4A and 4B) and outcome measures (Figs. 4C and 4D) plateaued approximately 100–120 min after tracer injection. The stability of the individual time-activity curves and outcome measures was calculated as the slope (linear regression analysis from 120 to 240 min) divided by the average value from 120 to 240 min multiplied by 100%. According to Table 1, individual BP_{1}, BP_{2}, and metabolite-corrected plasma radioactivity were stable from 120 to 240 min, with an hourly change of no more than 10%. Except for subject 2, the slopes of the plasma, BP_{1}, and BP_{2} regression lines from 120 to 240 min were not significantly different from zero, but even in this subject, BP_{1} and BP_{2} were similar to values calculated using kinetic analysis. The individual and average outcome parameters are listed in Tables 2 and 3. Average striatal BP_{1} and BP_{2} values as calculated with bolus/infusion analysis were 21.0 ± 1.2 and 4.3 ± 0.3, respectively. There was no significant difference between BP_{1} calculated using 2-tissue-compartment analysis compared with bolus/infusion analysis (paired Student *t* test, *P* > 0.8, Table 2) and BP_{2} calculated using simplified reference tissue analysis compared with bolus/infusion analysis (paired Student *t* test, *P* > 0.3, Table 3). For bolus/infusion analysis, we tested time points ranging from 120 to 180 min and from 180 to 240 min. The average striatal distribution volume was 25.9 ± 1.3 mL/mL, and the average occipital cortex distribution volume was 4.9 ± 0.3 mL/mL.

## DISCUSSION

So far, ^{123}I-PE2I has proven to be the ligand with the most favorable in vitro (1) and in vivo (2) characteristics for DAT quantification in humans using SPECT. The aim of the present study was to describe a method combining accurate, precise quantification of ^{123}I-PE2I binding to DAT and easy implementation in a clinical setting. By conducting the bolus and the bolus/infusion studies on the same subjects, we could eliminate the variation in DAT density that is due to genetic and environmental differences between subjects.

### Transient Equilibrium Analysis and Peak Equilibrium Analysis

We found that striatum and occipital cortex time-activity curves peaked within 30 min and that the ratio of striatum-specific binding to nonspecific binding stabilized at an average value of 5.6 ± 0.5 approximately 90 min after ^{123}I-PE2I bolus injection. For comparison, the ratio of striatum-specific binding to nonspecific binding of ^{123}I-FP-CIT, an *N-*fluoropropyl analogue of β-CIT, stabilizes at a value of 2.5 ± 0.6 after approximately 180 min (20,21). However, our findings suggest that if transient equilibrium analysis is to be used to calculate DAT density after bolus injection of tracer, ^{123}I-PE2I is preferable to ^{123}I-FP-CIT in terms of both total study time and target-to-background ratio. In addition, PE2I has the advantage of being selective for DAT.

In a clinical context, transient equilibrium analysis is easy with respect to tracer administration, data acquisition, and data analysis. However, in addition to transporter/receptor BP, simple tissue-to-blood ratios and tissue-to-tissue ratios calculated at transient equilibrium will reflect the terminal clearance rate from plasma (18). According to Table 1, the interindividual variability in the bolus-to-infusion ratios is not negligible (2.7 ± 0.7 h). Furthermore, the terminal clearance rate of ^{123}I-PE2I from plasma is comparable to the transfer rate from the tissue compartment to plasma. Thus, transient equilibrium analysis of ^{123}I-PE2I bolus data overestimates BP_{1} and BP_{2} values significantly, and BP_{1} SEM is large compared with the outcome of a kinetic analysis. In such cases, distinguishing between a normal and a pathologic DAT BP will be more difficult, thus reducing the usefulness of DAT scanning as a clinical tool.

There is no statistical difference between BP_{2} calculated using peak equilibrium analysis (40–80 min) and BP_{2} calculated using simplified reference tissue analysis, and the SEMs are also comparable. According to Figures 2C and 2D, outcome parameters using peak equilibrium analysis increase rapidly from 0 to 70–80 min, making identification of the correct acquisition period important. In theory, the correct acquisition time must be identified individually around the individual peak time of striatum-specific binding. In practice, a predefined experimentally determined acquisition period is often used. However, striatum-specific time-activity curves will peak earlier in subjects with low BPs than in subjects with high BPs. Thus, applying to Parkinson’s disease patients an acquisition time defined in healthy volunteers is likely to overestimate the true BP. Therefore, dynamic acquisition is a sine qua non of peak equilibrium analysis if one is to obtain reliable and comparable BP estimates.

### Kinetic Analysis and Logan Analysis

Kinetic analysis and Logan analysis of bolus data are considered gold standards for quantification of radioligand binding to synaptic molecules. Compared with kinetic modeling, Logan analysis is well known to underestimate BP because of the statistical bias associated with linear transformation of binding data (Tables 1 and 2) (22). The use of Logan analysis or kinetic analysis in clinical studies is hampered by the need for long study times and arterial blood sampling in case a suitable reference tissue does not exist. Figure 3 addresses the study time needed for accurate and precise quantification of ^{123}I-PE2I binding to DAT using kinetic analysis and Logan analysis. Kinetic analyses (simplified reference tissue analysis in particular) accurately quantify ^{123}I-PE2I binding to DAT starting approximately 60 min after bolus injection. However, for precise quantification of BP_{2} using kinetic analysis, the acquisition time must be extended to 90 min. In contrast, Logan analysis precisely quantifies BP_{1} and BP_{2} starting approximately 60 min after bolus injection. However, for accurate quantification of ^{123}I-PE2I binding to DAT using Logan analysis, the total acquisition time must be at least 90 min after bolus injection. A 90-min total acquisition time after bolus injection of ^{123}I-PE2I is shorter than previously found (120 min) (3)—a fact that probably reflects the improved statistical quality of SPECT data using state-of-the-art hardware.

### Bolus/Infusion Analysis

The limitations of the transient and peak equilibrium approaches related to nonsteady-state conditions in brain and plasma are overcome in bolus/infusion studies by administration of the tracer as a bolus followed by a constant infusion. As tracer steady state is attained in brain and plasma, the net flux of tracer between compartments becomes zero and the size of the compartments becomes constant, allowing the outcome parameters to be calculated as simple ratios. Several advantages with the bolus/infusion approach deserve consideration: Quantification of binding parameters is insensitive to changes in cerebral blood flow. For tracers without a suitable reference region, venous blood sampling replaces the more invasive arterial blood sampling. For drugs administered as a bolus plus constant infusion at pharmacologic doses, the acute effect on binding parameters may be calculated within a single scan session after a single radioligand synthesis. If scanning has to be aborted before the scheduled time because of patient discomfort or other causes, quantification of binding parameters may still be possible despite the reduced statistical quality of the data.

The bolus/infusion approach also has some disadvantages: To hasten steady state, a bolus of radiolabeled ligand must be administered, but the optimal bolus-to-infusion ratio required to hasten steady state may vary considerably because of differences in tracer clearance and receptor binding between individuals. In this study, individual bolus-to-infusion ratios ranged from 1.8 to 3.7 h (Table 1), and a bolus-to-infusion ratio of 2.7 h was used in all subsequent bolus/infusion studies. For fast attainment of steady state in plasma, a bolus-to-infusion ratio of 2.5 h (−1/average(a_{3})) would have been ideal. To hasten attainment of steady state in striatum, we increased the bolus-to-infusion ratio from 2.5 to 2.7 h. Post hoc computer simulations based on the bolus data suggested that a bolus-to-infusion ratio of 2.9 h would have more rapidly attained stable striatal BP_{1} and BP_{2} values. However, the average experimental data imply that a bolus-to-infusion ratio of 2.7 h quickly attains stable striatal ^{123}I-PE2I concentrations (Fig. 4B), with a modest overshoot in the plasma (Fig. 4A) and occipital cortex (Fig. 4B) ^{123}I-PE2I concentrations. Further increasing the bolus-to-infusion ratio and, thus, the overshoot in occipital cortex and plasma is likely to slow the attainment of stable values for BP_{1} (Fig. 4C) and BP_{2} (Fig. 4D). The size and sign of the percentage change in plasma ^{123}I-PE2I concentrations per hour were in agreement with the individual bolus-determined optimal bolus-to-infusion ratios. For BP_{1} and BP_{2}, the percentage change per hour, compared with the individual bolus-determined optimal bolus-to-infusion ratio, was less consistent with expectations. However, in all subjects, individual BP_{1}, BP_{2}, and metabolite-corrected plasma radioactivity were stable (defined as a change of no more than 10%/h) from 120 to 240 min after bolus/infusion of ^{123}I-PE2I, and BP_{1} and BP_{2} values calculated using bolus/infusion analysis were not significantly different from values calculated using kinetic analysis. This finding is remarkable considering the range of individual bolus-to-infusion ratios. However, as discussed in the Appendix, computer simulations demonstrate that a 2-fold variation in terminal clearance rate from plasma translates into only a 10% variation in the BPs calculated from 120 to 180 min. Furthermore, estimated a_{3} values are calculated from the noisy terminal part of the metabolite-corrected plasma time-activity curve, and the 95% confidence intervals are large. Thus, the individual “true” a_{3} values may be more similar than is indicated by the estimated a_{3} values. Comparing the individual size of BP_{1} calculated using transient equilibrium analysis (K_{1}/(k_{2} + a_{3})) (18) with the individual size of BP_{1} calculated using kinetic analysis (K_{1}/k_{2}) supports this idea.

## CONCLUSION

Graphical analysis and kinetic analysis quantify ^{123}I-PE2I-bolus data both accurately and precisely. However, in a clinical setting, a total scan time of 90 min may be too inconvenient. With respect to experimental simplicity, transient equilibrium analysis is an attractive and widely used method in nuclear medicine. However, for PE2I and many other ligands with terminal clearance rates from plasma comparable to the transfer rates from the tissue compartment, clinical feasibility is hampered by low accuracy and significantly reduced precision. According to our data from healthy volunteers, peak equilibrium analysis allows accurate, precise calculation of BP_{2}. However, accuracy and precision depend on precise identification of the peak time of specific binding, because the apparent BP_{2} value doubles from 40 to 80 min. Thus, in patients with changes in DAT density, total time spent in the scanner must be increased to identify individual peak times. The bolus/infusion approach quantifies ^{123}I-PE2I bolus/infusion data both accurately and precisely. According to experimental data and computer simulations, individual differences in terminal clearance rates from plasma do not affect outcome parameters after 120 min of constant ^{123}I-PE2I infusion. Some may consider the need for a constant infusion of tracer to be an important limitation for clinical studies. In our experience, the increase in experimental complexity is small compared with the advantages of the bolus/infusion approach. We have implemented the bolus/infusion approach for clinical studies of DAT using ^{123}I-PE2I SPECT.

## APPENDIX

It is possible to simulate the outcome of a bolus/infusion study using the kinetic parameters calculated from a bolus-alone study (23). The bolus input function is approximated to a sum of 3 exponential functions (∑_{i=1}^{3} A_{i}e^{ait}), and in the 1-tissue-compartment situation, K_{1} and k_{2} values are calculated using kinetic analysis:
Eq. 1A
Eq. 2A
Eq. 3A where B/I (h) is the bolus-to-infusion ratio, A_{i} (unitless) is the relative zero intercept of each exponential, and a_{i} (/min) is the elimination rate constant associated with each exponential. Figure 1A shows simulated outcome parameters from 0 to 240 min. Outcome parameters are calculated using Equations 1A–3A. Total distribution volume = C_{tot}(t)/C_{1}(t), reference distribution volume = C_{ref}(t)/C_{1}(t), BP_{1}(t) = (C_{tot}(t) − C_{ref}(t))/C_{1}(t), and BP_{2}(t) = (C_{tot}(t) − C_{ref}(t))/C_{ref}(t). Values have been normalized with the individual steady-state values. In all situations, B/I = 2.7 h, a_{1} = −0.6/min, a_{2} = −0.06/min, K_{1} = 0.42 mL/mL/min, k_{2} = 0.016/min, K_{1}^{ref} = 0.35 mL/mL/min, and k_{2}^{ref} = 0.068/min. Individual curves represent situations with different terminal clearance rates from plasma (a_{3}). In the keys, the individual a_{3} value is expressed as −1/a_{3} (h), representing the individual optimal bolus-to-infusion ratio. The simulations demonstrate 2 important points on the use of the bolus/infusion approach. First, calculations of BP_{1} and BP_{2} using a population-based average bolus-to-infusion ratio are clearly vulnerable to individual differences in terminal clearance rate from plasma. However, the vulnerability decreases with time. From 120 to 180 min, the average normalized BP_{1} values are 1.01 (−1/a_{3} = 1.7 h), 0.92 (−1/a_{3} = 2.7 h), and 0.87 (−1/a_{3} = 3.7 h) and the average normalized BP_{2} values are 0.99 (−1/a_{3} = 1.7 h), 0.92 (−1/a_{3} = 2.7 h), and 0.88 (−1/a_{3} = 3.7 h). Thus, a 2.2-fold variation in terminal clearance rate from plasma translates into only a 10% variation in the calculated BPs. Second, to hasten attainment of steady-state BPs, it is beneficial to increase the bolus-to-infusion ratio beyond the value calculated from the average a_{3} value.

## Acknowledgments

We thank Gerda Thomsen, Karin Stahr, Inge Møller, and Anja Pedersen for expert technical assistance. This work was supported by the Danish Health Research Council, the 1991 Pharmacy Foundation Health Insurance Fund, the Lundbeck Foundation, the Elsass Foundation, and the University of Copenhagen.

## Footnotes

Received Dec. 14, 2004; revision accepted Mar. 29, 2005.

For correspondence or reprints contact: Lars H. Pinborg, MD, Neurobiology Research Unit, Rigshospitalet, N9201, 9 Blegdamsvej, Copenhagen, DK-2100 Denmark.

E-mail: pinborg{at}nru.dk.