Cerebrospinal Fluid Pharmacokinetics and Pharmacodynamics of Intrathecal Neostigmine Methylsulfate in Humans 

The study was divided into two parts: an initial study of 14 volunteers in whom spinal catheters were inserted and a second study of 14 other volunteers who received a single injection of spinal neostigmine through a small-gauge needle. Both studies were approved by the Clinical Practices Committee, written informed consent was obtained, and volunteers reported to the in-patient General Clinical Research Center at 7:00 A.M. having had nothing to eat or drink since midnight. In each study, a peripheral intravenous catheter was inserted to infuse lactated Ringer's solution at 50-100 ml/h, and a second intravenous catheter was inserted and capped to sample venous blood. Baseline measures were taken before neostigmine injection and at times thereafter as indicated. Neostigmine was obtained under IND approval by the Food and Drug Administration in preservative-free saline from International Medication Systems (El Monte, CA). Neostigmine from this same commercial source was used in preclinical toxicity studies.

Based on data obtained in animals, an initial dose of 50 g neostigmine was chosen as likely to be approximately one half the minimal therapeutic dose. In this dose-escalation design, the first four volunteers received 50 [micro sign]g neostigmine; the next four received 150 [micro sign]g; the next four received 500 [micro sign]g, and the last two received 750 [micro sign]g. Neostigmine was diluted in a 4-ml volume with preservative-free normal saline and injected over 30 s through a Sprotte-tipped, 19.5-gauge spinal needle that had been inserted at the L3-L4 or L4-L5 interspace. Volunteers were positioned in a lateral position. Two minutes after neostigmine injection, a 21-gauge catheter was inserted through the Sprotte needle and advanced 3-5 cm beyond the needle tip. The spinal needle was then withdrawn. The CSF samples (total withdrawn volume per sample was 1.5 ml) were obtained 5, 10, 15, 30, 45, 60, 90, 120, 180, 240, 360, 720, and 1,440 min after neostigmine injection for neostigmine and acetylcholine assays. For each sample the initial 0.5 ml, representing 2X catheter dead space, was discarded, 0.5 ml was collected for the neostigmine assay, and 0.5 ml was collected in a tube containing 10^-5M neostigmine for the acetylcholine assay.

Drug Administration. Based on the pharmacologic effects observed in part 1, we chose an initial dose of neostigmine in part 2 of 200 [micro sign]g through a #25 or #27 Whitacre spinal needle. The first volunteer received 200 [micro sign]g neostigmine and experienced protracted, severe side effects, as did the second volunteer, who received 100 [micro sign]g. The third volunteer had only mild side effects after 50 [micro sign]g neostigmine. These three volunteers received neostigmine in a 2-ml volume of normal saline. We speculated that greater cephalad spread of neostigmine by this method of administration, (i.e., without catheter insertion and aspiration of CSF) was the cause of the severity of side effects and that injection in hyperbaric solution might decrease the likelihood of these side effects. The next volunteer received 50 [micro sign]g neostigmine in hyperbaric solution (5% dextrose in saline) and did not experience severe nausea. The remaining 10 volunteers received 100 [micro sign]g (n = 5) or 200 [micro sign]g (n = 5) neostigmine in 1 ml containing 5% dextrose. All dextrose-containing injections were administered in the sitting position, and the head of the bed was elevated at least 30 [degree sign] throughout the study. In all volunteers in part 2 of this study, a second #25 or #27 Whitacre needle was inserted at the same lumbar interspace as the original injection 60 min after neostigmine administration, and 1.5 ml CSF was aspirated for neostigmine and acetylcholine assays. This study ended 6 h after spinal injection. All CSF samples were immediately frozen on dry ice and stored at -70 [degree sign]C until analysis.

Analgesia and Side Effect Monitoring. The following measurements were obtained before and at 30 and 60 min, then hourly until 6 h after injection: blood pressure and heart rate (by a noninvasive oscillometric device), oxyhemoglobin saturation by pulse oximetry, end tidal carbon dioxide by capnography, respiratory rate, finger and toe skin blood flows by laser Doppler flowmetry, a screening neurologic examination, computer tests for attention and for short-term memory, motor coordination tests to screen for central cholinergic stimulation, assessments for level of sedation using a 10-cm visual analog scale (VAS), anchored at 0 =“not drowsy at all” to “as drowsy as possible,” and assessments for level of anxiety using a 10-cm VAS, anchored at 0 =“not anxious at all” to “as anxious as possible.” Analgesia was assessed at these same times by pain report using a 10-cm VAS after immersion of the hand, and 5 min later immersion of the foot, in stirred ice water. A 60-s cutoff time was used, although volunteers were allowed to remove their hand or foot before this time if they experienced unbearable pain. In part 1 of the study, these measurements were also obtained at 12 and 24 h after injection. Details of these measurements may be found in the report of pharmacologic effects in these volunteers. [8] 

Sample Analysis. Neostigmine was extracted and analyzed by high-pressure liquid chromatography with ultraviolet detection, as previously described. [13]The limit of detection was 0.5 ng/ml neostigmine, with an interassay coefficient of variation of 12%. Acetylcholine concentrations were determined by a different high-pressure liquid chromatography-electrochemical detection method. This method has an interassay coefficient of variation of 8% and a detection limit of 50 fmol. [7] 

Pharmacokinetic Analysis. The linearity of the pharmacokinetics with increasing dose was assessed by visual analysis of the dose-normalized concentration versus time curves. Parametric pharmacokinetic analysis was performed with NONMEN,[double vertical bar] using first-order conditional estimates. Both population (typical) pharmacokinetic and post hoc Bayesian (individual) pharmacokinetic parameters were estimated.

Because of the appearance of an initial “absorption” phase, which was likely to be the diffusion of drug from the injection site to the sampling sate, biexponential models of the form: C^scf= A^e-at- A^esup [small beta, Greek]t and triexponential models of the form C^scf= A^esup [small alpha, Greek]t + B^e-[small beta, Greek]t -(A - B)e^-107t were explored. Interindividual and intraindividual errors were modeled as log normally distributed. To model the intraindividual error as log normal, the log of the predicted concentrations were fitted to the log of the observed concentrations using an additive intraindividual error model.

The NONMEM objective function was -2 times the log likelihood. Goodness of fit was visually assessed by comparing the observed concentrations with the predicted concentration over time, and by visually examining the measured-predicted concentrations over time. Bias was calculated as the median weighted residual, and accuracy was calculated as the median absolute weighted residual, as previously described. [14] 

Pharmacodynamic Analysis. The analgesic response in the hand and foot, measured on the VAS scale, was related to the neostigmine concentration using a sigmoidal-E^maxrelation:Equation 1where E^maxis the baseline pain response, -E^maxis the maximum analgesic response (i.e., VAS = 0 [no pain]), C is the CSF neostigmine concentration, C⁵⁰is the neostigmine concentration associated with 50% of the peak response, and [small gamma, Greek] is the steepness of the sigmoidal concentration-response relation. An effect-site model was explored, where the effect-site neostigmine concentration was calculated as:Equation 2where Ce(t) is the effect-site neostigmine concentration at time t and k^eOis the equilibration rate constant between the CSF and the site of drug effect, as defined by Sheiner et al. [15]Two different sets of the five pharmacokinetic parameters (A, B, [small alpha, Greek], [small beta, Greek], [small gamma, Greek]) were explored: population estimates and individual post hoc Bayesian estimates. The effect-site neostigmine concentration was related to the analgesic response in the hand and foot using a sigmoidal-E^maxrelation:Equation 3where Ce is the effect site concentration, and the other terms are as previously described.

Goodness of fit for the pharmacodynamic measures was measured by the median residual and the median absolute residual, where the residual was the measured VAS response - the predicted VAS response.

The resulting pharmacokinetic-pharmacodynamic model was solved for the time of peak effect using the Solver function of Microsoft Excel (Redmond, WA). The pharmacodynamic model was then expressed as the dose associated with a given drug effect at the time of peak effect:Equation 4where D is the dose of neostigmine in micrograms, and D⁵⁰is the dose associated with 50% of the peak analgesic response. This conversion was made by dividing the C⁵⁰for analgesia by the effect-site concentration at the time of peak effect after a unit bolus.

Unless otherwise indicated, data are presented as mean +/− SEM. Pearson product moment correlation was used to determine the relation between log CSF neostigmine and log CSF acetylcholine and between these variables and analgesia or side effects. This analysis was also used to determine the relation between the administered dose and log CSF neostigmine and log acetylcholine. For graphic depiction, linear regression with 95% confidence limits was used. Because of multiple correlation testing, P < 0.01 was considered significant.

Of the 28 volunteers, 3 were excluded from data analysis in this report. Catheters from two volunteers (one volunteer who received 50 [micro sign]g and the other who received 150 [micro sign]g neostigmine) stopped functioning, and it was not possible to obtain CSF within 60 min of neostigmine injection. The first volunteer in part 2 of this study, who received 200 [micro sign]g neostigmine in saline, had severe nausea and vomiting that precluded our obtaining CSF 60 min after injection.

(Figure 1) shows the CSF neostigmine versus time data (upper panel), and the dose-normalized concentrations over time and the individual unit disposition functions (lower panel) for the 13 volunteers. Linearity with respect to dose was established by the lack of a relation between dose and the magnitude of the dose-normalized concentrations over time. The triexponential disposition function was preferred over the biexponential disposition function, based on an improvement in the NON-MEM objective function of 282. Table 1summarizes the pharmacokinetics of neostigmine. The CSF neostigmine concentrations were best described by a triexponential disposition function of the form Equation 5in which the most rapid half-life was 3.3 min and the terminal half-life was 1,666 min. The terminal half-life accounted for <1% of the decrease in neostigmine concentration after bolus intrathecal injection.

The triexponential disposition function described the general shape of the observations over time (Figure 1). The prediction was also unbiased over time, and the magnitude of the prediction errors was consistent over time (Figure 2), both for the population estimates (Figure 2, top graph) and the post hoc individual Bayesian estimates (Figure 2, bottom graph). Although the fit was unbiased (median weighted residual = 2% for both the population and individual estimates (Table 1), there was considerable variability in the population fit (median absolute weighted residual = 52%) because of interindividual variability.

Examination of the residual errors in the time domain (Figure 2) and concentration domain (Figure 3) does not show evidence of model misspecification. Indeed, the individual triexponential disposition functions predicted the observed CSF concentrations across four orders of magnitude with a median error of 25%(Figure 3, bottom graph). Thus the inaccuracy of the population estimate is due to interindividual variability and not to a fundamental limitation in the shape of a triexponential disposition curve to describe the observations.

The plasma neostigmine concentrations were at or near the limit of detection at all times (92% of values were <10 ng/ml with no dose dependency).

In volunteers in part 1 of this study, CSF acetylcholine increased from 13 +/− 2.6 pmol/ml before injection to >100 pmol/ml after injection. In contrast to CSF neostigmine, CSF acetylcholine concentrations remained at a plateau of 100-300 pmol/ml for 4-6 h after neostimine injection in most volunteers, and with no dependency on neostigmine dose administered (Figure 4). Similarly, there was no significant difference between CSF acetylcholine concentration 60 min after neostigmine injection in hyperbaric solution (median, 149 pmol/ml) and that after isobaric injection in the catheter study (median, 193 pmol/ml). There was no significant correlation between CSF neostigmine and CSF acetylcholine concentrations over time, consistent with their differing time courses and dose dependencies (data not shown).

Graphs relating CSF neostigmine concentrations to VAS scores of pain in the hands and feet demonstrated poor correlations. The parameters of a sigmoidal-E^maxmodel were estimated to relate both measured neostigmine concentrations and neostigmine concentrations predicted by the individual post hoc Bayesian pharmacokinetics to the VAS scores of analgesia. The results favored the use of predicted concentrations in modeling the concentration-response relation. The inclusion of k^eO, and this incorporation of an effect site into the model, yielded an improvement in the NONMEM objective function of 138 points in the model for analgesia of the foot.

Analysis began with individual post hoc Bayesian estimates of the effect-site neostigmine concentration associated with 50% analgesia, Ce⁵⁰. The mean Ce⁵⁰was 240, with a standard error in the log domain of 1.14.# Inspection of the data showed that the estimate of Ce⁵⁰was correlated with the dose-normalized plasma concentrations over the first hour, as shown in Figure 5. This correlation suggested that the concentration measured in the CSF was scaled by some arbitrary factor, such as the distance between the injection and sampling sites. We investigated whether the CSF concentrations predicted by the median pharmacokinetics (thick line in Figure 1) instead of the CSF concentrations predicted by the individual pharmacokinetics (thin lines in Figure 1) could eliminate this apparent scale parameter. The test would be whether the intraindividual variability in Ce⁵⁰was increased or decreased by the use of median pharmacokinetics. Using the effect model with median pharmacokinetics yielded a Ce⁵⁰of 244 with a SD in the log domain of 0.86. The decreased standard deviation in the log domain from 1.14 with individual pharmacokinetics to 0.86 with median pharmacokinetics confirmed that the typical CSF pharmacokinetics better predicted the time course of concentration than did the individual pharmacokinetics. It also eliminated the correlation seen in Figure 5, because the predicted neostigmine concentration at 5 min was the same in all persons.

(Figure 6) shows the pain scores and post hoc Bayesian pharmacodynamic models for analgesia of the hand and foot. Although the fits appear to be very tight, the paucity of data with low VAS scores limits confidence in any conclusion. Thus the hand data mostly demonstrate lack of an analgesic neostigmine concentration at cervical levels at the doses used in the study. The post hoc Bayesian models show individual estimates of Ce (⁵⁰) based on median pharmacokinetic data. Individual estimates of Ce⁵⁰for the foot ranged from 49 to 1,110 ng/ml.

(Table 2) shows the estimates of the pharmacodynamic parameters for the analgesic response of the foot (left columns) and hand (right columns). If the interindividual variability in Ce⁵⁰is not considered, the prediction of the analgesic response (Figure 7, left graphs) was less accurate than when the interindividual variability in response was considered (Figure 7, right graphs). The fits were unbiased, with median weighted residuals of <0.2 cm for all fits shown in Table 2.

(Table 2) shows the time of peak effect, and the dose associated with 50% analgesia at the time of peak effect. Figure 8shows the relation between dose and peak analgesic response.

In contrast to these results with CSF neostigmine, there was no significant correlation between pain report and CSF acetylcholine.

Intrathecal neostigmine injection was associated with nausea, vomiting, sedation, anxiety, and lower extremity weakness (full details can be found in the previous report of pharmacologic effects). [8]There was no significant correlation between log CSF neostigmine concentration and simultaneous sedation or anxiety scores. There was a positive correlation between log CSF acetylcholine and sedation score (P = 0.001; r = 0.462).

This is the first description of CSF pharmacokinetics and pharmacodynamics of neostigmine after intrathecal administration in humans. These results raise interesting questions regarding disposition of drugs in the intrathecal space and provide guidance in the introduction of intrathecal neostigmine in clinical practice.

The pharmacokinetics of neostigmine administered by bolus injection are linear with respect to bolus dose. These data do not indicate whether similar pharmacokinetics could be expected with an infusion, so we cannot extrapolate these findings beyond bolus dosing. Intrathecal neostigmine concentrations were best described by a three-compartment model with an absorption phase. The absorption phase was likely the delay between drug injection and diffusion to the sampling catheter. The time of the peak concentration ranged from 5 to 30 min after the intrathecal bolus. This is the same range in time to peak concentration reported by Sjostrom et al., [16]although the median peak in their study was at the first 5-min sample. The absorption phase was followed by a biexponential distribution and elimination phase. The resulting triexponential model produced an unbiased prediction of the concentrations in both the time domain (Figure 2) and the concentration domain (Figure 3). The performance of the individual post hoc Bayesian estimates across four orders of magnitude (Figure 3, bottom graph) indicates that the triexponential model structure was sufficiently flexible to model the data.

These results are consistent with previous studies showing that CSF concentrations after intrathecal administration are highly variable. [16-19]The median absolute weighted residual of 56% was almost twice as large as usually observed for intravenous anesthetic drugs. [20,21]As a result, the ability to predict CSF concentration based on dose alone is limited. However, the shape of the observed concentrations over time were well described by the shape of the triexponential disposition curve. This suggests that although the absolute magnitude of the concentration cannot be accurately predicted from dose alone, the relative change in concentration over time can be accurately predicted.

Pharmacokinetic models are often expressed as volumes and clearances to better understand physiologic implications of the pharmacokinetic modeling. In this case we believe that the polyexponential shape of the curve reflects, at least in part, the diffusion of neostigmine away from the site of injection. Diffusion is a fundamentally different process than distribution and clearance that govern systemic pharmacokinetics. Therefore we have not calculated volumes and clearances from our polyexponential disposition function.

The pharmacodynamic modeling demonstrates a concentration versus response relation between effect-site neostigmine concentrations and analgesia in the feet and hands. There was considerable intersubject variability in the Ce⁵⁰values for analgesia, so estimation of the concentration-response relation required use of population modeling approaches and examination of individual concentration-response relations based on post hoc Bayesian estimates of Ce⁵⁰in each individual.

The initial results from our pharmacokinetic and pharmacodynamic analysis showed an unexpected correlation between the magnitude of the observations and the drug potency (Figure 5). This can be explained by viewing the CSF samples as observations taken at a distance from both the sites of injection and drug effect. Consistently high concentrations indicate that the sampling site is close to the site of injection, and consistently low concentrations indicate that the sampling site is distant from the site of injection. These interindividual differences in magnitude thus do not reflect true differences in the time course drug concentration in the CSF and thus must be removed from the analysis. The concept of “observation at a distance” is explained in detail in Appendix 1.

Specific predictions can be made about the behavior of pharmacokinetics system in which diffusion plays a major role in drug distribution, and thus observations are local, at an unknown distance from the sites of drug injection and drug effect:

1. The observed concentrations over time should have similar shapes, but with different magnitudes. This was observed in this study, as shown in the dose-normalized concentrations and disposition curves seen in Figure 1.

2. The magnitude of the concentrations, normalized to dose, will correlate with the apparent potency. This is shown in Figure 5. The correlation is a result of both measures sharing a common offset, the distance from the site of injection. Note the distinction between this result and the expectation in “well stirred” models (e.g., intravenous pharmacokinetics) in which persons with higher concentrations after the same dose simply have more profound drug effect, but not a change in potency.

3. The Ce⁵⁰for analgesia of the hand should be higher than the Ce⁵⁰for analgesia of the foot. The Ce⁵⁰for hand analgesia was 860 ng/ml, and the Ce⁵⁰for foot analgesia was 244 ng/ml. Put another way, compared with the foot, a larger dose is required to produce analgesia in the hand, as shown in Figure 8.

4. The variability in magnitude of the concentration versus time profile is, in part, an artifact of the distance. This variability contributes to the variability in Ce⁵⁰for drug effect. If the variability in CSF concentrations is removed, for example by assuming that all persons are described by the population pharmacokinetics, then the variability in Ce⁵⁰will also be reduced. Calculating the neostigmine effect-site concentrations using population values of the pharmacokinetics (Figure 1, thick line) rather than the individual post hoc Bayesian estimates (Figure 1, thin lines) reduced the standard deviation of Ce⁵⁰in the log domain from 1.14 to 0.86. There was almost no influence on the goodness of fit from ignoring the individual effects incorporated in the post hoc Bayesian estimates. Were the “observation at a distance” hypothesis false, then calculating effect-site neostigmine concentrations from the population pharmacokinetics should increase the variability in estimates of Ce⁵⁰.

5. The t 1/2 k^eOshould be more rapid for the more proximal site of drug effect. We did not observe this in our data. T 1/2 k^eOfor the hand and foot were 98 and 114 min, respectively. However, this change produced only a trivial change in the time of peak effect in the hand and foot of 73 and 77 min, respectively. Given the wide variability in k^eOestimates (Table 2), we have given little weight to the discrepancy between our findings a more rapid t 1/2 k^eOin the hand and the prediction of an opposite result by the observation at a distance hypothesis.

Our neostigmine results suggest that CSF samples in this study represent observations at a distance. Because distance affects the magnitude of the observations, we need to find a common scale for CSF concentrations to reduce the variability of the estimates of drug potency. In finding a common scale, the pharmacodynamic modeling used the shape of the typical intrathecal concentrations over time (Figure 1, solid line) as given by the convolution of the input function (dose) and the disposition function:Equation 6that describes the concentrations, in nanograms per milliliter, after a 1-[micro sign]g bolus injection. This modeling approach reduced the variability in Ce⁵⁰, implying that individual differences in the pharmacokinetics were mostly an artifact of a scalar, which may be distance from the injection site and did not reflect true differences in drug concentrations in the CSF. Thus an important hypothesis is that CSF samples must be gathered at precisely known distances from the site of injection and the site of drug effect. If this is not possible then typical pharmacokinetic parameters in the population may be more accurate predictors of individual drug exposure than the actual measurements of concentration. This suggests the testable hypothesis that having established the shape of the concentration versus time curve for intrathecal neostigmine, under identical experimental circumstances there is little value to drawing intrathecal neostigmine concentrations in future pharmacodynamic studies. This hypothesis assumes that circumstances are unchanged (same dose, vehicle, subject position, subject population) and that the sampling itself dose not alter the CSF pharmacokinetics. If this hypothesis can be demonstrated prospectively, then it may facilitate research in the pharmacodynamics or intrathecally administered drugs by decreasing the necessary instrumentation of the participants.

Two striking observations in the current study are the sustained plateau of increased acetylcholine concentrations in CSF after intrathecal neostigmine and the lack of correlation between CSF acetylcholine concentration and analgesia. Low basal concentrations of acetylcholine in CSF are similar to those reported by others [22]and in keeping with the presence of cholinesterase activity in human CSF, [23,24]which would limit the accumulation of acetylcholine from synaptic spillover into the interstitial and CSF spaces. Although we did not measure inhibition of cholinesterase activity in the current study, it is likely that CSF neostigmine concentrations even after the lowest dose of neostigmine were adequate to significantly inhibit cholinesterases in CSF and allow a new steady state to be achieved. [25]Assuming a neostigmine concentration of 30 ng/ml is sufficient to cause 50% inhibition of cholinesterase, [20]the time until decay of neostigmine in CSF to this value was sufficiently long, ranging from 100 min for the 50 [micro sign]g dose to 800 min for the 750 [micro sign]g dose, to produce sustained increases in acetylcholine over this period. This may explain the sustained and relatively constant increase in CSF acetylcholine after neostigmine injection and the lack of relation to dose within the neostigmine dose range used.

The assumption that neostigmine causes analgesia by a spinal action is supported in the current study by the significant correlation between CSF neostigmine and analgesia in the lower extremities. The marked hysteresis (peak analgesia, 60-90 min after injection) is similar to that produced by morphine [9]and would be anticipated from neostigmine's hydrophilicity. It is assumed, based on the ability of cholinesterase inhibitors of widely varying structure to produce analgesia after intrathecal injection, and on their ability to potentiate analgesia from intrathecal injection of agents that increase spinal cholinergic activity, [6]that neostigmine causes analgesia by inhibiting acetylcholinesterase in the spinal cord dorsal horn.

Given the presumed cholinergic mechanism of neostigmine's analgesic action in the spinal cord, the lack of correlation between CSF acetylcholine concentrations and analgesia is surprising. The reasons for this lack of correlation may be complex. The earlier time to peak CSF acetylcholine concentrations (5-10 min) compared with peak analgesia suggests that the initial increase in CSF acetylcholine concentration relates to inhibition of cholinesterase activity in CSF itself, rather than at the site of analgesia. Given the widespread distribution of cholinergic blinding in the spinal cord, [1]there is likely a tonic source of acetylcholine spillover into CSF from various sources, and it may not be possible to measure a specific increase in spillover from the superficial dorsal horn against this high background of acetylcholine when CSF cholinesterases are inhibited. It would appear that in this circumstance, unlike that when spinal acetylcholine release is directly stimulated (by opioids or^2-adrenergic agonists [7]), measurement of acetylcholine in CSF reflects the poorly synaptic acetylcholine concentration in the dorsal horn.

The method of neostigmine administration in the initial 14 volunteers of this study (injection through a large-gauge spinal needle followed in 2 min by intrathecal catheter insertion and repeated sampling of CSF) does not mimic the clinical situation. We speculated that ongoing CSF losses because of the intrathecal catheter and dural rent may have limited cephalad spread of neostigmine, explaining the increased incidence of central side effects (nausea and vomiting) when neostigmine is injected in saline through a small needle without a catheter rather than with a catheter.

The addition of dextrose to local anesthetic solutions can, in conjunction with specific patient positioning, dramatically restrict the distribution of spinal anesthesia. Similarly, the addition of dextrose to neostigmine in the small needle injection part of this study avoided the protracted nausea and vomiting observed in the few volunteers who received neostigmine in saline. Compared with volunteers who received neostigmine in saline, those who received neostigmine in dextrose appeared to have similar or greater lumbar CSF neostigmine concentrations, supporting the concept of restricted cephalad spread with injection of hyperbaric solution. However, the number of volunteers studied was small, and confirmation of this hypothesis requires further testing.

Intrathecally administered neostigmine could produce side effects by local, spinal actions (lower extremity weakness, hypertension) or by central redistribution (nausea and vomiting, sedation). We measured neostigmine and acetylcholine in the lumbar intrathecal space in the current study, which may poorly reflect concentrations within the sites of action in the spinal cord or in the brain stem. For this reason, it is unclear whether the relation between CSF neostigmine concentration and the appearance of side effects reflects a causal relation or a mere dose dependency (e.g., vomiting occurred after higher doses of neostigmine than did weakness).

In summary, intrathecal neostigmine causes analgesia in humans that is correlated to dose. The CSF acetylcholine concentrations rapidly increase and plateau after intrathecal injection are complex and include an absorption inhibition of cholinesterase activity in CSF and probably does not reflect dorsal horn synaptic acetylcholine concentrations. Neostigmine pharmacokinetics in CSF after intrathecal injection are complex and include an absorption phase that likely reflects diffusion from the site of injection to the tip of the sampling catheter. Pharmacodynamic modeling demonstrated a concentration versus response relation for both foot and hand analgesia. The pharmacokinetics and pharmacodynamics observed in this study suggested that CSF samples represent “observations at a distance” in which the absolute magnitude of the concentrations are scaled by an arbitrary factor (e.g., distance of the observation site from the catheter and the site of drug effect). The pharmacodynamic model was transformed to a nonarbitrary scale by expressing it as the peak analgesic response after a bolus dose. This pharmacodynamic model would only be useful if the scalar could be known in advance or could be correlated to some physical property (e.g., the distance from the injection site to the effect site, volume of CSF), and the nature of these properties should be sought in hypothesis-driven studies. If the nature of this scalar cannot be determined, these results suggest that knowledge of CSF concentrations of a drug after intrathecal bolus administration tells us nothing about the drug effect.

Imagine injecting a drop of dye into the center of a clear cylindrical container of still liquid. The dye will gradually spread away from the injection point by the process of diffusion. The concentration of dye observed at every point in the container will be a function of the distance from the point of injection and the time of the observation. The actual relation among dye concentration, time, and distance for diffusion in two dimensions (caudad and cephalad) is given by Equation 7[26]: where C(r,t) is the concentration at a distance r (representing radius) and at time t. S is an arbitrary scaling factor (set to 10,000 in this example), D is the diffusion coefficient (set to 1 in this example), and e is the base of natural logarithms.

The spread of drug will follow the same relation as the spread of a visible dye. We can gain insight into diffusion of drug throughout the CSF by solving this Equation atfive different distances: 0, 1, 5, 7, and 11 arbitrary distance units. By definition, drug is injected at r = 0. Let us postulate two sites of drug sampling, r = 1 (close to the injection site) and r = 5 (distant from the injection site). Let us also postulate that the spinal site of analgesia for the foot is 7 distance units away from the injection site, and the spinal site of analgesia for the hand is 11 distance units away from the injection site.

(Figure 9) shows the result. Dashed lines in Figure 9show unmeasurable values, and solid lines show values that can be measured. The graphs on the left are concentration versus time, and the graphs on the right are drug effect versus time. Concentrations gathered near the injection site (r = 1) are higher than those gathered distant from the injection site (r = 5). The drug concentrations at the spinal sites of analgesia for the foot and hand, r = 7 and r = 11, respectively, are less than those at the sites of drug sampling.

To simplify this example, we will ignore the requirement that the drug enters the spinal cord to exert drug effect and will simulate the drug effect as though it instantaneously reflects the local CSF drug concentration. We can calculate the time course of drug effect by postulating a relation between CSF drug concentration at the site of drug effect and the VAS score for analgesia:Equation 8where C⁵⁰is 200, and the slope is 4 (values arbitrarily assigned). From this relation we can calculate the time course of foot (r = 7) and hand (r = 11) response, as shown in the two VAS score versus time graphs of Figure 9.

Pharmacodynamic modeling allows us to relate the drug concentrations to drug effect. The measures of concentration available in this simulation study are closer to the injection site (one and five units, in this example) than the sites of drug effect. This causes a delay between the time course of drug concentration at the sampling site and the time course of the drug effect. We modeled this delay the same way we modeled the delay with the real data from this study, using the effect-site model proposed by Sheiner et al. [15]For the purpose of this example, we implemented the effect site using the “nonparametric” approach described by Fuseau and Sheiner. [27] 

(Figure 10) shows the results of the pharmacodynamic analysis of the data from the simulation in Figure 9. The top panels show the true hand and foot concentration versus response relation, which are identical in this simulation. The middle panels show the foot and hand concentration versus response relations estimated from the VAS scores and the concentrations sampled from near the injection site (r = 1). The t 1/2 k^eOestimates for foot and hand analgesia were 26 min and 56 min, respectively. The Ce⁵⁰estimated for the analgesic response was greater than the true Ce⁵⁰of 200 because the model did not consider the dilution of drug as it diffused from the sampling site to the site of drug effect. This was more pronounced for the hand than the foot, because there is even greater dilution of drug during diffusion to the hand than to the foot. Thus the Ce⁵⁰for analgesia in the hand was greater than for the foot. Expressed another way, the model predicts that it will take more drugs to cause analgesia in the hand than in the foot, an expected result.

The lower panels in Figure 10show the concentration versus response relations estimated from the VAS scores and the concentrations sampled distant from the site of injection and closer to the site of action (r = 5). The concentrations are lower because the drug has been diluted into additional CSF in the process of diffusing to the sampling site. As a result, the estimates of Ce⁵⁰for the foot and the hand are less than when the drug was sampled close to the injection site. The t^1/2k^eOvalues for hand and foot analgesia based on samples taken at r = 5 are 4 and 25 min, respectively. The t 1/2 k^eOvalues from concentrations sampled at r = 5 are faster than those based on concentrations sampled at r = 1 because the CSF concentrations at r = 5 already exhibit much of the delay between the time course of concentration and the time course of drug effect. Thus, as the sampling site gets closer to the true site of drug effect, the need to include an effect site in the model decreases.

(Figure 11) demonstrates the relation between peak concentration and apparent potency from this simulation of a diffusion model. The numbers in parentheses are the distance of the drug sampling site, in the same arbitrary units, from the site of injection. The position of the numbers in parentheses reflect the concentration at 5 min (x axis) and the Ce⁵⁰estimated for foot analgesia (y axis). Near the site of injection, the concentrations are very high, and the estimated Ce⁵⁰is large. Further from the site of injection (r = 0), and hence closer to the site of drug effect (r = 7), the concentrations at 5 min become less and the Ce⁵⁰approaches the true value of 200.

The ability of the Equation fordiffusion in two dimensions to produce data resembling those arising from this study might suggest that we abandon polyexponential models entirely and model the pharmacokinetics using diffusion equations. We attempted this using equations for diffusion in two and three dimensions. [26]Our results, not shown, suggested that the appropriate model required inclusion of both diffusion and tissue distribution. In addition, the model required incorporation of diffusion of drug from the CSF into the spinal cord, which was not a part of the simulation. There is no closed-form Equation thatdescribes diffusion and distribution. We are developing approximate solutions based on diffusion-distribution that may better specifically incorporate the crucial role of distance in modeling these data. However, the best pharmacokinetic model for these data remains the polyexponential model described in the text.

The authors thank Carswell Jackson, M.D., for assistance in obtaining some measurements; Herbert M. Floyd, M. D., for assistance in the design of the second part of the study; and Ellen Tommasi for performing high-pressure liquid chromatography analyses.

[double vertical bar] Beal SL, Sheiner LB: NONMEM Users Guide. University of California San Francisco, NONMEM Project Group, San Francisco, 1992