INTRODUCTION...3 BACKGROUND...5. Neuromuscular Junction...5. Neuromuscular Blockade...5. Pharmacokinetics Pharmacodynamics...19 METHODS...

Transcription

1 INTRODUCTION...3 MOTIVATION...3 BACKGROUND...5 ANATOMY / MECHANISM OF ACTION...5 Neuromuscular Junction...5 Neuromuscular Blockade...5 MEASUREMENT OF MUSCLE RELAXATION TRAIN OF FOUR...7 SENSOR BACKGROUND...1 MODELING OF NMB AGENTS...13 Pharmacokinetics...13 Pharmacodynamics...19 ROCURONIUM...23 METHODS...25 EXPERIMENTAL SETUP...25 DATA ANALYSIS...28 PK Model Selection...31 Post Hoc Determination of Best-fit EC 5 and γ...33 Using Nonlinear Least Squares...33 Calculation of Patient Specific EC 5 and γ...33 RESULTS...35 TOF RATIO: PK MODEL SELECTION...35 TOF RATIO: NONLINEAR LEAST SQUARES DETERMINATION...35

2 2 OF BEST-FIT PD PARAMETERS, EC 5 AND γ...35 TOF RATIO: ADJUSTMENT OF PD PARAMETERS...35 T1 STRENGTH: PK MODEL SELECTION...39 T1 STRENGTH: NONLINEAR LEAST SQUARES DETERMINATION...39 OF BEST-FIT PD PARAMETERS, EC 5 AND γ...39 T1 STRENGTH: ADJUSTMENT OF PD PARAMETERS, EC 5 AND γ...44 DISCUSSION...48 LIMITATIONS...5 FUTURE WORK...52 APPLICATION: A DRUG DISPLAY...53 APPENDIX A...53 APPENDIX B...55 APPENDIX C...57 COMPLETE DATA SETS...57 REFERENCES...77

3 3 INTRODUCTION Motivation The purpose of relaxing a patient is to prevent unwanted muscular responses during surgery. Neuromuscular blocking agents are often used to facilitate intubation (1). One possible reaction to inadequate neuromuscular blockade would be contractions in the abdomen due to a surgical stimulus. The doctor does not want the patient s abdomen to contract while he or she has sensitive surgical instruments, such as a knife, in the area (2,3). Muscle relaxants (neuromuscular blocking agents) suppress reactions like this to allow easier care and management by healthcare professionals. A careful balance must be established so that there is adequate, but not too much paralysis (4). If too much of a neuromuscular blocking agent is administered, longer sedation times may be required to sedate the patient until muscle function returns and the patient can breathe spontaneously, allowing safe extubation (5,6). A display showing the pharmacokinetics and dynamics could be extremely beneficial to anesthesiologists in monitoring muscle relaxants (7). The more accurate the models are, the more benefit the clinician may have (7). This is because more accurate models may allow the clinician to better predict critical points in time, such as when to extubate the patient, or when and if it is necessary to administer a reversal agent or maintenance dose. This research consists of two major parts. The first part of this work is to choose the best set of models for

4 4 predicting neuromuscular blockade in this patient set. It then focuses on ways to reduce the model variability by exploring different methods of adjusting the model to each individual patient.

5 BACKGROUND Anatomy / Mechanism of Action Neuromuscular Junction To understand neuromuscular blockade we must first look at the anatomy and physiology of the neuromuscular junction. The neuromuscular junction is the interface between a motor neuron and muscle fiber. As an action potential travels down the nerve, it reaches the nerve terminal where there is an abundance of vesicles containing the neurotransmitter acetylcholine (Ach) (8,9). The action potential causes voltage-gated Ca ++ channels to open and as calcium flows into the presynaptic nerve terminal, the vesicles fuse with the cell membrane and Ach is released into the junction (8,9). Ach then binds to receptors in the postsynaptic membrane of the muscle cell. This binding allows ion channels to open, resulting in depolarization of the motor end plate and eventual muscle contraction. Figure 1 shows a basic diagram of vesicles in the nerve terminal releasing Ach, and then the Ach binding to the receptors in the muscle fiber cell (8,9). Neuromuscular Blockade The way that non-depolarizing neuromuscular blocking agents work is by competitive binding to the Ach receptors on the muscle cell. The blocking agents effectively block Ach from binding to the receptors and therefore prevent muscle contraction (Fig. 1). These blocking agents are administered intravenously and travel throughout the body to the synaptic cleft between the motor neurons and muscle fibers.

6 6 Motor Nerve Terminal Competitive Binding NMB ACh R R Motor End Plate Figure 1. A simple diagram of the neuromuscular junction. The nerve signal results in vesicular release of Ach, which then binds to receptors in the motor end plate cell. The sequence of events that follows results in muscle contraction. Neuromuscular blocking agents reduce muscular function by competitively binding to the receptors on the motor end plate, preventing Ach from triggering muscle contraction (adapted from reference 1). Various effect sites can be examined to determine the drug effect at each location. A standard effect site studied for NMB is the adductor pollicis, which causes thumb adduction. Recovery from neuromuscular blockade may be accelerated by the use of reversal agents. Drugs with anticholinesterase are effective at reversing blockade because they prevent Ach from breaking down. This allows the Ach concentrations to increase in the synaptic cleft and become more competitive for the binding sites on the muscle fibers. NMB agents may be safely and quickly reversed when the patient has regained 2-25% of their neuromuscular function (11). Caution must be taken when using a reversal agent: it must have a duration longer than the recovery time for the blocking agent. This is to ensure that when the reversal agent wears off, the NMB agent will be depleted and the

7 7 person will not become paralyzed again (4,11). This timing varies among drugs due to different activation and duration times. Reversal of NMB prevents prolonged muscle weakness after the surgery. Measurement of Muscle Relaxation Train of Four Monitoring of neuromuscular blockade and its effects are accomplished with train of four (TOF) stimulation and measurement of muscle response (12,13). TOF stimulation consists of four short pulses of current applied through surface electrodes attached to the skin, above the nerve of interest. The current is applied as a square wave with duration of.1-.3 msec at a frequency of 2 Hz, or.5 seconds between trains (Figure 2) (12). The most commonly used pulse duration is.2 msec (14-16). Pulse duration determines how much total stimulation is applied; the longer the stimulus, the stronger the resulting response. There must be a minimum of 1 seconds between trains to avoid partial tetanization, where the muscle has not fully recovered from the previous contractions. In this situation the twitches are smaller than one would expect, resulting in a measurement that shows more blockade than the actual levels (3). Current levels required for supramaximal stimulation are typically 3-6 ma (16,17). It is important to use supramaximal stimulation to calibrate the sensor and obtain a baseline/control response. This ensures that all fibers in the nerve will respond to the.1.5 sec Figure 2. TOF Stimulation pattern. Pulse duration can be from.1-.3 msec and pulses are.5 sec apart.

8 8 stimulation, which in turn minimizes fluctuation in the response (15). The minimum current required to elicit a full response is found by increasing the stimulating current until the twitch strength response reaches a maximum. The current is then increased by 2-1% to ensure that all nerve fibers and muscles bundles are stimulated (18). There are several different measurements that can be examined in response to TOF stimulation. These include the strength of the first twitch (T1 strength), ratio of fourth to first twitch (T4/T1, TOF ratio), and the number of twitch responses (TOF count) (12,13,19) When four twitches are present, the train of four ratio may be used. This is the ratio of the fourth to the first twitch strength. With time, following a bolus dose of rocuronium, the blockade levels increase and the twitch responses fade away. Depletion of Ach during a train of four stimulation pattern reduces each of the three successive twitch strengths. The more blocking agent present, the sharper this decline in twitch strength due to the competitive binding for receptor sites. Using this TOF ratio measure allows more fidelity than the TOF count in determining the degree of neuromuscular function and fade between twitches. The lower the ratio, the more relaxed a person is, because the motor function has a lower ability to respond to a given stimulus. This value tells how much fade in neuromuscular activity has occurred (Figure 3). A ratio of 1 means that the patient s neuromuscular function is normal and he/she responds with four 1% 5% Figure 3. As neuromuscular blocking agents block the Ach binding sites, successive twitch strengths decrease. This is known as fade, as muscle strength begins to fade away.

9 9 full strength twitches. At a ratio below.7, the patient is unable to breathe regularly on his/her own, and must be intubated to provide mechanical ventilation (13,2). At a TOF ratio of zero, neuromuscular function is reduced to less than 2-25% of full function. The TOF count is another measure of percentage of blocked receptors (degree of muscle blockade / relaxation). A patient with no blockade will respond with four twitches. The number of twitches roughly indicates the percent of receptors occupied and therefore degree of the blockade (Table 1) (12,22-24). As more receptors are blocked the patient will respond with three, two, one, and finally zero twitches. At zero twitches the neuromuscular blockade is in near full effect and the patient is very relaxed and muscles should not respond to a painful surgical stimulus. Different types of surgery stimulate the muscles more and require a more intense block throughout the procedure. It is clinically desirable to keep a patient at one to two twitch responses during surgery to allow for a prompt and effective reversal (21). The strength of the first twitch is very useful as well, because it exists over the full range of the TOF count, as well as throughout most of the rise in the TOF ratio. Extubation time can be predicted by the first twitch strength, as well. When the strength of the first twitch recovers to 9-95%, the patient should be able to breathe on his or her own (23). The TOF count is the most commonly used in the operating room (OR), because it is simple to measure visually. When one or more twitch responses are present, the T1 strength may be used. When all four twitches are present, the TOF ratio may be used. Both TOF ratio and T1 strength are more sensitive to changes in relaxant levels than the TOF count, but they are also more difficult to assess in the OR due to the fact that

10 1 Table 1. Extent of neuromuscular blockade distinguished by different twitch count responses. The extent of blockade is determined by the percentage of receptors that are occupied by the NMB agents, preventing ACh from binding (12,22-24). Disappearance of Twitch # T1 Depression (from a TOF stimulus) (% baseline) 1 1% 2 9% 3 8% 4-75% clinicians most commonly use visual and tactile observations rather than sensor measurements to determine NMB (25). Neuromuscular blockade can be measured at the adductor pollicis (thumb adduction), at the orbicularis oculi (laryngeal muscles in the face), or as dorsiflexion of the foot (26). Anesthesiologists most often use the laryngeal muscles because they are the easiest to access in the operating room. The facial nerve is more resistant to relaxants and often results in an underestimate of the degree of blockade, which can result in an overdose of NMB agents (27). The adductor pollicis has been established as the location of standard practice and has many PK/PD models. In addition, the adductor pollicis is a good choice because stimulation at the wrist ensures that the nerve rather than the muscle is stimulated (2). Sensor Background The most commonly used technique for measuring the TOF response is visual assessment of the twitch response (25). The clinician will apply the stimulus and watch the thumb, facial muscles, or foot movement in response to the nerve stimulator. The advantages of this method are that it is very simple to set up and is inexpensive because

11 11 there is no sensor to quantify the response. The disadvantage is that it provides very limited information to the clinician. It has been shown that experienced observers are often unable to detect fade in the TOF ratio, at ratios as low as.4, when using only tactile and visual evaluations (2,28,29). One device used for stimulation only is the Microstim Plus (by NeuroTechnology), which is an extremely portable stimulator that easily fits into a pocket. There are several different sensors available today for the TOF measurement. The sensors fall into three categories: mechanomyogram (MMG), electromyogram (EMG), and Kinemyogram (KMG). Each type of sensor has its advantages and disadvantages. MMG and EMG are typically used in research environments, whereas KMG sensors are often used clinically due to ease of use (2). The MMG measures the force of isometric muscle contraction (3,31). The thumb and index finger are held at a fixed angle with a small preloaded applied to the muscle. A force transducer measures the isometric force of the thumb and index finger in response to the stimulus. The preload and fixed position of the hand must remain constant for accurate results. The F1 Grass, Relaxometer, and Myograph 2 are examples of MMG sensors. The MMG method is the gold standard, but is not practical for the operating room environment because the arm must immobilized (32,33). The EMG is measured by placing electrodes over the muscle group and recording the electrical activity (summation of action potentials) of the muscle in response to the stimulus (3). Advantages of this method include greater flexibility and choice in muscles monitored, portability, and no immobilization required. The big disadvantage of this technique is that a small change in electrode placement can result in a big change in

12 12 the monitored response. In addition, different EMG monitors often produce different results with the same patient (2). The KMG phrase was termed by Datex-Ohmeda, although any sensor dealing with measuring the motion of the twitch can fit under this category. The first type of sensor in this category is the accelerometer. This sensor measures the acceleration of the thumb or index finger during the twitch response (Figure 4) (34,35). The principle is that if a twitch is stronger then the acceleration will be greater. The accelerometer has been shown to have a fixed relationship with the MMG measurement and is therefore considered a reliable measure of NMB. There are also a few piezoelectric sensors (the Datex mechanosensor as well as one for the ParaGraph monitor). These sensors record movement and have been shown to be clinically reliable measures of NMB, but not interchangeable with the MMG measurement (36). The Datex mechanosensor was chosen for this study because it is easy to use clinically and does not interfere with the surgery. It integrates easily into the AS/3 and S5 monitoring systems used in the OR, and also data can be easily collected through a computer. Another important advantage of the mechanosensor is that it works well both when the arms are out and when the arms are tucked next to the patient s sides during the Figure 4. The accelerometer sensor is a wafer thin piezoelectric material that is taped to the thumb. It detects thumb movement in any direction.

13 13 surgery. The mechanosensor, consists of a piezoelectric strip placed between the thumb and index finger. The plastic strip that fits between the thumb and index finger applies a small fixed pretension on the adductor pollicis, although the thumb and finger are not fixed in place as with the MMG. Movement of the adductor pollicis is then recorded by the bending of the piezoelectric strip during a twitch response. (As the strip bends, it changes resistance. Over time this captures the acceleration of the muscle, which can then be related to force (36).) Modeling of NMB Agents Pharmacokinetic and pharmacodynamic models are used to predict the effects of the blocking agents. Pharmacokinetic models are those that predict the concentration of the drug in the patient s bloodstream over time, and the pharmacodynamic models take this drug concentration and predict an effect on the patient at any given concentration. Pharmacokinetics Pharmacokinetics are often described using multicompartment models. Compartment models simulate the basic kinetics of drug absorption, distribution, and elimination (37). The central compartment represents the plasma compartment, with the most rapid change in concentrations. It is assumed that all drug elimination occurs through this central compartment. It is also assumed that there is uniform and instant distribution of the drug. A three-compartment model takes into account transfer of the drug from the blood into the muscle and fat tissue compartments (Figure 5). First order rate transfer constants describe the behavior of the drug as it distributes between these

14 14 Figure 5. Three-compartment model. Drug is transferred between the main plasma compartment and two tissue compartments, one at a fast rate (muscle tissues) and the other at a slower rate (deep fatty tissues). The effect compartment represents the neuromuscular junction at the adductor pollicis, and there is a negligible amount of drug transferred from the central compartment to the effect site (38,39). compartments and the central compartment. The elimination rate constant describes the drug leaving the body and is shown as k 1 in Figure 5. The effect compartment relates the amount of drug in the blood with that at the effect site, based on the elimination rate, k 14 (37,38). Mathematically, the change in drug concentration over any period of time is the amount of drug entering the compartment minus the amount of drug leaving the compartment, divided by the volume of the compartment (37). Using that, Equations 1-5 apply: da dt p = k A + k A k A k A k A [1] 21 m da dt da dt m f 31 f 12 p 12 p 21 m 13 p 1 p = k A k A [2] = k A k A [3] 13 p 31 f

15 15 daeff = k 14 Ap k eo Aeff dt [4] where DrugAmount Concentrat ion = CompartmentVolume [5] A is the drug amount in each compartment (eff is at the effect site (4), p is the plasma compartment (1), m is the muscle compartment (2), and f is the fat compartment (3)). The k represents the first order rate constants determining the amount of drug transferred to and from each compartment. These equations are all differentiated with respect to time, t. A visual representation of the model and the constants is shown in Figure 5. Combining and rearranging these equations, Equations 6-13 shows the solution for the drug concentration at the effect site, C eff, α, β, and γ may be calculated using Steven Shafer s Convert.xls spreadsheet available through the Stanford Anesthesia website, or by solving Equations αt ( k α)( k α) e ( k β)( k β) βt Dose*k e A e (t) = Ve keo α keo β [6] γt δt ( k )( ) ( )( ) 21 γ k31 γ e k21 δ k31 δ e keo γ keo δ If we assume steady state: eo e = 14 1 [7] Vekeo Vekeo k 14 = = V1 Vc [8] Then Equation 6 turns into: αt βt Dose*k ( )( ) ( )( ) eo k21 α k31 α e k21 β k31 β e A e (t) = Vc keo α keo β [9] γt δt ( k )( ) ( )( ) 21 γ k31 γ e k 21 δ k31 δ e keo γ k eo δ where α β + γ + δ = k + k + k + k + k + k + [1] k eo

16 αβ + γδ = αγ + γδ + βγ + βδ + αβγ αβδ ( k1 + k13 + k14 + k31 ) + k31( k1 + k12 14 ) k eo ( k1 + k12 + k13 + k31 + k21) + = k 21k31 ( k1 + k14 ) + keo k21( k1 + k13 + k31 ) + k k ( k k eo + + ) k + 21 k + 2 k = k eo k 21k31k1 16 [11] [12] αγδ + βγδ + αβγδ [13] The solution to this equation is implemented in Equations (39). Calculate the total amount of drug entering/leaving each compartment at time t: k 14 =.1*k eo [14] k 41 = k eo [15] a 1 = da 2 *k 21 + da 3 *k 31 + da 4 *k 41 - da 1 *k 1 + DrugAmount [16] a 2 = da 1 *k 12 - da 2 *k 21 [17] a 3 = da 1 *k 13 - da 3 *k 31 [18] a 4 = da 1 *k 14 - da 4 *k 41 [19] Add the amount of drug to each compartment over the course of the time step: da 1 = da 1 + a 1 * t [2] da 2 = da 2 + a 2 * t [21] da 3 = da 3 + a 3 * t [22] da 4 = da 4 + a 4 * t [23] da4 C eff (nt) = V [24] c where DrugAmount = amount of drug administered to the patient at time t a n = amount of drug added to compartment n at time t da n = total drug amount in compartment n at time t t = the time step used in the simulation V c = volume of the central (plasma) compartment nt = time step n, with T = t

17 17 Note the assumption that the amount of drug entering and exiting the effect compartment (with rate constants k 14 and k 41 ) is negligible. The other assumption is that the drug distributes into the plasma compartment instantaneously as it is administered. The three main compartments consist of the bloodstream, muscle tissues, and deep fatty tissues. The effect site is the negligible compartment, representing the neuromuscular junction at the adductor pollicis. Four different pharmacokinetic models for rocuronium were considered in this study; the Plaud two-compartment model (plasma and general tissue compartments), and the Cooper, Szenohradszky, and Wierda three-compartment models. Table 2 summarizes these experiments. The parameters of each model are summarized in Table 3 (4-44). The k eo values (Table 4) were calculated using Minto s method, which accounts for differences inherent in combining PK and PD models from separate studies (45). The idea behind Minto s method is that, because both studies use the same drug, the time to peak effect in each study should be the same. The time to peak effect in the kinetic study is therefore used to calculate the k eo, rather than the naïve method of using the k eo derived in the PD study. Note that because the Plaud study was a combined PK/PD study, the original k eo value was used. One limitation to the calculated k eo values is that the maximum onset time was used rather than the time to peak effect. This affects k eo because the measured effect saturates such that the time to maximum effect is earlier than when the peak effect would occur, resulting in a larger k eo value. This also has the effect of shifting the EC 5 prediction such that it appears higher than the actual value.

18 18 Table 2. Summary of pharmacokinetic models considered in this study. Model Name # Patients # Compartments Anesthesia Administered Delivery Method (rocuronium) Surgery Type Plaud 8 2 propofol, alfentanil infusion at 1 µg/(kg*min) over 5 minutes elective, non hemorrhagic Cooper 9 3 fentanyl, thiopentone, isoflurane, nitrous oxide bolus (.6 mg/kg) elective opthalmic or dental Szenohradszky 1 3 midazolam, thiopental, isoflurane, nitrous oxide 6 µg/kg rapid IV injection elective, minor Wierda 8 3 halothane, nitrous oxide bolus (.45 mg/kg) then infusion to maintain specific levels of T1 control (steady states) elective

19 19 Table 3. Summary of the model parameters of each pharmacokinetic model used in the study. Plaud Wierda Cooper Szenohradszky v c (*mass) (L) k 1 (min -1 ) k 12 (min -1 ) k 13 (min -1 ) k 21 (min -1 ) k 31 (min -1 ) Table 4. K eo values calculated for each PK model using Minto s method to compensate for separate PK/PD studies. (The Plaud k eo value is from the original PK/PD study.) Plaud Wierda Cooper Szenohradszky k eo (min -1 ) Pharmacodynamics The pharmacodynamic model converts the drug concentration levels into an effect (46). The Hill equation describes this sigmoidal relationship and can be used to calculate the strength of the first twitch (from the effect site drug concentration, at the hand) (4). From this information the train of four ratio and first twitch response strength can be estimated. Equation 25 describes the general Hill Equation (37): γ Ceff Effect = E + ( Emax E ) γ γ [25] EC + C 5 eff where E max is the maximum effect, E is the effect at no drug concentration, EC 5 is the effect site concentration at which 5% of the effect is produced, and C eff is the effect site

20 2 concentration of the drug. See Figure 6 and 7 for a graphical example. Change in EC 5 results in a shift in the curve, whereas change in gamma (γ) results in a different slope of the curve. In this study, the effects are depression of T1 strength and TOF ratio. When no drug is present in the body, the effect (E ) is 1% T1 strength, and a TOF ratio of 1. (four full strength twitches). The maximum possible effect is full depression of all four twitches. This effect (E max ) is % of the baseline T1 strength, and a TOF ratio of. Plugging these numbers into Equation 25 results in Equations 26 and 27: γ Ceff T1 strength = 1 ( 1) γ γ [26] EC + C TOF ratio 5 eff γ C eff 1 γ [27] EC5 + Ceff = γ Adding Plaud s PD parameters of EC 5 = 823 ng/ml and γ = 4.79, the resulting pharmacodynamic equations are shown in Equations 28-29: 4.79 Ceff T1strength = 1 ( 1) [28] C eff 4.79 = C eff TOFratio [29] C 79 eff where C eff is either measured or calculated from the PK models using Equations

21 21 C eff (ng/ml) Figure 6. The Hill equation describes the relationship between the effect site concentration and the effect of the drug. This sigmoidal relationship is shown graphically.

22 22 Ceff (ug/ml) Figure 7. A graphical example of the how Hill equation is used. The top graph shows the effect site rocuronium concentration predicted from the kinetics. The bottom graph shows the result of the Hill equation, using the drug concentration from the top graph to predict the T1 strength for a given patient. At each time, the modeled effect site concentration corresponds to a modeled effect (T1 strength).

23 23 The pharmacodynamic model used in this study is the Plaud model, with parameters of γ = 4.79 and EC 5 = 823 ng/ml (4). Plaud measured effect-site concentrations (by collecting blood samples and using HPLC methods to find the concentration) as well as the T1 strength using TOF stimulation. Plaud s study was performed on 8 patients using IV infusions to hold the plasma concentrations constant at varying levels, and then to measure the effect at each concentration. Anesthesia used was propofol and alfentanyl, and the TOF measurement at the hand was accomplished using a force-transducer sensor (MMG). Most models in the literature refer to the T1 strength even though it is not often measured in the OR. There are no well-known models to predict the TOF count. Instead, a general relationship between the T1 strength and the TOF count has been established (47). Rocuronium Rocuronium is the neuromuscular blocking agent used in this study. Rocuronium is commonly used in the operating room because it has a rapid onset (6-9 seconds) as well as an intermediate duration of action (6-7 minutes) (48,49). This means that it acts quickly enough for intubation, and it is acts long enough so that one bolus may be enough to last for the duration of the surgery. The plasma concentration (PK) behavior is best described as a three compartment open model, although the Plaud PD values used widely are based off of his two compartment kinetic model and results. It is eliminated via both hepatic and renal pathways (42). It has been found that repetitive maintenance doses do not result in a clinically significant accumulation of effects. Rocuronium is reversible with

24 24 anticholinesterase agents after it reaches a T1 strength of 25% of the baseline value. Neostigmine is a common reversal agent for rocuronium (5,51). Inhalational agents such as nitrous oxide and isoflurane are known to enhance the neuromuscular blockade effects of rocuronium, which is why Total IV Anesthetics (TIVAs) were used in this study.

25 METHODS This study was approved by the hospital s Institutional Review Board. Informed written consent was obtained from each patient. The population contained only patients scheduled for laparoscopic surgical procedures (gall bladder removals/cholecystectomies, fundoplications/gastroesophogeal refluxes/acid refluxes/lap-nissens and hernias). Patients with known neuromuscular disorders were excluded from the study. All cases were total intravenous anesthetics (TIVAs) administered through a dorsal vein in the hand. Propofol and remifentanyl were the primary anesthetics used for sedation and analgesia throughout the surgery. Two research nurses and two biomedical engineering graduate students collected the data throughout the case. They recorded the anesthesiologist s assessment of events throughout the surgery. Data collected included rocuronium and neostigmine doses and the times in which they were administered. The neuromuscular data collected were the palm temperature, TOF count, TOF ratio, T1 strength, and the amplitude of each twitch. The TOF data were measured in 2 second increments, using the Datex-Ohmeda Mechanosensor and NMT module (Datex-Ohmeda AS/3 and S5 monitors, Helsinke, Finland). Experimental Setup At the beginning of each case the NMT module was plugged into the Datex. A Toshiba Satellite Pro Pentium III laptop running Windows XP was connected to each

26 26 device. The Datex monitor was connected directly through the serial port. Rugloop was used to collect all information from the Datex monitor. The infusion pumps were positioned near the head of the patient and boluses were given through the IV line. During preparation for surgery in the operating room, the Datex Mechanosensor was placed on the patient s thumb and index finger and taped in place (tape was applied between the thumb and index finger to prevent the sensor from moving during surgery, see Figure 8). The sensor was placed on the most convenient arm. Preference was given to the arm without the IV (the sensor was placed on the right arm in most cases). The arm was then wiped with an alcohol pad to remove oil from the skin and allow better electrode performance. A Smiths STS-4 disposable skin temperature sensor was placed on the palm and connected to the Datex monitor. As soon as the patient lost consciousness, the electrodes were placed on the wrist, above the ulnar nerve. Time permitting, small stimulations from the Microstim Plus were used (Figure 9) to help locate the ulnar nerve at the arm and determine the optimal position for electrode placement. The Datex monitor automatically set the supramaximal current by delivering single twitch stimulations starting at 4 ma, and then increasing current levels in 5 ma increments until the twitch response reached a maximum strength. Then the current was automatically increased 2% for supramaximal current. This maximum twitch response was the baseline value for the T1 strength. In the cases that a maximum response was not found, the stimulator current was set to deliver 7 ma, and the twitch response was automatically set as the baseline the T1 strength. Train-of-four response was measured

27 27 Figure 8. Train of four stimulator and sensor. Figure 9. Microstim Plus was used to find the ulnar nerve location for effective electrode placement.

28 28 every 2 seconds using a stimulation pulse duration of 1 µsec. We recorded the times when recovery of 9% T1 baseline strength and.7 TOF ratio were reached. The sensor and electrodes were removed before the patient regained consciousness. Data Analysis Patient details are summarized in Table 5. Patient data were excluded from analysis due to the following criteria: the NMB agent succinylcholine was administered, data were noisy, such that oscillations greater than 3% signal strength were recorded throughout the case, the T1 strength did not recover to at least 9% of baseline before reversal, and if the TOF ratio did not recover to.7 before reversal. One patient was excluded due to a communication problem with the computer and the equipment. Table 6 summarizes the data excluded from analysis. There were 7-8 patients whose maximum T1 response (baseline) shifted during surgery. In these patients, the final T1 response was used as the baseline value. Six patients met the inclusion criteria for the T1 strength, and 6 patients met the inclusion criteria for the TOF ratio. The acceptable patients were then renumbered (1-6) for the analysis. The data analysis focused on the recovery phase only of each patient s neuromuscular function. Figure 1 shows an example of how the data were clipped for this analysis. In order to focus on the recovery phase, the data set was clipped after the onset, or maximum effect, occurred. Data were also clipped before administration of reversal agent, so that recovery results of only rocuronium were studied. In the cases where maintenance doses of rocuronium were delivered, the data were clipped before the maintenance dose was administered.

29 29 Table 5. Subject details: age, weight, height, gender, and surgery type. The grayed subjects were those that did not meet the inclusion criteria for either T1 strength or TOF ratio. Subject # Age Weight Height Gender Surgery Type (years) (kg) (cm) (all Laparoscopic) Male Hernia - Ventral Female Nissen Fundoplication Female Cholecystectomy w/ Cholangiograms Male Cholecystectomy w/ Cholangiograms Female Cholecystectomy Female Cholecystectomy * Female Cholecystectomy w/ Cholangiograms Female Cholecystectomy w/ Cholangiograms Female Cholecystectomy Male Hernia - Inguinal Male Hernia - Bilateral ** Female Cholecystectomy Male Nissen Fundoplication Male Nissen Fundoplication Male Hernia - Inguinal Male Hernia - Inguinal Male Hernia - Ventral Male Cholecystectomy Female Cholecystectomy Female Cholecystectomy Mean M / 1 F St. Dev * used in TOF analysis only ** used in T1 strength analysis only Table 6. Summary of data excluded from analysis for both T1 strength and TOF ratio # Patients Excluded Exclusion Criteria T1 Strength TOF Ratio Succinylcholine Administered 2 2 Noise 1 2 Insufficient recovery 1 9 Computer Communication Problem 1 1

30 3 T1 Strength vs. Time T1 Strength T1 Strength Data Predicted Response Clipped Data Points for calculating new EC5 Points for calculating new gamma 2 T1' T Time (minutes) Figure 1. The shaded regions of the figure show where the data was clipped. (Notice the sharp rise in T1 due to neostigmine administration near the end of the data set.) The unshaded region is the recovery portion of the data used for analysis. The dashed line represents the model predicted response. The difference between the points on the modeled and measured curves T1 -T1 is used in calculating the RMSE. The points highlighted as dots are the three points used to calculate a new EC 5 value. The points highlighted with circles show which points were used to calculate a new gamma value.

31 31 PK Model Selection The first step in the analysis was to choose the PK-PD model combination that best fit the data. Plaud s PD model (EC 5 = 823 ng/ml γ = 4.79) was combined with each of the Cooper, Plaud, Szenohradszky, and Wierda PK models (PK constants summarized in Tables 7 and 8). K eo values were calculated using an improved method from Minto et al. This method uses the time to peak effect, t peak, from each original kinetic study to correct for differences between the pharmacokinetic and pharmacodynamic models created in different studies. The idea behind this is that the time to peak effect is the same in all studies for a particular drug. The time to peak effect is then used with the kinetic data to calculate an improved k eo from the derivative of the C eff equation (Equation 4) (45). The next step was to choose the model that produced the least difference between the modeled/predicted, T1, and the measured, T1, single twitch strength following the TOF stimulus (Figure 1). The Root Mean Squared Error (RMSE) was calculated for each model and subject using Equation 3. At each point in time, the difference between these values is designated as T1-T1. (The datasets used in this analysis were approximately 6 minutes long, with 3 measurements collected each minute, resulting in an approximate dataset length of 18 points.) Equation 3 is used to calculate the RMSE: T1 = measured first twitch strength (% baseline) T1 = model predicted first twitch strength n = a specific datum point in time (one every 2 seconds throughout the surgery) N = number of data points

32 32 Table 7. Summary of the model parameters of each pharmacokinetic model used in the study. Plaud Wierda Cooper Szenohradszky v c (*mass) (L) k 1 (min -1 ) k 12 (min -1 ) k 13 (min -1 ) k 21 (min -1 ) k 31 (min -1 ) Table 8. K eo values used with each PK model, calculated using Minto s method. (The Plaud k eo is from the original Plaud PK/PD study.) Plaud Wierda Cooper Szenohradszky k eo (min -1 )

33 33 RMSE N n= 1 = ( T1(n) - T1'(n) ) N 2 [3] Post Hoc Determination of Best-fit EC 5 and γ Using Nonlinear Least Squares A nonlinear least squares method was performed in MATLAB to find the best-fit pharmacodynamic parameters, EC 5 and γ, which predict the effect (T1 strength or TOF ratio) using the Hill equation, Equation 31. (C eff was calculated using the Cooper PK model, Equations with coefficients from Table 6. The final equation is summarized as Equation 32). The best fit RMSE was then calculated using Equation 33. The RMSE was also calculated for each patient using the average of the best-fit PD parameters, γ and EC 5. Effect = E + eff ( Emax E ) γ γ EC C 5 γ + C eff [31] where C eff (t) =.1*((da 4 )/(V ceff )) [32] RMSE N n= 1 = ( T1(n) - T1'(n) ) N 2 [33] Calculation of Patient Specific EC 5 and γ When the T1 twitch strength recovered to 2% of baseline, or the TOF ratio recovered to.2, a new EC 5 was calculated using Equation 34 and Equation 35, derived in Appendix A. (We calculated C eff using PK coefficients from Table 6 and Equations ) The EC 5 was calculated and averaged over three data points (the first minute above the recovery threshold). This averaging method was used to reduce the variability, as well

34 34 as to reduce the influence of possible spikes in the data when calculating the new EC 5 value, hopefully resulting in a more accurate prediction. ( T 1strength ) ( T1strength 1) 1/ γ EC5 = C [34] eff ( TOFratio ) ( TOFratio ) 1/ γ 5 1 EC = C [35] eff Adjustment of γ was also explored. The new γ was calculated using a rearranged Hill equation (Equation 36 and Equation 37, derived in Appendix B). γ was calculated using the newly adjusted EC 5 value at each point between 2-3% recovery of baseline T1 strength, or recovery of.2-.3 TOF ratio. The gammas calculated were averaged to find a new, patient specific γ. ( T 1strength) ( T1strength 1) Ln γ = [36] EC5 Ln C eff ( TOFratio ) ( TOFratio 1) Ln γ = [37] EC5 Ln C eff

35 RESULTS TOF Ratio: PK Model Selection Figure 11 (a) shows C eff as predicted by the Plaud two-compartment model and the Wierda, Cooper, and Szenohradszky three-compartment kinetic models. Figure 11 (b) shows TOF ratio as predicted using the standard Plaud PD values (EC 5 = 823 ng/ml, γ = 4.79). The RMSE values for all four models in each of the six patients are summarized in Table 9. The Wierda model provides the lowest average RMSE value. The Wierda three compartment pharmacokinetic model was used to calculate the effect site concentration for all data analysis related to the TOF ratio. TOF Ratio: Nonlinear Least Squares Determination of Best-fit PD Parameters, EC 5 and γ Table 1 shows the γ and EC 5 parameter values for each subject, which resulted in the lowest RMSE when the Wierda PK model was used to calculate C eff. The average EC 5 and γ are then used to show the RMSE resulting from this patient population, shown in Table 11. TOF Ratio: Adjustment of PD Parameters Table 12 shows the RMSE values for each patient, when EC 5 was adjusted during recovery. The EC 5 value was adjusted at recovery ratio of.2. Table 13 shows

36 36 Ceff vs. Time Ceff Ceff (ug/ml) (ug/l) Plaud Wierda Cooper Szenohradszky (a) TOF Ratio Time (minutes) Plaud Wierda Cooper Szenohradszky Data TOF Ratio Time (minutes) (b) Figure 11. A comparison of the Plaud two-compartment model and three other three-compartment kinetic models; Wierda, Cooper, and Szenohradszky. (a) Predicted effect site concentrations, C eff for each PK model. (b) Predicted TOF Ratio, using the Plaud PD values (EC 5 = 823 ng/ml, γ = 4.79). Table 9. RMSE between the measured and the predicted TOF Ratio, using 4 PK models and Plaud s EC 5 = 823 ng/ml, γ = RMSE Patient # Plaud Wierda Cooper Szenohradszky Average Std. Dev

37 37 Table 1. Gamma and EC 5 values that provide the lowest RMSE for TOF ratio data in each subject. Units for EC 5 are ng/ml. Post hoc Nonlinear Least Squares Calculations of γ and EC 5 Subject EC 5 γ RMSE Average Std. Dev Table 11. Average gamma and EC 5 values and the resulting RMSE between measured and predicted TOF ratio in each subject. EC 5 units are ng/ml. Average Population calculations Subject EC5 γ RMSE Average 15.9 Std. Dev. 7.

38 38 Table 12. EC 5 was calculated/adjusted at.2 TOF ratio recovery. The resulting RMSE is shown. EC 5 units are ng/ml. Individual, Real time EC 5 calculations (post hoc simulation) Subject EC 5 γ RMSE Average Std. Dev Table 13. γ was calculated from.2-.3 TOF ratio recovery. RMSEs from the data and model with newly calculated EC 5 and γ are shown. EC 5 units are ng/ml. Individual, Real time EC 5 and γ calculations (post hoc simulation) Subject EC 5 γ RMSE Average Std. Dev

39 39 the RMSE results when γ was also adjusted, at a recovery ratio of At a TOF ratio recovery of.3, the EC 5 was adjusted again. Table 14 shows the RMSE values resulting between the data, adjusted γ, and EC 5 adjusted at TOF =.3. The times to.7 TOF ratio recovery, measured and predicted (before and after model adjustments), are shown in Tables The resulting time differences in estimating extubation (TOF =.7) are also shown. Adjusting the EC 5 value at.3 recovery (Table 18) results in a closer prediction of extubation time than the EC 5 adjustment at.2 recovery (2.8 rather than 3.5 minutes). T1 Strength: PK Model Selection The RMSE values for all four kinetic models, combined with the Plaud dynamic model, are summarized in Table 19. The Cooper model provides the best estimation as determined by the lowest RMSE value of 14.1 (± 6.7), which allows a more accurate prediction of the effect of rocuronium. The Cooper three compartment pharmacokinetic model was used to calculate the effect site concentration for all further data analysis. T1 Strength: Nonlinear Least Squares Determination of Best-fit PD Parameters, EC 5 and γ When using Cooper s PK model, we found that a γ of 7. ± 3.8 and an EC 5 of 829 ± 162 ng/ml provided the best fit between measured and model predicted T1 strength. The best possible RMSE for this dataset and model is 4.7, found using the optimum γ and EC 5 for each patient (Table 2). The results for this study are compared with Plaud s optimum values in Table 21.

40 Table 14. γ was calculated from.2-.3 recovery. EC 5 was calculated again at a recovery of.3 TOF ratio. RMSEs from the newly calculated EC 5 and γ are shown. EC 5 units are ng/ml. 4 Individual, Real time EC5 and γ calculations (post hoc simulation) Subject Adjusted EC 5 Adjusted γ RMSE Average Std. Dev Table 15. The time to recovery of.7 TOF ratio, in minutes, using the average population γ and EC 5. The difference between the measured and predicted times are also shown. EC 5 units are ng/ml. Time to TOF Ratio Recovery of.7 (in minutes) (using average population EC 5 and γ) Predicted Subject EC 5 γ Measured Time Time Difference Average 8.3 Std. Dev. 4.2

41 41 Table 16. The time to recovery of.7 TOF ratio, in minutes, using the average population γ and EC 5 adjusted at recovery of.2 TOF ratio. The difference between the measured and predicted times are also shown, in minutes. EC 5 units are ng/ml. Subject Time to TOF Ratio Recovery of.7 (in minutes) (with EC 5 calculations) Adjusted EC5 γ Measured Time Predicted Time Difference Average 3.5 Std. Dev. 2.5 Table 17. The time to recovery of.7 TOF ratio, in minutes, using γ calculated from.2-.3 TOF ratio recovery, and EC 5 adjusted at recovery of.2 TOF ratio. The difference between the measured and predicted times are also shown, in minutes. EC 5 units are ng/ml. Time to TOF Ratio Recovery of.7 (in minutes) (with EC 5 and γ calculations) Subject Adjusted EC5 Adjusted γ Measured Time Predicted Time Difference Average 3.4 Std. Dev. 2.7

42 Table 18. The time to recovery of.7 TOF ratio, in minutes, using γ calculated from.2-.3 TOF ratio recovery, and EC 5 adjusted at recovery of.3 TOF ratio. The difference between the measured and predicted times are also shown, in minutes. EC 5 units are ng/ml. 42 Subject Time to TOF Ratio Recovery of.7 (in minutes) (with EC 5 and γ calculations) Adjusted EC5 Adjusted γ Measured Time Predicted Time Difference Average 2.6 Std. Dev. 1.3 Table 19. RMSE between the data and the predicted T1 strength, using each PK model. The PD model used was Plaud s (EC 5 = 823 ng/ml, γ = 4.79). RMSE Patient # Plaud Wierda Cooper Szenohradszky Average Std. Dev

43 43 Table 2. Optimized γ and EC 5 values to best fit the T1 strength data for each subject. EC 5 units are ng/ml. Post hoc Nonlinear Least Squares Calculations of γ and EC 5 Patient # EC 5 Gamma RMSE Average Std. Dev Table 21. Summary of the PD parameters found from the Plaud and Mills studies. EC 5 units are ng/ml. PD Values Summarized Plaud Mills γ 4.8 (±1.7) 7 (±3.8) EC (±157) 829 (±162)

44 44 Using the average EC 5 value from this study, the average RMSE was shown in Table 22. T1 Strength: Adjustment of PD Parameters, EC 5 and γ Tables 23 and 24 show the adjusted PD parameters for each patient, adjusted during recovery. The EC 5 value was adjusted at 2% recovery. The γ value was adjusted at 2-3% recovery. The RMSE values resulting from the adjusted parameters and the measured data are shown. Extubation times measured, and predicted before and after model adjustments are shown in Tables The adjusted, patient specific EC 5 and γ resulted in a lower RMSE value than the average population EC 5 and γ, signifying a better overall fit to the data than before model adjustment. This was significant for adjustments in the T1 strength; p =.5 from EC 5 adjusted at T1 = 2%, p =.9 from γ adjusted at T1 = 2-3%. Differences in RMSE were not significant for the first 2 adjustments of the TOF ratio prediction; p =.7 from EC 5 adjusted at the TOF ratio =.2, and p =.9 from γ adjusted at the TOF ratio = Difference in RMSE was significant for the final TOF ratio adjustment of EC 5 at.2, p =.3.

45 45 Table 22. RMSE values of the data with the predictions using Plaud s average values for EC 5 and γ. EC 5 units are ng/ml. Average Population calculations Subject EC 5 γ RMSE Average 17.4 Std. Dev. 7.2 Table 23. RMSE resulting from the adjustment of EC 5 at 2% recovery. The newly calculated EC 5 values are also shown. EC 5 units are ng/ml. Individual, Real time EC 5 calculations (post hoc simulation) Subject EC5 γ RMSE Average Std. Dev

46 46 Table 24. Adjusted PD parameters. EC5 was calculated at 2% recovery. Gamma was calculated at 2-3% recovery. EC 5 units are ng/ml. Individual, Real time EC 5 and γ calculations (post hoc simulation) Subject EC5 γ RMSE Average Std. Dev Table 25. Extubation time differences, in minutes. Shows how close the predictions were to the measured extubation time (7% recovery), using average population EC 5 and γ. EC 5 units are ng/ml. Time to 9% T1 Recovery (in minutes) (using average population EC 5 and γ) Subject EC5 γ Measured Time Predicted Time Difference Average 16.1 Std. Dev. 11.4