Multiple model approach to uptake and distribution of halothane: the use of an analog computer

Inert gas transport in blood and tissues

This article establishes the basic mathematical models and the principles and assumptions used for inert gas transfer within body tissues-first, for a single compartment model and then for a multicompartment model. From these, and other more complex mathematical models, the transport of inert gases between lungs, blood, and other tissues is derived and compared to known experimental studies in both animals and humans. Some aspects of airway and lung transfer are particularly important to the uptake and elimination of inert gases, and these aspects of gas transport in tissues are briefly described. The most frequently used inert gases are those that are administered in anesthesia, and the specific issues relating to the uptake, transport, and elimination of these gases and vapors are dealt with in some detail showing how their transfer depends on various physical and chemical attributes, particularly their solubilities in blood and different tissues. Absorption characteristics of inert gases from within gas cavities or tissue bubbles are described, and the effects other inhaled gas mixtures have on the composition of these gas cavities are discussed. Very brief consideration is given to the effects of hyper- and hypobaric conditions on inert gas transport.

Predictive accuracy of a model of volatile anesthetic uptake

A computer program that models anesthetic uptake and distribution has been in use in our department for 20 yr as a teaching tool. New anesthesia machines that electronically measure fresh gas flow rates and vaporizer settings allowed us to assess the performance of this model during clinical anesthesia. Gas flow, vaporizer settings, and end-tidal concentrations were collected from the anesthesia machine (Datex S/5 ADU) at 10-s intervals during 30 elective anesthetics. These were entered into the uptake model. Expired anesthetic vapor concentrations were calculated and compared with actual values as measured by the patient monitor (Datex AS/3). Sevoflurane was used in 16 patients and isoflurane in 14 patients. For all patients, the median performance error was -0.24%, the median absolute performance error was 13.7%, divergence was 2.3%/h, and wobble was 3.1%. There was no significant difference between sevoflurane and isoflurane. This model predicted expired concentrations well in these patients. These results are similar to those seen when comparing calculated and actual propofol concentrations in propofol infusion systems and meet published guidelines for the accuracy of models used in target-controlled anesthesia systems. This model may be useful for predicting responses to changes in fresh gas and vapor settings.

IMPLICATIONS

We compared measured inhaled anesthetic concentrations with those predicted by a model. The method used for comparison has been used to study models of propofol administration. Our model predicts expired isoflurane and sevoflurane concentrations at least as well as common propofol models predict arterial propofol concentrations.

PKQuest: volatile solutes - application to enflurane, nitrous oxide, halothane, methoxyflurane and toluene pharmacokinetics

BACKGROUND: The application of physiologically based pharmacokinetic models (PBPK) to human studies has been limited by the lack of the detailed organ information that is required for this analysis. PKQuest is a new generic PBPK that is designed to avoid this problem by using a set of "standard human" default parameters that are applicable to most solutes. RESULTS: PKQuest is used to model the human pharmacokinetics of the volatile solutes. A "standard human" value for the lipid content of the blood and each organ (klip) was chosen. This set of klip and the oil/water partition coefficient then specifies the organ/blood partition for each organ. Using this approach, the pharmacokinetics of inert volatile solute is completely specified by just 2 parameters: the water/air and oil/water partition coefficients. The model predictions of PKQuest were in good agreement with the experimental data for the inert solutes enflurane and nitrous oxide and the metabolized solutes halothane and toluene. METHODS: The experimental data that was modeled was taken from previous publications. CONCLUSIONS: This approach greatly increases the predictive power of the PBPK. For inert volatile solutes the pharmacokinetics are determined just from the water/air and oil/water partition coefficient. Methoxyflurane cannot be modeled by this PBPK because the arterial and end tidal partial pressures are not equal (as assumed in the PBPK). This inequality results from the "washin-washout" artifact in the large airways that is established for solutes with large water/air partition coefficients.PKQuest and the worked examples are available on the web www.pkquest.com.

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.

Improving regulation of mean arterial blood pressure during anesthesia through estimates of surgery effects

In this paper, a scheme for improvement of the regulation of mean arterial blood pressure (MAP) during anesthesia based on model predictive control (MPC) and estimates of the effects of disturbances (surgical events) is proposed. A linear model for the combined effects of surgical stimulations and volatile anesthetics on MAP is derived from experimental data. Based on it the potential improvement in blood pressure regulation is evaluated via a simulation study. The simulation study shows that when information about the effect of the surgical events on MAP is utilized by the controller maximum MAP deviations can be reduced by as much as 50% even when this information is inaccurate. At worst, (highly inaccurate information) no improvement is obtained.

Noninvasive monitoring of nonshunted pulmonary capillary blood flow in the acute respiratory distress syndrome

OBJECTIVE

Noninvasive monitoring of nonshunted pulmonary capillary blood flow, using the alveolar amplitude response technique (AART) in a porcine model of the acute respiratory distress syndrome.

DESIGN

Experimental animal study.

SETTING

University center for animal experiments.

INTERVENTIONS

In 12 mechanically ventilated pigs, the nonshunted pulmonary capillary blood flow was varied by means of lung lavages and the application of positive end-expiratory pressure.

MEASUREMENTS AND MAIN RESULTS

Nonshunted pulmonary capillary blood flow was determined by AART. Cardiac output (determined by the thermodilution method) corrected for venous admixture was used for comparison (r2 varied between .58 and .94; p < .01). The trend in the development of nonshunted pulmonary capillary blood flow as measured with AART was in agreement with the trend detected by cardiac output corrected for venous admixture in 92% of all events.

CONCLUSIONS

We conclude that AART can be used to monitor changes in nonshunted pulmonary capillary blood flow in cases of acute respiratory distress syndrome noninvasively and continuously.

A tidal breathing model of the forced inspired inert gas sinewave technique

We have shown previously that it is possible to assess the cardio-respiratory function using sinusoidally oscillating inert gas forcing signals of nitrous oxide and argon (Hahn et al., 1993). This method uses an extension of a mathematical model of respiratory gas exchange introduced by Zwart et al. (1976), which assumed continuous ventilation. We investigate the effects of this assumption by developing a mathematical model using a single alveolar compartment and incorporating tidal ventilation, which must be solved using numerical methods. We compare simulated results from the tidal model with those from the continuous model, as the governing ventilatory and cardiac parameters are varied. The mathematical model is designed to be the basis of an on-line, non-invasive, cardio-respiratory measurement method, and will only be useful if the associated parameter recovery techniques are both reliable and robust. We demonstrate, in the presence of simulated measurement errors, that: (a) accurate recovery of the ventilatory parameters end-tidal volume, VA, and airways series dead-space, VD, are possible using the tidal breathing model; and (b) that a robust technique for recovery of pulmonary blood flow, QP, can be obtained using the more familiar continuous ventilation model.

Computer simulation of cerebrovascular circulation: assessment of intracranial hemodynamics during induction of anesthesia

OBJECTIVE

The purpose of this project was to develop a computer model of cerebrovascular hemodynamics interacting with a pharmacokinetic drug model to examine the effects of various stimuli on cerebral blood flow and intracranial pressure during anesthesia.

METHODS

The mathematical model of intracranial hemodynamics is a seven-compartment, constant-volume system. A series of resistance relate blood and cerebrospinal fluid fluxes to pressure gradients between compartments. Arterial, venous, and tissue compliance are also included. Autoregulation is modeled by transmural pressure-dependent, arterial-arteriolar resistance. The effect of a drug (thiopental) on cerebrovascular circulation was simulated by a variable arteriolar-capillary resistance. Thiopental concentration was predicted by a three-compartment, pharmacokinetic model. The effect site compartment was included to account for a disequilibrium between drug plasma and biophase concentrations. The model was validated by comparing simulation results with available experimental observations. The simulation program is written in VisSim dynamic simulation language for an IBM-compatible PC.

RESULTS

The model developed was used to calculate the cerebral blood flow and intracranial pressure changes that occur during the induction phase of general anesthesia. Responses to laryngoscopy and intubation were predicted for simulated patients with elevated intracranial pressure and non-autoregulated cerebral circulation. Simulation shows that the induction dose of thiopental reduces intracranial pressure up to 15%. The duration of this effect is limited to less than 3 minutes by rapid redistribution of thiopental and cerebral autoregulation. Subsequent laryngoscopy causes acute intracranial hypertension, exceeding the initial intracranial pressure. Further simulation predicts that this untoward effect can be minimized by an additional dose of thiopental administered immediately prior to intubation.

CONCLUSION

The presented simulation allows comparison of various drug administration schedules to control intracranial pressure and preserve cerebral blood flow during induction of anesthesia. The model developed can be extended to analyze more complex intraoperative events by adding new submodels.

A mathematical evaluation of the alveolar amplitude response technique

The underlying mathematical model of the forcing sinewave alveolar amplitude response technique (AART) for measuring lung volume and perfusion is investigated. Making use of numerical techniques, we are able to to evaluate the effects of several assumptions which are implicit in the original technique introduced by Zwart et al., J. Appl. Physiol. 41: 419-429, 1976, and development by several other workers. In particular we are able to show that AART is appropriate for gases of a wider range of solubilities than originally suggested, allowing it to be used with agents, such as nitrous oxide, which are more clinically acceptable. In addition, we are able to show that the effects of recirculation times are likely to be very small using figures for standard man. A least squares parameter recovery technique proves to be very robust to simulated measurement errors and is used to quantify the effects of the modelling assumptions.

Simulation of inhalational anaesthetic uptake using a lung model with charcoal

A physical lung model for simulation of volatile anaesthetic uptake is described. Two communicating water-filled chambers simulate pulmonary mechanics allowing adjustment of functional residual capacity, resistance and compliance. The uptake of the volatile anaesthetics is reproduced by pumping gas from the lung chamber through a charcoal absorber at different rates; using a second pump for a bypass an arterial to end-tidal gradient can be generated. Changes of cardiac output are simulated by adjusting pump speed and of alveolar ventilation by adapting the ventilator setting. The results are reproducible and correspond with patient studies and computer stimulation, not necessitating empirical correction factors as in a previously described oil-based lung model. The model can serve as a teaching instrument, for the comparison and testing of anaesthetic equipment and the development of feedback systems.

Cardiovascular simulation using a multiple modeling method on a digital computer--simulation of interaction between the cardiovascular system and angiotensin II

A cardiovascular system model that simulates interactive responses to drugs has been developed on a small digital computer. The overall model basically consists of three models. The first is a momentum transport model that represents relations between blood pressure and flow in the cardiovascular system. In this model, the cardiovascular system is divided into 14 components and modeled by using equivalent electrical circuits. The second is a mass transport model comprising 14 compartments corresponding to the respective components of the cardiovascular system. This model represents the distribution of the administered drug in the various cardiovascular components. The third is an interaction model that represents the relationships between the momentum and mass transport models. This model causes variations in the resistance and capacitance parameters of the momentum transport model as a function of the current drug concentrations in the appropriate compartments of the mass transport model. The capacitances representing the ventricles are varied in a time-dependent fashion to simulate the beat of the heart. Simulation is performed by using the Euler method to solve a system of 28 ordinary differential equations governing the momentum and mass transport models on a 32-bit microcomputer, a Macintosh II. The model was assessed by performing two demonstrations of the cardiovascular response to the vasopressor angiotensin II (AT II). They first examined the interaction between the cardiovascular system and AT II. The effect of AT II on the cardiovascular system was incorporated into the interaction model. Administration of AT II as a constant infusion (200 micrograms/hr) resulted in an elevation of mean arterial pressure from approximately 100 to 150 mm Hg.(ABSTRACT TRUNCATED AT 250 WORDS)

Multi-compartment model to study the effect of air-blood and blood-tissue partition coefficients on concentration-time-effect relationships

The influence of the air-blood (lambda) and blood-tissue partition coefficients of substances on the concentration-time-effect relationship E = [aCnT]b was studied by model simulation of uptake and distribution of gases. The model consisted of a lung compartment and four tissue compartments. Rat and human model parameters were obtained from physiological data, and substance-dependent variables. The observable effect E (righting reflex, mortality, etc.) for directly acting systemic agents was supposed to be related to the (arbitrarily chosen) concentration of the substance in the arterial blood or in the liver compartment. We conclude that for a directly acting systemic agent n greater than or equal to 1. If n less than 1 other mechanisms such as metabolism must be incorporated in the model which, however, should not be excluded when n greater than or equal to 1. If the observable effect is related to arterial concentration of the substance, n increases with decreasing lambda. If the liver concentration is related to the observable effect, man and rat may behave quite differently. This has major consequences for the extrapolation of animal results to the human situation in risk assessment.

A simulation of neuromuscular function and heart rate during induction, maintenance, and reversal of neuromuscular blockade

We developed a two-compartment model to simulate neuromuscular function and heart rate following the administration of four nondepolarizing neuromuscular blocking agents (atracurium, vecuronium, pancuronium, and d-tubocurarine), three neuromuscular block reversal agents (edrophonium, neostigmine, and pyridostigmine), and two anticholinergic agents (atropine and glycopyrrolate). Twitch depression, train-of-four ratio, and heart rate were modeled during fentanyl, halothane, enflurane, or isoflurane anesthesia, optionally supplemented with nitrous oxide. Simulation results, compared with published values for each drug, fell within the clinical accuracy range (onset time 6.1 +/- 3.9% [mean +/- SEM]; duration, 1.7 +/- 3.5%, 50% effective dose, 0.5 +/- 5.7%; and 95% effective dose, 2.1 +/- 1.1%). The simulation graphically demonstrates the pharmacokinetics, pharmacodynamics, and interactions between neuromuscular blocking agents, reversal agents, and anticholinergic agents. During a simulation, the need for frequent monitoring and repeated delivery of a neuromuscular blocking agent to keep neuromuscular blockade stable becomes apparent, especially with the intermediate-acting neuromuscular blocking agents. When inhalational agents are given concomitantly, the task becomes even more difficult, since potentiation changes with anesthetic uptake. Recurarization, tachycardia, or bradycardia may be seen with the simulation if an improper drug regimen is followed. Concurrent simulation of two identical patients allows comparison of different modes of administration, choice of anesthetic agents, and drug doses.

The pharmacokinetics of volatile anesthetic agent elimination: a theoretical study

The theoretical groundwork for a rate constant formulation of inhaled anesthetic elimination kinetics is discussed. In an effort to simulate recent experimental results a linear flow-limited five-compartment model was used comprising lung, vessel-rich tissue, muscle, nonvisceral fat, and an additional compartment, marrow-visceral fat whose functional existence recently has been experimentally demonstrated. Hypothetical but plausible parameters for the marrow-visceral fat compartment were used. The theoretically predicted values were in good agreement with experimental results suggesting that this model is appropriate for the elimination kinetics of agents that are not metabolized to any significant degree. Simple approximate expressions for the rate constants were also derived and were in reasonable agreement with experimental results. The model was also employed to clarify the effect of anesthetic duration on subsequent elimination kinetics.

A flight simulator for general anesthesia training

A simulator of general anesthesia is described. It consists of an integrated set of physiologic computer models and a graphics display. The model predicts many of the physiologic and pharmacodynamic changes associated with general anesthesia. It is a multiple model consisting of circulatory, respiratory, pharmacokinetic, and pharmacodynamic models and their interactions. The model can account for many pathologic states of the cardiorespiratory system plus poor renal and hepatic function. Both intravenous and inhalation agents are included. Examples of its capabilities are presented, including pharmacokinetic changes associated with thiopental administration to a hypovolemic subject, administration of oxygen in several pulmonary pathologic conditions, and a simulation of an induction using fentanyl or thiopental. The model, combined with the graphics interface, becomes a real-time simulator useful for training students and residents.

Extravascular transport in normal and tumor tissues

The transport characteristics of the normal and tumor tissue extravascular space provide the basis for the determination of the optimal dosage and schedule regimes of various pharmacological agents in detection and treatment of cancer. In order for the drug to reach the cellular space where most therapeutic action takes place, several transport steps must first occur: (1) tissue perfusion; (2) permeation across the capillary wall; (3) transport through interstitial space; and (4) transport across the cell membrane. Any of these steps including intracellular events such as metabolism can be the rate-limiting step to uptake of the drug, and these rate-limiting steps may be different in normal and tumor tissues. This review examines these transport limitations, first from an experimental point of view and then from a modeling point of view. Various types of experimental tumor models which have been used in animals to represent human tumors are discussed. Then, mathematical models of extravascular transport are discussed from the prespective of two approaches: compartmental and distributed. Compartmental models lump one or more sections of a tissue or body into a "compartment" to describe the time course of disposition of a substance. These models contain "effective" parameters which represent the entire compartment. Distributed models consider the structural and morphological aspects of the tissue to determine the transport properties of that tissue. These distributed models describe both the temporal and spatial distribution of a substance in tissues. Each of these modeling techniques is described in detail with applications for cancer detection and treatment in mind.

Physiologically based pharmacokinetic models for anticancer drugs

The rationale and history of the development of physiologically based pharmacokinetic models are briefly reviewed in this paper. The methods of model construction and the previous application of this type of model to anticancer drugs are discussed. Future research should be focused on the following areas: (1) interspecies scaling, (2) the effects of disease states on the pharmacokinetics of anticancer drugs, and (3) the applications of pharmocokinetics to the studies of growth behavior of cancer cells. The ultimate goal will be to utilize this basic information to design an optimal dosage regimen and treatment schedule for the safe and effective cancer chemotherapy of each individual patient.

Physiological perfusion model for cephalosporin antibiotics I: Model selection based on blood drug concentrations

Various cephalosporins with different degrees of protein binding were administered to human volunteers. Blood samples were collected as a function of time and were assayed for drug content by a microbiological assay. A pharmacokinetic analysis of the data was performed using a two-compartment model with and without protein binding in the central compartment and a perfusion model. Both the two-compartment model without protein binding and the physiological perfusion model adequately described the blood levels of all three cephalosporins.