Simulation in Medical Education: Focus on Anesthesiology
D. John Doyle, MD PhD FRCPC
This article presents an overview of the application of computer-based simulation to medicine, focusing on anesthesiology and critical care medicine, including discussions on physiological and pharmacological simulation, virtual experiments, software only clinical simulators, and specialized hardware/software simulators for specialty teaching, as in airway management and in regional anesthesia. While many successes in using simulation in medical education can be identified, because the field is quite young, much remains to be done to demonstrate the scientific and clinical utility of simulation technology, especially in the context of the Fitzpatrick model of program evaluation.
Simulation refers to the artificial (and almost always simplified) representation of a complex real-world process with sufficient fidelity to achieve a particular goal, such as in training or performance testing. Simulation has likely been a part of human activity since early times. Simulation has long been important in a number of kinds of technical or professional training. For instance, the rehearsal of animal hunting activities and of warfare was a likely occasion for simulating the behavior of prey or enemy warriors. Simulation using technology probably dates back to Roman times or earlier. Good and Gravenstein1 point to the Roman quintain (a post or an object mounted on a post, used as a target in tilting exercises) as a device that crudely but effectively simulated the behavior of an opponent during sword fighting. If the swordsman did not duck at the appropriate time after striking a blow, he would be hit by the quintain.
In modern times, preparation for war has been a powerful stimulus to the development of simulation technologies especially for aviation. Although some aircraft simulators were built as early as the pre World War I era, none of these early “static” models could provide the proper “feel” of the aircraft because they could not dynamically reproduce its behavior.2 However, in 1930 Edwin Link filed a patent for a pneumatically driven aircraft simulator that heavily influenced the development of simulation in aviation. The "Link Trainer", as it was known, soon became a standard tool for flight training before World War II; the onset of the war greatly accelerated its use as well as the further development of flight simulation technology in general.
In the 1950s, advances in electronic technology lead to electronic controls replacing pneumatic systems. With the advent of computer technology the aircraft simulator achieved the beginnings of its current form in the 1970’s, but it has been continuously refined, as computer technology has advanced. At the moment these simulators are so realistic that pilots are routinely certified to fly new aircraft (i.e., obtain a “type rating”) without actually having ever entered the real aircraft!
Another area where simulators have been used extensively is in nuclear power plants. One of the key factors that determines the safety of a nuclear power plant is the training and technical knowledge of its reactor. Simulators provide training tools for reactor operators in normal operations, as well as in training for responding to emergency situations.3
Computer-Based Simulation in Medical Education
In recent years simulators have seen increasing use in training health care providers. Although the origins of computer simulation in medicine date back some four decades4, it is only now, with the advent of inexpensive computers, that this field has really taken off.
This paper is concerned with presenting an overview of the issues in the use of simulators in medicine (see Table 1), with a particular focus on simulation anesthesiology and critical care medicine. Topics discussed include physiological and pharmacological simulation, anesthesia and critical care simulators, as well as simulation in trauma, airway management and regional anesthesia. In all cases, the simulations are computer-based. Simulation technology based on computers is just one of many applications of computers in medicine (see Table 2).
Computer-based simulators used in medical education fall into four general categories: (1) Screen-based text simulators, (2) Screen-based graphical simulators, (3) Mannequin-based simulators, and (4) Virtual reality trainers.
Screen-based text simulators create verbal scenarios in which the user picks one of several responses and, based on the chosen response, a new text scenario is produced. For instance, in a scenario involving a patient presenting with a severe headache, the user may be offered options such as prescribing an analgesic such as Tylenol or getting a CT-scan of the head. Based on the user’s choice, a new narrative is then generated and more management choices are offered. Being purely text-based, screen-based text simulators are relatively simple to construct and require little memory, making them popular in early medical simulation efforts. However, since they are lacking in graphical elements, they are rarely used today.
Screen-based graphical simulators such as 'Gasman' and 'Body'5,6 aim to recreate elements of reality in graphic form on a computer screen, often to elucidate the pharmacokinetic and pharnacodynamic processes associated with drug administration. Usually, only a mouse interface is involved. While these simulations help one understand the conceptual theory underlying clinical practice, they usually do not confer actual practical skills. Their strength lies in an ability to help one understand abstract concepts while remaining portable and relatively inexpensive. These simulators are particularly well-suited to physiological and pharmacological modeling (vide infra).
Mannequin-based simulators come in various levels of complexity, but are almost always expensive. The advanced models include a physical model of the human body and provide continuous signals representing physiological parameters such as electrocardiogam, blood pressure wave, capnogram signal and pulse oximetry signal. While some earlier systems required the intervention of a trainer to actively 'stage manage' the scenario in response to interventions, others make use of complex computer models of human physiology and pharmacology to automatically generate appropriate responses in the mannequin and signal outputs.7 In contrast to screen-based simulations, these simulators appear to recreate enough elements of reality to allow the acquisition of skills that are transferable back to the clinical environment.
Virtual reality trainers are just beginning to gain popularity, especially amongst surgical trainees. They offer a transition from the two-dimensional world of the textbook to the three dimensional world of simulated patients. The principle problem so far has been the lack of reality modeling in terms of offering a tactile 'feel'. However, this problem is being actively tackled in research centers using micro-engineering techniques.
Early work on physiological modeling and simulation followed the advent of digital computers in academic medical centers and universities. For instance, Guyton and others8,9 have been using mathematical models of complex human physiology for years to help predict complex interactions of different organ systems. Even before that, Dickinson10-14 worked on educational physiologic models in the 1970s.
The Mechanical Ventilation Simulator (http://www.ajdcomputing.com/pccm) is one example of a simulation intended to enhance the teaching of the principles of mechanical ventilation to medical students and other individuals. The simulation allows the student to manipulate the ventilator settings of a hypothetical patient and see the results of the blood gases and other physiologic data. Such simulations are usually based on an explicitly expressed mathematical model.
In general, two steps are involved in the development of satisfactory computer models for physiological and pharmacological applications: (1) the development of a mathematical model that describes the behavior of the processes involved; and (2) translation of the model into a computer programming language or spreadsheet. Not infrequently, the models involve the solution of a system of differential equations.
Although many physiological problems are readily solved by direct analytical methods, not infrequently their solution is hampered by non-linearities, self-referencing (circular) equations, or other complexities. (An example of a non-linearity is the equation y = x ^ 2; an example of a self-referencing equation set is the equation pair y = 1/x; x = y + 1.) Many conventional spreadsheet programs (e.g. early versions of Microsoft Excel) are poorly equipped to solve systems of this kind, not being generally designed for iterative equation solving methods.
There are many questions in physiology that are not easily answered by direct experimentation, either because it is impractical, or impossible, to control all the pertinent variables or because of ethical considerations. Consider the case of studying the influence of blood hemoglobin concentration on pulmonary gas exchange indices. It would be difficult to rigorously control cardiac output, total body oxygen consumption, and other variables to experimentally study the issue, while modeling the problem using simple equations offers several advantages:
It relies on well-established physiological relationships (e.g. alveolar gas equation, pulmonary shunt equation).
Three drawbacks to the virtual experimentation exist and must be reviewed with each model developed:
Finally, note that one potential difficulty with all such modeling methods is that the obtained results may depend critically on the equations used. In cases where the equations are known from first principles (e.g. alveolar gas equation, pulmonary shunt equation) this need not be an issue, but where an equation is empirical, alternative equations may possibly produce differing results. One example is the equation for the oxyhemoglobin dissociation curve, which has many competing formulations.
Where more than one set of equations exist to describe a physiological relationship, one can explore the effect of equation choice on the way the model behaves. One would expect however, that if several equations existed that all did a good job of representing the underlying data, that equation choice would generally not have a great influence on obtained results. By conducting virtual experiments, in the case of a few days (or even a few hours) one can obtain meaningful information about the interaction of several physiological variables, provided that the relationships describing the variables are available in equation form. By contrast, actual real experimentation takes time, funds and effort that may not always be available. In fields such as oxygen transport, many relevant equations are simple and well-known, such as:
To the extent that one accepts these physiological principles, the results obtained should also be credible (provided that model design and implementation have been done correctly). In this respect, three issues exist:
When can such a mathematical model be useful? Consider an example. In a particular patient with severe adult respiratory distress syndrome (ARDS) and resulting severe hypoxemia, clinicians might be interested in knowing, how extracorporeal membrane oxygenation (ECMO) could improve oxygenation. From pulmonary artery catheterization and arterial blood samples one can obtain the following important oxygen modeling data:
Based on a model constructed for that time point, one could explore the effect of augmenting cardiac output and/or mixed venous oxygen tension in an ECMO situation. Without a model to describe this problem, the best we can do is fit empirical curves to experimental data. However, with a model one can easily ask "what-if" questions: for example, what happens when the ratio of pump oxygenator flow to cardiac output is set at a particular value.15
Another example of modeling utility, this time from respiratory physiology is: How does a patient's alveolar-arterial oxygen tension difference change with reduced inspired oxygen tensions. The first attempt in answering this question16 used pulse oximetry to infer arterial oxygen tension in volunteers subjected to controlled hypoxia by rebreathing. A subsequent study17 took a more direct approach by canalling the radial artery of elderly respiratory patient volunteers and drawing off serial arterial blood samples as the patients were subjected to hypoxemia in a hypobaric chamber. This latter study is sufficiently invasive (and even, perhaps, sufficiently risky) that many hospital ethics committees would not approve it under existing guidelines. By contrast, the model-building approach can (and does) provide insight to the problem, and predicts that the alveolar-arterial tension gradient decreases with amplitude.18-20 Pharmacologic modeling is similar to physiological modeling in a great number of respects. All that is required is that the relevant equations be known (see Appendix) and that a means exists to solve and display them.
Simulation in Anesthesia and Critical Care Medicine
Computer simulation methods are potentially useful for training anesthetists and for quality assessment programs. In particular, crisis simulation offers a “safe” environment to study individuals' responses to anesthetic errors, equipment failure, critical incidences and other unplanned incidents. Also, adherence to practice standards and guidelines can be studied during simulated crises.
of the first attempts at electronic simulation in anesthesiology was the
SIM-1 system.21 Although technically sophisticated for the
time (late 1960s), it was not satisfactory for serious clinical training,
and simulation technology in anesthesia would wait another three decades
for the required computer technology to come to the stage. With the development
of high-performance microcomputer technology a number of developments
in anesthesia simulation became practical.
The Virtual Anesthesiology Training Simulation System from CAE/Eagle/MedSim (the name reflects a series of corporate sales and takeovers) is a modern anesthesiology simulator conceived for a number of training applications, such as to train anesthesiology residents, for practice with new technology or instruments, for rehearsing anesthetic emergencies, and possibly for future testing, certification, or recertification of anesthesiologists.22-25 It is also of potential use outside the operating room, in such situations as Critical Care Training, Emergency Room Training, Advanced Cardiac Life Support Training, and the training of physicians or nurses with new monitoring equipment.
The system is composed of a mannequin, associated attachments and computer hardware and software to drive human-like behavior by the mannequin and to simulate various anaesthetic catastrophes. The mannequin includes an anatomically correct head and neck assembly that allows the trainee to intubate the larynx. The lungs can breath spontaneously or passively by hand or mechanical ventilation. Anatomically located loudspeakers in the chest provide heart sounds and breath sounds that can be detected in the usual chest locations with a stethoscope. Servo-controllable lungs “produce” carbon dioxide using a computer-controlled gas metering system. The airway anatomy is such that endobronchial or esophageal intubation is possible. Palpable pulses at the carotid artery and radial artery are also present using real-time simulation. Sites in the mannequin's arm into which intravenous lines can be inserted and drugs infused also exist, although no means to determine automatically what drug or dose was given exists. A simulated twitch response in one of the mannequin's thumbs can be used for the assessment of neuromuscular blockade. Table 3 outlines the system’s many capabilities.
mannequin interfaces with anesthesia machines, respiratory gas analysis
devices (capnograph, agent analyzer), pulse oximeters, and other patient
monitoring equipment. It is intended to drive all commercially available
monitors without modifying setups used in routine clinical care. In all,
the following outputs are provided: ECG, arterial pressure, central venous
pressure, pulmonary artery pressure, temperature, and pulse oximetry (both
waveform and percent saturation). In additon, radial and carotid pulses,
as well as non-invasive blood pressure measurements, are available using
computer-controlled hydraulics. Many simulated events can be introduced
by the operator, including anaphylaxis, aspiration, hemorrhage, malignant
hyperthermia, coronary artery constriction, and vagally-mediated bradycardia.
I expect that this technology will help considerably to reduce the risk of mistakes due to clinical inexperience. However, it also raises some interesting questions. How realistic are the algorithms on which the simulations are based? Who should cover the costs of running the simulator? Should a trial run at the simulator be part of the final examination process in order to graduate as a physician or for certification as a specialist? What role should this technology play in the formal evaluation of physicians who have been identified as "dangerous"?
One final issue is how to provide feedback to students testing out under the simulator. If a student performs poorly, there are a number of approaches to dealing with the problem without excessively “bruising” the student. Some authorities recommend that your "patient" should not be allowed to be brought to "death" because it may be emotionally traumatic to fail so profoundly. Similarly, in the world of aviation simulation, there is an issue about the wisdom of running pilot simulations under such extreme conditions that a crash would be inevitable.
Software Only Simulation
only simulation has many advantages, especially with regard to portability
and low cost, and has been used for some time in general medical education.
For instance, the Diagnostic Reasoning Cases (DxR cases) software system
is a practice based learning package that allows medical students to take
a history, examine a virtual patient, order laboratory investigations,
and generate clinical hypotheses in the course of diagnosing an actual
clinical problem. (See http://medweb.usc.edu/dxr/index.htm for some DxR demonstration cases.)
Several companies offer software-only packages for medical simulation in CD-ROM format. For instance, the Anesoft Corp. (www.anesoft.com) offers anesthesia and critical care software simulation software that are not only educational, but (in my opinion) actually fun to use. These packages were developed at the University of Washington Department of Anesthesiology. Three programs for Windows and Macintosh systems are available; the best-known is called Anesthesia Simulator and at the time of writing was in its third release. Critical incidents supported in this program include anaphylaxis, cardiac arrest, latex allergy, pneumothorax, renal failure and much more.
The Anesoft ACLS simulation package is an interactive teaching and testing program that contains algorithms, medications, and dosages from the American Heart Association Textbook of Advanced Cardiac Life Support. One is required to interpret electrocardiogram traces, defibrillate, intubate and so on. The 28 simulated cases presented in the package cover asystole, ventricular fibrillation, ventricular tachycardia, atrial fibrillation, atrial flutter, pulseless electrical activity, heart blocks and more. An expert system included in the package for teacher management in shows you what went wrong and what to do next. It can even take over the case for you if you get tired or frustrated. Finally the system provides tutorials on rhythm recognition and treatment as well as tutorials on cardiac medications.
The third package, Critical Care Simulator, offers 20 different critically ill patients for whom one must manage the airway, ventilation, fluids, and drugs to improve the patient's condition.
Mad Scientist Software (http://www.madsci.com/) is a company that also offers a number of medical simulation packages such as their Trauma One! teaching package. Gas Man®5 is another software-only simulation package concerned with anesthetic gases. It is intended to be used as a tool for teaching, simulating and experimenting with anesthetic gas uptake and distribution. The Gas Man computer model graphically simulates the pharmacokinetics of anesthesia administration, showing the time course of gas uptake in each compartment of the body - lungs, heart, brain - as well in as the breathing circuit and vaporizer. It is available from Gas Man Software (http://www.gasmanweb.com). Finally, a free simulation of the anesthesia machine has been produced in Web format by the University of Florida.26 It is available online at www.anest.ufl.edu/~eduweb/vam/.
Simulation in Clinical Airway Management
In recent years, clinical airway management has become a focus of simulation technology. Two area of effort are involved. The first is to develop computer-based models of fluid dynamics to describe gas flow in the tracheo-bronchial tree; this field, while important, is of limited interest to clinicians.
The other field of airway simulation is more clinical, and focuses on training clinicians. The goal here is simply to produce an instrumented mannequin that can be used in training and performance evaluation. The Laerdal Corporation is the best known in this regard. Its capabilities are listed in Table 4.
Simulation in Regional Anesthesia
Regional anesthesia is a technique which is frequently performed to avoid the need to perform general anesthesia on a patient. One particularly common regional anesthesia technique is epidural anesthesia, a technique that is popular both for childbirth as well as for lower extremity surgery. Recent research efforts have been directed towards simulating this and other regional anesthesia procedures.
Regional ABC is a hands-on, Web-based regional anesthesia guide from Duke University Medical Center. It focuses on regional anestheia of the lower extremity and may be viewed at http://anesthesia.mc.duke.edu/regional/abc/index.html. It is intended both as an educational tool and a patient care resource. Much of the information on this site can be exported to handheld computers for use at the patient bedside. Blocks described include: (1) Lumbar plexus: Femoral nerve, Genitofemoral nerve, Ilioingunial nerve / Iliohypogastric nerve, Lateral Femoral Cutaneous nerve, Obturator nerve, Spinal nerve (2) Sacral plexus: Sciatic nerve, Posterior Femoral Cutaneous nerve, Gluteal region block. While the site is more instructional/informational than an actual simulation, it covers the topic of regional anesthesia rather comprehensively.
The Biomedical Applications Research Group at the Ohio Supercomputer Center (OSC) (http://www.osc.edu/) has for some time been interested in high performance computing applications. One application they have focused on is entitled "Virtual Simulation of Regional Anesthesia" and is intended to help train anesthesiologists in learning epidural anesthesia and other forms of regional anesthesia. The following project description, summarized from their Web site, explains their goals.
"Epidural analgesia is one of the most frequently used techniques for the relief of pain during surgery. In most hospitals with an obstetric anesthesia service, epidural analgesia is the most prominently used anesthesia technique for vaginal childbirth and cesarean section. The procedure involves the injection of a local anesthetic or opiod into the epidural space of the spinal column. Although a single degree-of-freedom task, it is a delicate manual operation that requires the placement of a catheter into the epidural space using only haptic cues to guide the needle. By feeling the resistive forces of the needle passing through the various tissues, the anesthesiologist must maneuver the tip of the needle into the correct space without perforating and damaging the spinal cord in the process. Limitations of physical models such as mannequins include lack of patient variance, inaccurate representation of biological tissue, and physical wear from repeated use. The use of cadaveric material offers limited opportunities and associated risks. The best method of training residents on this delicate and dangerous manual task remains the use of live patients, a scenario obviously not optimal for patients. In addition, teaching this technique requires highly intensive tutorial interaction with faculty due to the significant learning curve in understanding exact placement of the needle. This ongoing collaborative effort between researchers at The Ohio State University Hospitals, Immersion Corporation, and OSC is to create and test a virtual simulator for training residents in the use of regional anesthesiology. Under funding from the Department of Defense, we are creating a system for teaching a specific method of regional anesthesia, the epidural technique. Our methods include the application and integration of virtual technologies. Our system components include a high-performance graphics workstation capable of stereo display, a real-time volume renderer, a voice-activated interface, and a one-dimensional haptic probe capable of simulating the resistive forces of penetrated tissues. The system will enable the resident to investigate various three-dimensional reconstructed data sets in a nonthreatening environment. The system can be cued through voice activation to provide additional information in text, audio, or graphical form. Furthermore, the system incorporates the necessary components to allow the resident to "feel" the technique as performed by the expert. By providing a new form of procedural training in a nonthreatening environment, the simulator will increase the proficiency level of the resident in technique delivery and improve competency required for live human trials. "
Kirkpatrick's “Four Levels of Evaluation” Applied to Medical Simulation
Evaluation of teaching programs and other initiatives is important to determine if effort and money has been spent wisely. One well-known approach to program evaluation is Kirkpatrick's “Four Levels of Evaluation”, first developed in 1959. At the time, Donald Kirkpatrick was a professor of marketing at the University of Wisconsin. His four levels of evaluation involve four kinds of measurement:
Level 1: Reaction – measurement of satisfaction
Level 2: Learning - measurement of learning
Level 3: Behavior - measurement of behavior change
Level 4: Results - measurement of results
Questions associated with each level that guide the measurements are as follows:
Level 1: (Reaction) Were the participants pleased with the program? How would they rate their experience? What suggestions can be made to improve the experience?
Level 2: (Learning) What skills, knowledge, insights or attitudes have changed from the program?
Level 3: (Behavior) Did the participants change their behavior based on what was presented in the program?
Level 4: (Results) Did the change in behavior positively affect the organization or influence an objective outcome?
Although this particular paradigm is popular in the worlds of business and education, it is less well-known in clinical circles, so that few specific evaluations of medical simulations programs in this particular context have been made. However, a number of related studies have been undertaken to address related issues.
In a study carried out at the University of Toronto27 the authors “wished to determine whether a simulator-based evaluation technique assessing clinical performance could demonstrate construct validity and determine the subjects' perception of realism of the evaluation process.” The simulation involved preoperative patient evaluation, anesthesia induction, and maintenance of anesthesia. Each problem presented to the subject as part of the simulation in a structured manner; examples of problems included atelectasis, coronary ischemia, and hypothermia. After the simulation, participants rated the realism of their experience on a 10-point visual analog scale (VAS). The overall realism VAS score was 7.8. The subjects rated the realism of the test scenario highly (Kirkpatrick level 1), but the other levels were not explicitly examined.
In a study at the University of Washington28 investigators sought “to determine whether an advanced cardiac life support (ACLS) computer simulation program improves retention of ACLS guidelines more effectively than textbook review.” Using a randomized, controlled trial in an academic medical center, forty-five anesthesia residents and faculty were tested 10 to 11 months after ACLS provider course training. Participants were randomized to textbook or simulator training and asked to prepare for a mock resuscitation (Mega Code). The examination sessions were videotaped and scored; participants who used the ACLS simulation program scored significantly higher than participants who reviewed using a textbook . The authors concluded that “use of a computerized ACLS simulation program improves retention of ACLS guidelines better than textbook review.” This was a study which focused on Kirkpatrick’s level 2.
Another simulator study carried out at the University of Washington29 sought to measure the effectiveness of screen-based simulator training with debriefing on the response to simulated anesthetic critical incidents using a mannequin-based simulator. Thirty-one anesthesia residents were randomized into two groups. Their approach examined Kirkpatrick’s levels 2 and 3. The intervention group was presented with ten anesthetic emergencies using the screen-based anesthesia simulator program and received written feedback on their management, whereas the control group was asked to study a handout covering the same ten emergencies. All residents were then evaluated on their management of 4 standardized scenarios in a mannequin-based simulator. The authors found that “residents who managed anesthetic problems using a screen-based anesthesia simulator handled the emergencies in a mannequin-based anesthesia simulator better than residents who were asked to study a handout covering the same problems” and they concluded that “computer simulations with feedback are effective as a supplement to traditional residency training methods for the management of medical emergencies.”
Simulation can be used as a powerful tool for studying human performance issues (training, teamwork, fatigue) as well as for exploring human-machine interactions, and for the studying design flaws in medical equipment. Table 5 lists some of the many research issues in this area. Note that many of these issues center on situational awareness and clinical crisis management and draw on experience developed in the aviation industry.
Although computer-based simulation in anesthesiology and critical care medicine is in its early years, already much has been accomplished. Applications range from scientific modeling to clinical performance appraisal in the setting of crisis management. Still, much remains to be done to demonstrate its scientific and clinical utility, especially in the context of the Fitzpatrick model.
The author has no financial interests in the technology described.
I am indebted to Dr. Pat Fahy, Athabasca University, Alberta, Canada, for helpful discussions.
Ukrainian translation Provided by Galina Miklosic at this link.
Doyle DJ. Simulation in medical education: Focus on Anesthesiology. Med Educ Online [serial online] 2002;7:16. Available from http://www.med-ed-online.org
Dr. D. John Doyle
Pharmacokinetics in a Nutshell
In simple technical terms, pharmacokinetic modeling is playing with first order linear differential equations. The simplest model, involving only a central compartment which the drug enters, is summarized in equation format below.
Mathematical Details of the Three Compartment Model
There is no simple solution to this set of equations. Analytical solutions have been published, but it is not especially difficult to solve the equations numerically, for example, using Euler's method [Maitre PO, Shafer SL. A simple pocket calculator approach to predict anesthetic drug concentrations from pharmacokinetic data. Anesthesiology. 1990; 73:332-6].
However, these equations govern the mass (amount) of drug in each compartment; to go from drug mass to drug concentration one must divide the mass by the volume the drug is dissolved in, or "volume of distribution". Since generally we are only interested in drug concentration in the central compartment (compartment 1), only the volume of distribution for the central compartment (V1) is of interest to most pharmacokineticists.
Thus, you need to know seven things to develop a three-compartment pharmacokinetic model: R, V1, Ke, K12, K21, K13, and K31. (Actually, you also need to know some initial condition data about the drugs on board at time zero, but we generally set all that to zero.)
Given these seven parameters [which are not always easy to obtain in the real world] one can predict the drug concentration that might be expected in an "average" patient for a given pattern of drug delivery into the patient's IV. The prediction is based on average pharmacokinetic data from study patients; specific pharmacokinetic data for a particular patient is unlikely to ever be clinically practical. Your patient may vary very much from the "average" if, for example, he or she is in renal failure or is quite elderly. Other influences might be expected in patients taking other drugs concurrently (e.g. cimetidine) or with pharmacokinetic disorders (e.g. atypical plasma cholinesterase). Thus, a particular set of PK parameters has meaning only for the group they were obtained for, usually not-so-elderly patients with good hepatic and renal function taking minimal concurrent medication.
Some older reports use simpler 2 or 1 compartment models to describe pharmacokinetic behavior. For a 2-compartment model, let K13 = K31 = 0. For a 1-compartment model, in addition, let K12 = K21 = 0. This gives us the simplest pharmacokinetic model - a one-compartment model; here, the drug entering mixes instantly in the central compartment and is eliminated according to the elimination rate constant Ke:
dA / dt = R - Ke A