Anesthesia: Applications of mathematics
Anesthesia is a medical practice designed to induce insensibility, allowing patients to undergo surgical and dental procedures without pain. Evolving from ancient herbal remedies, modern anesthesia encompasses three primary types: local, regional, and general. Each type is carefully administered based on mathematical calculations to determine appropriate drug dosages, which are often calculated in milligrams of drug per kilogram of patient weight. Monitoring during anesthesia is critical, involving various measurements like heart rate, oxygen saturation, and blood pressure, all of which require mathematical understanding to ensure patient safety.
The depth of anesthesia is a complex balance; too deep can lead to cardiovascular issues, while too light can result in pain or consciousness. Advanced techniques, such as analyzing EEG signals and respiratory patterns, utilize mathematical models to gauge the anesthetic level in real-time. Anesthesiologists and anesthesia providers undergo rigorous training that includes a comprehensive understanding of pharmacokinetics and statistics, highlighting the integral role of mathematics in effective anesthesia practice. Overall, the application of mathematics in anesthesia is essential for optimizing patient outcomes and ensuring safety during procedures.
Anesthesia: Applications of mathematics
Summary: Anesthesia dosages must be precisely determined and the patient must be monitored for signs of too high or low a dosage.
The word “anesthesia” was coined from the Greek word anaisthesis meaning “insensibility.” As early as 4200 b.c.e, opium poppies were used as an herbal remedy in Samaria and, later, in Cyprus, India, and China. The three main types of anesthesia are local (loss of sensation in a small area of the body by the blockage of nerve signals), regional (loss of sensation in a larger area of the body), and general (loss of consciousness), are used to relieve the feeling of pain during medical and dental procedures. Anesthesia uses mathematics in variety of ways including the calculation of appropriate drug dosages, the monitoring of patients under general anesthetics during surgery and recovery, and the design and use of anesthetic equipment including vaporizers, ventilators, and pressure gauges.
Non-pharmacological anesthetic techniques historically have included local anesthetics such as ice and rum. Nitrous oxide (“laughing gas”), ether, and chloroform were used as general anesthetics in the 1800s during childbirth and surgery.
Applications of Mathematics
Anesthetic drug dosages per minute are based on milligrams of drug per kilogram weight of the patient. The rate of elimination of drugs from the body per unit of time is proportional to the amount of drug in the body. The time taken for the drug concentration in the plasma to be reduced by 50% is called the elimination half life.
The measurements monitored while a patient is under general anesthetics can include data such as temperature; heart rate via ECG (electrocardiogram); oxygen saturation via pulse oximetry; ratio of oxygen, carbon dioxide, and nitrous oxide from the patient’s inspired and expired gases; urine output; arterial blood pressure; central venous pressure; pulmonary artery occlusion pressure; cerebral activity via EEG (electroencephalogram); and neuromuscular function.
A major concern is keeping the patient at the appropriate level of anesthesia. The cardiovascular system is threatened if the anesthetic is too deep, but if the anesthetic is too light, the patient may experience pain or regain consciousness.
Researchers have attempted to measure the depth of anesthesia by monitoring on a graph and on a time scale EEG signals generated by electrical discharges of neurons near the brain surface. One method is to administer a gaseous anesthetic drug and hypothesize that the concentration of the drug in the expired air is proportional to the blood-plasma concentration. An alternative research technique is to observe respiratory sinus arrhythmia (RSA), which is the variation in heart rate during a breathing cycle. The heart rate increases during inhalation and decreases during exhalation. On the graph of an ECG, each heartbeat is referred to as an R peak. The difference between two consecutive R peaks is an RR interval, which is shortened during inspiration and lengthened during expiration.
Anesthesia Providers’ Educational Backgrounds
The academic and clinical preparation for an anesthesiologist in the United States consists of four years of college, four years of medical school, one year of internship, and three years of anesthesiology residency. A description of Steven Cruickshank’s 1998 book Mathematics and Statistics in Anaesthesia states that anesthesia residents are required to study and understand pharmokinetics (the study of what the body does to a drug) and statistics as “a core part of their training.” In addition to physician anesthesiologists, anesthesiologist assistants or Certified Registered Nurse Anesthetists (CRNAs) can apply anesthesia or sedation while working with healthcare professionals. CRNAs complete four years of college, at least one year of acute-care nursing, and a 24- to 36-month master’s degree program before passing the required certification examination. Anesthesiologist assistants (AAs) with master’s degrees may practice under the supervision of an anesthesiologist in several states.
Bibliography
Chen, Z., et al. “Linear and Nonlinear Quantification of Respiratory Sinus Arrhythmia During Propofol General Anesthesia.” http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2804255.
Cruickshank, Steven. Mathematics and Statistics in Anaesthesia. New York: Oxford University Press, 1998.
Neligan, Pat. “Pharmacokinetics.” http://www.scribd.com/doc/39115053/Pharmacokinetic.
Widman, G., T. Schreiber, B. Rehberg, A. Hoeft, and C. E. Elger. “Quantification of Depth of Anesthesia by Nonlinear Time Series Analysis of Brain Electrical Activity.” http://arxiv.org/PS‗cache/nlin/pdf/0007/0007027v1.pdf.