The importance of Mathematics and its impacts in the field of Pharmaceutical Science PDF

Preview

Summary

The importance of Mathematics and its impacts in the fieldof Pharmaceutical ScienceAbstractMathematics has a significant impact on various studies and understandings on the human biology, physiology, and biochemistry, which in turn allow it influence to have a critical role in the field of health sc...

Description

The importance of Mathematics and its impacts in the field of Pharmaceutical Science Abstract Mathematics has a significant impact on various studies and understandings on the human biology, physiology, and biochemistry, which in turn allow it influence to have a critical role in the field of health science. One such case is the field of pharmaceutical, which uses mathematical models and analytical techniques to establish theories and improved the practical effectiveness of drugs and methods. According to Dr Sumanta Mondal, pharmacology refers to the study of therapeutic value and potential toxicity of chemical agents on biological systems. Mathematics models are utilized in pharmacology to further investigate the impact of newly developed drugs and drug therapies on the human body. The type of mathematical models used in research includes the logarithmic and exponential model, analytical models and simulation models. In addition, graphs are also used a tool to analysis data and statistics in many testing procedures. From something as simple as figuring out the weight of chemical within a particular drug to analyzing the electrical remodeling on drug therapy, mathematics will always have an impact on pharmacology.

History of Mathematical models in pharmacology One of the two earliest mathematical models used in pharmacy were in 1972, in which a simulation models were used to investigate the number of outpatient pharmacies (Bryony et al) 1997). Firstly, a study by Johnson et al was trying to investigate the number of pharmacists needed to perform minimum standard and its impacts on the number of prepackaged medication. The second study was by Brooks and Feiglin, in which they also used a simulation model to explore between a patient arrival rate and the time to dispense prescription had an effect on their waiting time. A similar study was also conducted in 1974, in which Harmon and Novotny also used a simulation model to compare to waiting time in military hospital. Analytical models were used in pharmacology. In 1987, Moss used an analytical model to identify the relationship between patient arrival rate, staffing level and waiting times in a British outpatient pharmacy. The author used probability to determine the waiting time for patients when the average arriving rating and dispensing time are known. The study concluded when it was found out that if staffs were to work in parallel, it would reduce the waiting time for patients.

Analytical model Analytical models is a mathematical models that is used to represent system terms of a set of mathematical equation that specific relationships and their connection to functions such as time, space or various other parameters (Sanford et al 2012). There are two type o analytical models, which are deterministic analytical model and stochastic. A deterministic analytical model is a model that does not consist of probability inputs. One major example of a deterministic analytical model is when Michaelis and Menten used this mathematical model to establish

relationship between the dose and plasma concentration for drugs with metabolism such as Km × D phenytoin. An equation was used C p = V max−D    

C P is the concentration in plasma D is the daily dose in milligrams V max is a constant that represents the maximum rate of metabolism in milligrams per day K m is a constant that represent the plasma concentration

This is a useful tool in the field of pharmacology because it allows drugs to be tested and analyzed to ensure the right does for the human body. A stochastic model is model that have one or more probabilistic inputs, in which the probability is randomize therefore variable. An example of a stochastic model is to determine the number of patients that would arrive at the outpatient pharmacy within a 10-minute time period. The number of patients arriving is not likely to be the same, however the average number of patients could be determined. Assuming that the average arrival rate is constant and the patient’s arrival time is independent, this could be used to determine the arrival patterns of the patients (Bryony et al).

Fig 1: The probality of different number of patients arriving in a 10-minute interval

Simulation Model A simulation model is used to imitate behavior in the real world, it is a system that is designed to consider the difference aspects and components of how the process works. Rather than determine the result based on the output and input, it uses behavior to describe the whole sequence of the simulation. There are two type of simulation models, they are the continuous time simulation and discrete event simulation. In a continuous time simulation, there is an uninterrupted flow of

materials that changes in the relation of passing time. For example, the elimination of drugs in the human body....