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Healthy with Math Index
Annual health checks are something we all should do regularly. because even though the body seems to be healthy And does not have any abnormalities, but a thorough examination of the functions of various organs in the body may allow us to find problems early, which will lead to timely prevention and treatment of diseases. before the symptoms of the disease spread until it is too late
Annual health check each time The doctor will recommend various checklists according to the examiner’s age. Usually, the doctor will do a general physical examination, blood tests, urine and stool tests. This may include X-rays and ultrasound to examine internal organs. In these physical examination methods, mathematical knowledge is used in a variety of ways. For the purpose of each examination is another very interesting example of applying mathematics to life.
This article provides an example of how math can be applied to your annual health check. which has a wide variety of measurements to compare with the standard values calculated from people with normal health It is divided into examining different parts of the body as follows:
1. General physical examination ( Physical Examination)
It is an examination of the external condition of the body. including the nature of the shape that is proportional or not Most basic examinations are direct measurements of quantities, such as height and weight measurements, which are measured in meters or centimeters and kilograms, respectively. or too busy or too thin would not be able to see from the weight alone But compared to the person’s height, medical scientists have come up with an index that is a ratio of weight to height to indicate What does a person’s shape look like? This index is known as the Body Mass Index (BMI), which is calculated from the ratio of weight in kilograms. with the height in meters squared as follows:
BMI = kg/m2
Body Mass Index is a simple calculation using a person’s height and weight. The formula is BMI = kg/m2 where kg is a person’s weight in kilograms and m2 is their height in metres squared. A BMI of 25.0 or more is overweight, while the healthy range is 18.5 to 24.9. BMI applies to most adults 18-65 years.
2. Blood Chemistry
It is a measure of the amount of various chemicals present in the blood that are usually not directly measured. Rather, it is measured by the masses of different substances compared to the volume of blood. The levels of substances that doctors often measure in the blood include glucose levels, cholesterol levels, and cholesterol levels. (Cholesterol) Triglycerides (Triglyceride) High Density Lipoprotein (HDL) and Low Density Lipoprotein (LDL) as well as the level of uric acid (Uric acid), which may be more or less different. go together The levels of these substances present in the blood are measured using the ratio of the metabolites in milligrams (mg) to 1 deciliter (dL) of blood in mg/dL, with reference values of Appropriate levels of various substances as shown in the following table.
Using this characteristic of the 1 deciliter mass-to-blood volume ratio allows physicians to compare the levels of various substances in the body with the appropriate reference values. The concentrations of various substances in the blood are equal throughout the body. The doctor was therefore able to take a small sample of the blood for examination. and then deduce the effect on all the blood circulating in the body.
In addition to measuring the levels of various substances in the blood, blood chemistry tests are also popular for screening liver function. The values of Aspartate transaminase (AST) and Alanine transaminase (ALT) are normal levels of both of these enzymes. But if the body cells or liver cells are destroyed will increase the level of these two enzymes. Measuring the levels of both enzymes can therefore indicate that something is wrong in the body. or the liver also gets rid of foreign bodies Is it good?
However, since AST and ALT are enzymes that catalyze chemical reactions in the body, Measuring it by mass may not be very helpful, so medical scientists measure the level of enzymes in the blood with the Enzyme Unit (U), which is the enzyme activity potential. compared to 1 liter of blood, instead of directly measuring the amount of the enzyme The measured values thus show the potential of the enzymes present in the body. which is also using mathematical ratios The ideal reference value for these two enzyme levels in the body should not exceed 40 Enzyme Units per liter of blood.
3. Complete Blood Count
In addition to chemical measurements In physical examination, we are also interested in the appearance and quantity of different blood cells in the body. The measurement of the nature and quantity of blood cells is a measure of the completeness of the blood, also known as CBC (Complete Blood Count).
Blood integrity measurements often use different blood indices, such as the level of hemoglobin, the protein in red blood cells that transport oxygen gas. Hemoglobin is measured as a ratio of the mass of hemoglobin in grams (9) to one deciliter of blood (dL is obtained in grams per deciliter (9/dL), while the level of white blood cells and platelets is commonly measured. with the ratio of the number of white blood cells or platelets to the volume of blood in billions of cells per 1 liter of blood (x10 9 cells/L).
In addition to measuring the level of hemoglobin in red blood cells, white blood cells and platelets in the blood Physicians are also interested in the ratio between the volumes of packed red blood cells that are extracted from the blood. Compared to the total blood volume, this index or ratio is called Hematocrit (Hct), which is an index or ratio that compares volume to volume together. Therefore, it is considered a dimensional quantity. (Dimensionless Quantity and preferably expressed as a percentage or %. Appropriate Hematocrit levels are 40 – 54% for males and 37 – 47% for females.
The size of red blood cells in the body is another important factor in measuring the integrity of the blood. The normal body should have red blood cells that are the same size, not so big or small that they are different. Because our body has an enormous number of red blood cells. Assessing the size of individual red blood cells requires the use of statistical principles from the blood samples collected for integrity testing. Your doctor determines the size of red blood cells by taking the arithmetic mean of the volume of one red blood cell, known as the Mean Corpuscular Volume (MCV), and the red blood cell distribution width, known as the Red blood cell Distribution Width (RDW).
The MCV value tells how large or small the average red blood cell is, while the RDW, or amplitude in the red blood cell volume distribution, tells how much the red blood cell is different in size compared to that. arithmetic average.
Since human red blood cells are very small, the MCV is often referred to as a unit. Femtoliter or L, which is equal to 10*:L, whereas RDW, which is the coefficient of variation in red blood cell volume, which is the ratio between femtoliters and femtoliters, is therefore commonly represented by The percentage, or %, normal in vivo MCV value is 80 – 99 fL and optimal RDW is 11.6 – 14.5%.
Another measure of the integrity of the blood that doctors pay attention to is A measure of the mean mass of hemoglobin found in one red blood cell. Also known as Mean Corpuscular Hemoglobin (MCH), this can be calculated from the amount of hemoglobin found in the sample red blood cells and because the amount of hemoglobin in each red blood cell is very little Therefore, MCH is commonly quoted in picograms, or pg, which is equal to 10’2 grams.
The use of femtoliters (1) and picograms (pg) in MCV and MCH is an example of the use of prefixes in the metric system. To denote very high or very low measurement values, we may be accustomed to using other prefixes such as centi- milli- deci- nano- or kilo- to represent 10 -2 , 10 -3 , 10 -1 , 10 – . 9 , 10 3 , respectively, but for values that are much higher or lower than common quantities, we can use other prefixes to express quantities with multipliers from 10 -24 to 10 24 as shown in the prefix table in this metric system.
As for the white blood cell test In addition to the method of measuring the number of cells per liter mentioned above. Physicians also need to determine the number of different types of white blood cells including the five different types of white blood cells: neutrophil, lymphocyte, monocyte, eosinophil, and basophil. This requires the principle of finding the ratio of multiple numbers, preferably as a percentage or % of the number of white blood cells of that type to the total number of white blood cells.
However, it is preferable to give an appropriate reference value of the ratio between the cell counts of these five types of white blood cells as a range based on the statistics of those with normal physical condition. If the ratio of the number of white blood cells of each type is within the reference range will assume that the body is normal The reference values of the ratio between the number of white blood cells for each type are shown in the table below.
4. Urinalysis
in the urine test It uses a different method than a blood test. by using scientific methods to examine the properties of urine such as acidity – alkalinity and specific gravity
Normal urine should be weakly acidic, with a pH in the range of 4.5-8.5. This pH or positive potential of the hydronium ions is a measure of the hydronium ion concentration in mol. per liter using the mathematical decimal logari according to the following formula
This is because pH is calculated from the logarithm of the hydronium ion concentration. The unit is moles per liter. The pH value is therefore a scale indicating the acidity – alkalinity without scientific units, and the pH of various substances is only between 0 – 14. For urine testing, the normal pH level is 4.5 – 8.5.
specific gravity This is a comparison of the ratio between the density of urine and the density of water at the same temperature. Although the density of liquids is commonly measured in grams per cubic centimeter (g/cm 2 ), specific gravity is the ratio between the density of a substance and the density of water.
Therefore, specific gravity is a dimensionless quantity that has no units. measuring the specific gravity of the urine Make the doctor know that the urine contains more substances than normal or not. In case the specific gravity is too high The normal level of urine specific gravity is 1.003 – 1.030.
In addition to measuring the acidity – alkalinity and specific gravity In a urinalysis, your doctor will also test if there are significant levels of protein or sugar in your urine. If protein or sugar is found in the urine That can indicate physical abnormalities or impaired kidney function. Checking for protein or sugar in the urine.
Two qualitative data are displayed: positive, indicating a significant level of protein or sugar, or negative, indicating that no significant level of protein or sugar was found similar to the base number system. Two that use only two symbols, 1 and 0, represent positive or negative results, respectively. In normal people, urine protein and sugar should be negative.
From the samples of measurements by various methods in this variety of physical examination Demonstrates the use of a number of mathematical principles such as ratios, ratios between multiples, exponents, statistics, index numbers, logarithms, and even binary system. To be used to measure various medical values that want to quantify and determine each component in the body in a different way.
Depending on the measurement objectives, a wide range of mathematical knowledge is a tool that professionals can apply to flexibly and broadly solve professional problems. An example of the use of mathematics to measure physical fitness is presented in this article.
Bibliography
Faculty of Medical Technology Mahidol University. (2016). Health Status Assessment Book for Employees, NSTDA, Bangkok.
Dr. San Jaiyodsilp. (2011). Teaching the reading of CBC results (blood count). Retrieved on 27 June 2016. From http://visitdrsant.blogspot.com/2011/07/cbc.html.
Dr. San Jaiyodsilp. (2012). Teaching methods of interpreting blood chemistry results. Retrieved on 27 June 2016. From http://visitdrsant.blogspot.com/2012/10/blog-post_4.html.
Institute for the Promotion of Teaching Science and Technology. (2013. Textbooks, additional subjects, Mathematics, Volume 3, Mathayomsuksa 4-6. Bangkok: Trade Organization of the NESDB.
Institute for the Promotion of Teaching Science and Technology. (2015). Textbook, additional courses, Chemistry, Volume 3, Secondary School 4-6. Bangkok: A commercial organization of the NESDB.
