Mathematical Solutions In Healthcare Essay Examples

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Introduction
Mathematical skills are vital in the healthcare field, since many problems in different areas require measurements, formulae and calculations to be applied. This paper reviews two healthcare problems which suggest mathematical solutions for effective management of the patients.

Pain Management

WHO analgesic ladder (1996) supposes the patients with mild\mild –to-moderate pain receiving combination preparations of a weak opioid plus non-opioid should be transferred to strong opioids when the pain increases. The dose calculation is crucial in these cases: if it is too small, the effective pain relief will not be provided; if the opioid is overdosed, the side effects can be serious up to life-threatening respiratory depression (Watsone et al., 2013). Opioid conversion tables for steps 2 and 3 of the analgesic ladder require mathematical skills to calculate correctly starting and subsequent doses of opioids.
The calculation for opioid conversion is based on the different opioids dosage equivalency, as all these drugs are different in their potency and pharmacokinetics (short-life, half-life, immediate or extended release). Besides, some standard opioid preparations are quoted in both mg and ml (e.g. morphine 10 mg in 5 ml), and it is easy to make an error confusing measures.
The hypothetical situation of conversion of the patient taking maximum dose of co-codamol (paracetamol + codeine) (2 tablets 30/500 4 times a day) (WHO, 1996) to immediate release morphine for strong pain relief will look as follows:
Step 1. The dosage of both substances should be quoted im mg, to avoid confusion. Co-codamol is administered in tablets and 2 tablets of co-codamol 30/500 contain 60 mg of codeine and 1000 mg of paracetamol. For morphine solution, the concentration should be defined in mg as well, e.g. 10 mg\5ml.
Step 2. The daily co-codamol dosage should be calculated: 60 mg of codeine and 1000 mg of paracetamol taken 4 times a day will equal to 60*4\1000*4 = 240\1000 mg of codeine\paracetamol.
Step 3. The conversion table to determine the equivalent of starting morphine dose should be used. It shows that 240 mg of codeine a day is equivalent to 30 mg of immediate release morphine administered each 4 hours, or 6 times a day.
Step 4. The calculation of one-time dose of 4hourly immediate-release morphine needed is made: 30mg administered each 4 hours, 6 times a day, will give the dosage of 30 divided by 6 = 5mg, or 2,5ml (given 10mg per 5 ml concentration).
Step 5. It depends both on mathematical skills and clinical judgement as there are no precisely correct answers in all opioid conversions (Watson et al., 2013). At this stage the provision for conversion to another opioid should be made. The individual patients factors as age, hepatic and renal function can have impact on the new drug tolerability. So the general rule is to provide 30-50% dose reduction for cross-tolerance (Chou et al., 2009). Thus it means the chosen dosage of 30 mg morphine daily will initially be reduced approximately up to 15-20 mg of morphine (15 mg is 50% of 30 mg and 20(21) mg corresponds to 30% reduction of 30mg dosage). Again, it is started to be administered 6 times a day which means the division of this reduced dose by 6 ( 2,5-3,5mg of morphine each 4 hours).
The ability to calculate common opioid dose conversion is crucial for medical staff to such extent that FDA includes in drugs information warning on accidental overdosing explaining in detail the relation between strenghth, concentration and its mathematical expressions (FDA,2011). Both effectiveness and safety of the pain management are ensured through correct opioids dose calculation. So the medical staff working in acute or palliative care needs to have these skills, and the safe management of the patients who are receiving opioids depends on this staff competency.

Nutrition

Working with the patients with obesity, diabetes or metabolic syndrome requires providing these patients with diets based on glycemic indexes of food. Glycemic index is a number assigned to a particular food showing how much it increases blood sugar level. Still, the glycemic index should be applied not on its own as it does not show how the particular quantity of the food increases the sugar. It does not take into account the amount of carbohydrates content in particular food either. There are tables which present the glycemic index of foods and carbohydrate content in different products of different countries( Foster-Powell, Holt, & Brand-Miller, 2002), and there is a mathematical equation which should be solved to calculate the sugar increase for a particular person on a particular diet plan, or a so-called glycemic load calculation.

In hypothetical situation of diet elaboration for a person with metabolic abnormalities, the subsequent example calculation will be done.

Step 1. The quantity of serving for a particular person has to be determined, e.g., 1 glass(250 ml) of low-fat yougurt (Yakult, Australia) and 300 g of white rice (Canada)(Foster-Powell et al.,2002). It gives approximately 4 standard portions of yougurt (250 ml divided by a portion size of 65 ml) and 2 portions of rice (300g divided by a portion size of 150 g).
Step 2. The glycemic index for these products should be identified using glycemic index tables (Foster-Powell et al.,2002). These give a value of 46 for yougurt (65 ml) and 51 for rice (150 g cup).
Step 3. The net carbohydrates amount for these particular products should be derived from the table. For yougurt, it is, 12 and for rice, 42. (Foster-Powell et al., 2002).
Step 4. The value of glycemic index should be multiplied by the quantity of carbohydrates in a serving of the product and divided by 100 to get a glycemic load. For yougurt, 46 * 12/100 will give approximately 6, and for rice, 51*42/100=21, per serving.
Step 5. The total glycemic load for a particular meal should be calculated. For 4 portions of yougurt the glycemic load will equal 4*6= 24, and for 2 portions of rice, 2*21=42.
The values derived will be used by dieticians to estimate if the overall meal value is appropriate for the patient. The weight loss or sugar control programs are based on glycemic load calculation, so mathematical skills used to calculate these values will finally have impact on the outcome of the diets and overall effectiveness of these programs.

Conclusion

The medical staff working in the areas of palliative and acute care, nutrition, metabolic diseases and diabetes control should use mathematical skills to correctly calculate the dosage of medications and the glycemic load of food for patients. These are only two of many healthcare areas where mathematical abilities of the clinicians and nurses can ensure effective patients’ management.

References

1. Chou, R., Fanciullo, G.J, Fine PG, Adler, J.A., Ballantyne, J.C., Davis, PMiaskowski, C. (2009). Clinical guidelines for the use of chronic opioid therapy in chronic noncancer pain. J Pain.,10 (2),113-130.
2. Foster-Powell, K., Holt, S., & Brand-Miller, J.C.(2002). International table of glycemic index and glycemic load values: 2002. The American Journal of Clinical Nutrition, 76,5-56.
3. US Food and Drug Administration (FDA) (2011). Morphine Sulfate Oral Solution 100 mg per 5 mL (20 mg/mL): Medication Use Error - Reports of Accidental Overdose.Retrieved from: http://www.fda.gov/Safety/MedWatch/SafetyInformation/SafetyAlertsforHumanMedicalProducts/ucm239559.htm
4. Watson, M., Lucas, C., Sadler, C., & Hazell, C. (2013).European Certificate in Essential Palliative Care. Princess Alice Hospice.10th Ed. Esher.
5. World Health Organization (WHO) (1996).WHO analgesic ladder. WHO, Geneva.