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# MEDICATION DOSAGE AND INTRAVENOUS FLUID CALCULATION

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basic drugs dosage and fluid calculation for health ward staff with intravenous infusion

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### MEDICATION DOSAGE AND INTRAVENOUS FLUID CALCULATION

1. 1. MATHEMATICS FOR MEDICAL PRACTITIONERS DRUG CALCULATION DR MUSA MARENA  Drugs are prescribed by their generic (official) name or trade (brand) names and are packaged in an average unit dosage  Tablets and capsules contain a solid concentration of drugs (paracetamol gr x) whereas solution contain a specific amount of drug (usually gram weight) dissolved in a specific amount of solution (usually mL‘s or cc‘s) (promethazine 20mg per ml)  Parenteral medications (IM, SC, IV) are package in vials, ampoules, and pre-measured syringes. Dosages usually ranges from 1 to 3 ml  Medication orders refer to drug dosages, so calculation will be necessary if dosage prescribe is different from available dosage  Some drugs are measured in units (heparin, insulin, penicillin), and others are in solutions as mEq (grams per 1ml of solution). Some solutions need to be reconstituted from a` powder form.  Infants and children cannot receive the same dose of medication as adult  Basic Math skills are needed to calculate most dosage and solution problems encounter today in clinical practice  Accurate dosage calculation are an essential component of total nursing role in safe administration of medication  NURSING STAFF HAVE a range of sophisticated electronic devices at their disposal for delivering essential drugs, fluids and nutritional therapy to patients in the healthcare setting.  Accurate, low-flow-rate, small-volume infusions can be controlled by means of a syringe pump  Medium-to-high flow rates can be controlled by a volumetric infusion pump  Basic fluid replacement can be delivered by the age old method of gravity infusion – more commonly known as the ‗drip'.  Gravity infusion relies solely on the user setting up the infusion using a safe and sturdy drip stand, and then manually adjusting a plastic roller clamp, fitted to a disposable administration set, to achieve the desired drip rate.  A controller electronically regulates drop rate by gravity  An infusion pump consistently exerts pressure against the tubing or the fluid at preselected rate. Syringe pump exert pressure through the tubing Barriers to Calculation Success Top ten reasons why healthcare professionals don‘t think they need to maintain competency in calculations:  The computer does it  The pharmacy does it  The IV infusion pump does it  We have charts and tables that do it  The drug companies take care of it  We use unit dose  It‘s just a nursing school exercise  We have a unit-based pharmacist
2. 2.  Math is just not one of my strengths  It‘s not a good use of my time Responsible professionals cannot afford to become complacent with drug calculations as they are accountable for all drugs they administer TYPES OF IV FLUIDS IV fluids are packaged in sterile plastic bags or glass bottles. It is essential to choose the correct IV fluid to avoid serious fluid and electrolyte imbalance that may occur from infusing the wrong solution. Physicians and healthcare providers order IV fluids and the IV flow rate. If you have any doubt about the correct IV solution, always double-check with another healthcare professional. COMMON ABBREVIATIONS FOR IV FLUIDS ABBREVIATION DEFINITION D Dextrose W Water NS Normal (or isotonic) saline D5W 5% dextrose in water 0.9% NS 0.9% saline in water (sometimes termed normal saline) 0.45% NS 0.45% saline in water (sometimes termed 1⁄2 normal saline) 0.33% NS 0.33% saline in water (sometimes termed 1⁄3 normal saline) LR Lactated Ringer’s solution (or Lactated Ringers) D5NS 5% dextrose in normal saline KINDS OF IV DRIP FACTORS IV fluids are administered through infusion sets. These consist of plastic tubing attached at one end to the IV bag and at the other end to a needle or catheter inserted into a blood vessel. The top of the infusion set contains a chamber. Sets with a small needle in the chamber are called microdrip because their drops are small. To deliver 1 mL of fluid to the patient/client, 60 drops drip in the drip chamber (60 gtt 1 mL). Commonest microdrip sets deliver 60gtt/mL. Others are 50gtt/ml and 40gtt/ml. Infusion sets without a small needle in the chamber are called macrodrip (Fig. below).
3. 3. Drops per milliliter differ according to the manufacturer. For example, Baxter-Travenol macrodrip sets deliver 10gtt/mL, so10 drops drip in the drip chamber (10gtt 1 mL); Abbott sets deliver 15gtt/mL, so 15 drops drip in the drip chamber (15gtt 1mL). The package label states the drops per milliliter (gtt/mL). Sometimes the drop factor is also stated on the top part of the chamber. To calculate IV drip rates, you must know this information. The tubing for these sets includes a roller clamp (Fig. below) that you can open or close to regulate the drip rate;
4. 4. Use a watch or a clock with a second hand to count the number of drops per minute in the chamber (Fig. below). The Dial-a-Flow device (sometimes referred to as Dial-a-Flo) is an extension IV tubing that attaches to the primary IV tubing. It is calibrated in milliliters per hour; you ―dial‖ the rate, and the device regulates the flow. The roller clamp must be open all the way. Usually, these devices are not used with an infusion pump. The rate is still an approximate amount, and changes in the patient/client position can affect the flow rate. INFUSION PUMPS Electric infusion pumps also deliver IV fluid. Some are easy to operate; others are more elaborate. You must enter two pieces of information: the total number of milliliters to be infused and the number of milliliters per hour. Pumps used in specialty units also allow you to input the
5. 5. name of the medication, the concentration of the medication, the amount of fluid, and the patient/client‘s weight. The infusion rate is set in milliliters per hour, and the pump automatically calculates the dose in milligrams, micrograms etc. There are several manufacturers of IV pumps; some pumps use regular IV tubing, while other pumps use tubing specific to that IV pump. All IV pumps allow you to program the primary IV rate, volume to be infused, secondary IV rate, and total volume that has infused over a period of time. The pump can also calculate the dosage based on weight. The tubing factor for an IV infusion pump is 60gtt/mL; however, the rate is stated and programmed as milliliters per hour. A Buretrol is an IV delivery system with tubing and a chamber that can hold 150mL delivered as microdrip (1mL = 60drops). (This device is sometimes referred to as a Volutrol.) The top of the Buretrol has a port so that a reservoir of fluid can be added. The Buretrol is a volume control because no more than 150mL can be infused at one time
6. 6. .LABELING IVS Every IV must be labeled so that any professional can check both the fluid that is infusing and the drip rate. A typical order includes the following information:  Patient/client name, room, bed number, date, and time  Order: 500 mL D5W1⁄2NS. Rate: 50 mL/hr. Many factors can influence this drip rate in gravity infusion once it has been calculated and set. These include positional problems, temperature and other external factors. However, this method has no means of alerting staff to impending errors, or any other infusion-related problems. Furthermore, it is reliant on using the force of gravity to deliver the fluid accurately to the patient. Apart from fluid viscosity, type of cannula and clinical complications after set up, other factors can affect the initial rate of infusion. These include static pressure, temperature, fluid level, patient position and drip factor Many factors may interfere with the drip rate. When you are not using an infusion pump, gravity will cause the IV to vary from its starting rate; you will need to observe and assess the infusion and IV site frequently. You‘ll need to monitor other conditions as well. As the amount of fluid decreases in the IV bag, pressure changes occur—and they, too, may affect the rate. The patient/client‘s movements can kink the tube and shut off the flow; they can change the position of the needle or catheter in the vein. The needle can become lodged against the side of the blood vessel, thereby altering the flow, or it may be forced out of the vessel, allowing fluid to enter the tissues (infiltration). (Signs of possible infiltration are swelling, pain, coolness, or pallor at the insertion site. If you notice any of these signs, discontinue the IV and start a new one at another insertion site.) Infusion pumps have an alarm system that beeps to alert you when the rate cannot be maintained or when the infusion is nearly finished. Be sure to check the infusion pump frequently, and know how to troubleshoot the various alarms.  STATIC PRESSURE: The pressure (in mmHg) exerted on the fluid varies according to the height difference between the patient access site and the fluid bag. An optimum height of one meter above the patient should be sufficient to overcome initial venous
8. 8. • contraindications • nursing implications in administration • signs of effectiveness • possible drug interactions  The nurse should be aware of the patient/client‘s diagnosis and medical history, especially relative to drugs taken. Be especially alert to over the counter drugs (OTC) or herbal remedies which patients/clients often do not consider important. Check for drug allergies.  Assess the patient/client‘s need for drug information. Be prepared to implement and evaluate a nursing care plan in drug therapy. SIX RIGHTS BEFORE ADMINISTERING MEDICATIONS  Right medication  Right patient/client  Right dosage  Right route  Right time  Right documentation. MEDICATION ORDERS GUIDELINES  Only licensed physicians or health care providers can write orders/prescriptions. Nurse practitioners are licensed in all states to write orders, although some restrictions apply and vary state to state.  Medical students may write orders on charts, but orders must be counter signed by a house physician before they are legal. Medical students are not licensed.  In states that allow nurses or paramedical personnel to prescribe drugs, these caregivers must follow hospital guidelines when carrying out orders.  Do not carry out an order that is not clear or is illegible. Check with the physician or healthcare provider who wrote the order—do not assume anything.  Do not carry out an order if a conflict exists with nursing knowledge. For example, Demerol (meperidine) 500 mg IM is above the average dose. Check with the physician or healthcare provider who wrote the order.  Nursing students should not accept oral or telephone orders. The student should refer the physician to the instructor or staff nurse.  Professional nurses may take oral or telephone orders in accord with institutional policy. The nurse must write these orders on the chart, and the physician or healthcare provider must sign them within 24 hours. Verbal orders are discouraged, and the physician should write the order if physically present in the nursing unit. Physicians and nurse practitioners order medications using the six rights of medication administration including the: 1. Right patient 2. Right drug 3. Right dosage 4. Right route 5. Right time 6. Right documentation Right Patient
11. 11.  blood products  medications • A PHYSICIAN’S ORDER for intravenous fluid therapy must include  the type/name of solution  the dose  the unit of dose is expressed as a quantity to be given in unit time and it includes the following two: • quantity of solution in mililitres, litres, milligrams, grams, international units, or equivalent • unit time period/duration for administration in seconds, minutes or hours  the quantity of the solution to be administer or the total time duration of administering the dose  infusion rate in milliliters per second, minute or hour or drops per second, minute or hour) e.g. some institutions or areas (paediatrics) • THE NURSE is responsible for regulating infusion rate by:  Calculating flow rate { milliliters per hour (ml/h)}  Choosing a drop factor and Selecting the appropriate IV set with chosen drop factor  Calculating the drip rate (gtt/min) that is needed to deliver the ml/h with the chosen drop factor.  Regulating the number of drops entering the drip chamber by using the roller clamp on the tubing to adjust the flow rate ( count number of drops for one minute) or the infusion pump  Regularly checking whether the drip is flowing at the calculated rate i.e. hourly • The flow rate is regulated either  manually by straight gravity  via an electronic infusion pump or controller  A controller electronically regulates drop rate by gravity  Whereas an infusion pump consistently exerts pressure against the tubing or the fluid at preselected rate. • Intravenous set or intravenous tube has a drip chamber at one end of the IV tubing that connects the tubing to the IV solution (bag or bottle) • The IV solution must pass through this drip chamber which has an opening that regulates the drops/ml (gtts/ml) that enters the tubing. IV SET/GIVING SET/INFUSION SET: A drop is abbreviated gtt, with gtts used for the plural. These abbreviations come from gutta, the Latin for drop .The gtt/ml (drop factor), which varies according to the manufacturer of the tubing will be displayed on the tubing package. The eye of the dropper greatly influences the actual number of drops required to move 1 mL of fluid into the drip chamber. Drop factor is the number of drops through the eye of dropper of a given set that is required to move (infuse) 1ml of the fluid into the drip chamber (i.e. patient). The label on the tubing box will indicate the dropper capacity of the specific tubing used*. The calibration of IV tubing in gtt/ml is known as the drop factor. Common macrodrop factors are 10 gtts/mL, 15gtts/mL, 20gtts/mL and the common microdrop factor are 40gtts/ml, 50gtts/ml and 60gtts/mL. Determine drip capacity by choosing the microdrop chamber or macrodrip chamber.
12. 12. If you are infusing UNDER 60 ML/HR., then choose a MICRO OR MINI DRIP SET which delivers 40-60gtts/ml. The SIZE OF CANNULA required will be determined by the type of fluid to be infused and the size and condition of the patient’s veins. The smallest gauge capable of achieving the required flow rate should be used (RCN 2010). The administration sets are constructed so that the orifice in the drip chamber delivers a predictable number of drops for each milliliter of fluid. The most common sets are called macrodrip sets. These deliver 10-20drops per ml. These sets do vary, so consult the manufacturer‘s package for a correct figure. Remember that this figure is correct for regular, water-type fluids; when very viscous fluids, such as those containing amino acids and fats, are given, the drops per ml may be fewer. (The figure is usually supplied with the product). Most manufacturers also supply microdrip sets. These sets deliver 40-60 drops per ml and can be identified by the fine metal orifice in the drip chamber. Blood administration sets are characterized by a larger lumen, which delivers fewer drops per ml, and a large built-in filter in the drip chamber, which removes any clots or precipitates in the blood. Giving set is to replace every 72hours for safety and prevent entry of microorganism. Blood or parenteral nutrition giving sets should be change more frequently *Check tubing package-may be 10, 15, 20 (macrodrip) or 40, 60(microdrip) gtt/ml. Microdrip is selected if Flow Rate calculated or stated is less than 60 ml/hr. Patients can receive a medication through a port in an existing IV line. This is called INTRAVENOUS PIGGYBACK (IVPB): The medication is in a secondary bag. The secondary bag is higher than the primary bag so that the pressure in the secondary line will be greater than the pressure in the primary line. Therefore, the secondary medication infuses first. Once the secondary infusion is completed, the primary line begins to flow. Be sure to keep both lines open. If you close the primary line, when the secondary IVPB is completed the primary line will not flow into the vein. A typical IVPB order might read: cimetidine 300 mg IVPB q6h in 50 mL NS infuse over 30 min. This is an order for an IV piggyback infusion in which 300 mg of the drug cimetidine diluted in 50 mL of a normal saline solution must infuse in 30 minutes. So, the patient receives 300 mg of cimetidine in 30minutes via a secondary line, and this dose is repeated every 6 hours. A primary IV line (right) and an IVPB (or secondary) line (left). Fluid flows continuously through the primary line into the patient/client’s vein. At timed intervals, medication placed in an IVPB is attached by tubing to the primary IV for delivery to the patient/client. The primary fluid is lowered and the IVPB fluid flows. After the IVPB has infused, the primary fluid begins infusing again. An IV infusion pump may also be used, where medication in the IVPB is infused through the pump.
13. 13. Some IV medications are administered not continuously but only intermittently, such as every 4, 6, or 8 hours. This route is termed intravenous piggyback or (IVPB). The term admixture refers to the premixed IVPB. Most of these drugs are prepared in powder form. The manufacturer specifies the type and amount of diluent needed to reconstitute the drug; later, you, the nurse, connect the IVPB (containing the reconstituted drug) by IV tubing to the main IV line. Some IVPB medications come premixed from the manufacturer. For other medications, the institutional pharmacy may reconstitute and prepare IVPB solutions in a sterile environment using a laminar flow hood. This procedure saves nursing time, because when you are ready to administer the drugs, they have already been prepared, labeled, and screened for incompatibilities. Nevertheless, the nurse still bears considerable responsibility: You must check the diluent and volume. You must also check the dose and the expiration date of the reconstituted solution; note whether the IVPB should be refrigerated before use or whether it can remain at room temperature until hung. Finally, you must calculate the drip rate and record this information on the IVPB label before hanging the bag. CHOOSING THE INFUSION SET Experience will enable you to judge which IV tubing to use. In clinical settings, the guidelines below will help you make your choice. An electric infusion pump poses no problem, because it will deliver the amount programmed. Specialized pumps in neonatal and intensive care units can deliver 1 mL/hour and even less. Specialized syringe pumps also can deliver less than 1 mL/hour. When an IV pump is not available, consider these guidelines: Use microdrip when • The IV is to be administered over a long period • A small amount of fluid is to be infused • The macrodrops per minute are too few (Without an infusion pump, IV fluids flow by gravity. Blood flowing in the vein exerts a pressure. If the IV is too slow, the pressure of the blood in the vein may back up into the tubing, where it may clot and cause the IV to stop infusing.) Use macrodrip when • The order specifies a large amount of fluid over a short time • The microdrips per minute are too many, and counting the drip rate becomes too difficult INFUSION RATE CALCULATION Generally there are at least three methods employed in medication calculation. These are dimensional analysis, proportion and formula method. No one method is best for solving every type of problem. Several good approaches are available, however one of the best is dimensional analysis as the name implies, in dimensional analysis we use the units (dimensions) that are a part of measurements to help solve (analyze) the problem. Rule #1 in drug calculations - STICK TO ONE METHOD!
14. 14. 1: DIMENSIONAL ANALYSIS/DEDUCTION METHOD Is a process of manipulating units, which are actually descriptions of numbers, to solve mathematical equations. This method of mathematic problem solving is used in chemistry with great success. The goal of this approach to drug calculation problem solving is to: CANCEL OUT UNWANTED UNITS LEAVING ONLY THOSE UNITS YOU WANT YOUR ANSWER TO BE EXPRESSED AS! Think of Unit Equivalence as a link that will help you get the desired units you are solving for. It involves calculating the unknown variable using its units to deduce a formula. (Also known as factor analysis, factor-label method, or unit-factor method, “chemistry math”). This method involves the logical sequencing and placement of a series of ratios (termed factors) into an equation. The ratios are prepared from the given data as well as from selected conversion factors and contain both arithmetic quantities and their units of measurement. Some terms are inverted (to their reciprocals) to permit the cancellation of like units in the numerator(s) and denominator(s) and leave only the desired terms of the answer. One advantage of using dimensional analysis is the consolidation of several arithmetic steps into a single equation. The Mathematical Foundation for Dimensional Analysis Dimensional Analysis relies on two simple mathematical concepts. Concept 1: When a nonzero quantity is divided by the same amount, the result is 1. For example: Because you can also write a division problem in fractional form, you get Since is a fraction equal to 1, and the word ―unit‖ means one, the fraction is called a unit fraction. In the preceding unit fraction, you may cancel the 7s on the top and bottom. That is, you can divide both numerator and denominator by 7. Units of measurement are the ―labels,‖ such as inches, feet, minutes, and hours, which are sometimes written after a number. They are also referred to as dimensions, or simply units. For example, in the quantity 7 days, days is the unit of measurement. The equivalent quantities you divide may contain units of measurement. For example: Or in fractional form: In the preceding unit fraction, you may cancel the number 7 and the unit of measurement days on the top and bottom and obtain the following: Going one step further, now consider this equivalence: Because 7 days is the same quantity of time as 1 week, when you divide these quantities, you must get 1.
15. 15. So, both and Or in unit fractional form: and Other unit fractions can be obtained from the equivalences. Equivalents for some common units of measurement 12 inches (in) = 1 foot (ft) 2 pints (pt) = 1 quart (qt) 16 ounces (oz) = 1 pound (lb) 60 seconds (sec) = 1 minute (min) 60 minutes (min) = 1 hour (h or hr) 24 hours (h or hr) = 1 day (d) 12 months (mon) = 1 year (yr) Concept 2 When a quantity is multiplied by 1, the quantity is unchanged. In the following examples, the quantity 2 weeks will be multiplied by the number 1 and also by the unit fractions and Consider the previous line again. This time you cancel the week(s)! ( ) uivalents for Some Common Units of Measurement So, This shows how to convert a quantity measured in weeks (2 weeks) to an equivalent quantity measured in days (14 days). With the Dimensional Analysis method, you will be multiplying quantities by unit fractions in order to convert the units of measure. This procedure demonstrates the basic technique of Dimensional Analysis. Many of the problems in dosage calculation require changing a quantity with a single unit of measurement into an equivalent quantity with a different single unit of measurement; for example, changing 2 weeks to 14 days as was done above. Other problems may involve changing rates of flow to equivalent rates of flow. It is important to understand the following four terms that provide the basis for dimensional analysis.  Given quantity: the beginning point of the problem commonly the doctor‘s order.  Wanted quantity: the answer to the problem  Unit path: the series of conversions necessary to achieve the answer to the problem  Conversion factors: equivalents necessary to convert between systems of measurement and to allow unwanted units to be canceled from the problem.
16. 16. Each conversion factor is a ratio of units that equals 1. UNIT - a dimension that is given to a number. For Example - If you are to give 50, you would ask, 50 what? This could be mg, mL, tablets, teaspoons, etc. (mg, mL, tablets, tsp. are the units) UNIT EQUIVALENCIES - the value of equivalencies between two units. For Example: 1 kg = 2.2lbs, 5mL = 1tsp, 30mL = 1ounce, 1gram = 1000mg, 60minutes = 1hour, 15gtt = 1mL, 1grain = 60mg, 1IU=1000mIU CONVERSION FACTOR - it is a unit equivalency written as a fraction. or (The above is simply stating that 60 mg is equal to 1 grain or 1 grain is equal to 60mg….both mean the same thing regardless of how they are set up). Conversion factors are derived from information provided in the dosage problem. Dimensional analysis is a method of calculation in which a series of ratios or factors, organized in the form of fractions, are multiplied.  Factors are two quantities that are related, such as 30 mg in 2 ml.  In dimensional analysis, factors are expressed as fractions.  30 mg in 2 mL may be expressed as: o or One unit of measurement is converted to another unit of measurement by means of conversion factors or unit equivalence. A conversion factor is a unit equivalence expressed as fraction such as 2.2lb = 1 kg or 1,000 mcg = 1 mg. ie or  Conversion factors link units of measurement of what is desired with units of measurement of what is available.  Conversion factors are arranged in the form of a fraction. o 1,000 mcg = 1 mg may be expressed as: o or For example: Covert 50 lb to kg The Unit Equivalence (link) is: 2.2 lb = 1 kg Note: is another way of saying that 2.2 lb = 1 kg The desired units we are seeking are kg in this example. Using Dimensional Analysis in the above example, we set the problem up in the following format: Problem: Covert 50 lb to kg 50 lb X = 22.7 kg (lb cancel one another out and we are left with kg, the units we want) Another way of stating this problem is: How many kg are there in 50 lb? or 50 lb is equal to how many kg? In this example, the units of lbs cancel each other out, leaving behind kg (the units we want our answer to be in). We have eliminated the units we don‘t want and are left with the units we do want.
18. 18. Step 3. Establish the unit path (to go from the given quantity and its unit to the arithmetic answer in the wanted unit), and identify the conversion factors needed. This might include:  (a) A conversion factor for the given quantity and unit, and/or  (b) A conversion factor to arrive at the wanted unit of the answer. Step 4. Set up the ratios in the unit path such that cancellation of units of measurement in the numerators and denominators will retain only the desired unit of the answer. Step 5. Perform the computation by multiplying the numerators, multiplying the denominators and dividing the product of the numerators by the product of the denominators. To create an equation using dimensional analysis:  Collect all data (variables) for the questions.  Step 1: draw a long straight line (‗magic line‘) and place an equals to sign at the right end of the line.  Figure out what are you solving for (ask yourself what am I solving for?) and write its unit on the right side of the equals to sign. With space between the equals to sign and the unit so that the value of unknown variable (what you are looking for) can be written in the space provided after solving the equation  Step 2: Identify the first variable to be written on the left side. It can either be:  The doctor‘s order (given quantity)  or  It is determined by the ‗numerator unit‘ of the unknown variable. The numerator unit of the first variable should be the same as the numerator unit of what we are solving for.  The variables are written such that the numerators and their units are on top of the magic line. The denominator and its unit are below the magic line.  If the similar unit of the selected variable is the ‗Numerator unit‘ then the variable is written directly. If the similar unit of the selected variable is the denominator unit then the variable is written as an inverse so as to position the similar unit as the numerator.  Step 3: Each subsequent variable is written as a product of the previous variable and the subsequent variable is determine by o The denominator unit of the previous variable. A variable with one of its units similar to the ‗denominator unit‘ of the previous variable is selected as the next variable. The ‗numerator unit‘ of this selected subsequent variable should be similar (SI unit) to the ‗denominator unit‘ of the previous variable. If the similar unit is the numerator unit of the subsequent variable then the subsequent variable written directly as a multiple. If similar unit is also a denominator in the subsequent variable then the variable should be written as an inverse so that the similar unit can be the numerator. o Conversion factor for the previous variable to be able to cancel out the unwanted units  Step 4: More variables are added until all the unwanted units on the left side cancelled out except the wanted units (one as numerator and other as denominator) similar to those units of the unknown variable (units of what you are looking for)  Note check whether each variable needs conversion and convert it (by multiplying it with a conversion factor) before writing the subsequent variable.
19. 19. Note if a variable has two units first one is the numerator and the second the denominator. Multiplying by variable as an inverse is equal to dividing by the variable. A/B= 1÷B/A so if the desire unit is in a position opposite to its required position then we inverse the variable. If drops is the ‗numerator unit‘ of the unknown variable or the ‗denominator unit‘ of the previous variable, then we need to identify a variable with one of its units as drop to be selected as the first variable after the equals to sign or as the subsequent variable respectively. Secondly if drops is the ‗numerator unit‘ of the selected variable then the selected variable be written directly for the first variable on the left side of the equals to sign but if it‘s the denominator units of the selected variable then the subsequent variable will be written as an inverse. The variables are written as a product of one another (multiplication). The next variable to be multiple is determined by the ‗denominator unit‘ of the previous variable. USING SEQUENTIAL METHOD (OTHER WAY) Start with the unit of measurement that is to be calculated: o For example, to convert mcg to mg, mg are desired, so start with:  mg = Find the quantity with the same unit of measurement or the conversion factor with the same unit of measurement as what is desired (1 mg = 1,000 mcg) and place this (mg) in the numerator.   Remember, fractions are set up as the numerator over the denominator: o The fractions are arranged so that unwanted units cancel out and desired units remain.  A single quantity not associated with a related quantity is expressed as a fraction by placing it in the numerator and placing 1 in the denominator. o If mcg are available and mg are desired, arrange the conversion factor such that mcg may be cancelled out to leave mg remaining:  Mg= × Cross out the identical units that are across and diagonal:  Mg= × In dimensional analysis, fractions are multiplied. To multiply fractions, first multiply across the numerator, and then multiply across the denominator. Finally, divide the numerator by the denominator. Equations involving multiple factors are arranged so that the unit of measurement in the denominator of one factor is placed in the numerator of the following factor and so on. Unwanted units are then cancelled.  Remember: o A single quantity not associated with a related quantity is expressed as a fraction by placing it in the numerator and placing 1 in the denominator. o Factors are two quantities that are related. Related quantities are arranged as fractions. Process of calculating dosage using dimensional analysis:
20. 20. MEDICATIONS: STEP 1: What is to be calculated? What is the unit of measurement that is to be calculated? STEP 2: What quantities are needed? Needed = desired The quantity needed may be the prescribed dosage. STEP 3: What quantities are available? Available = have STEP 4: Are conversion factors needed to find the units that are to be calculated? Conversion factors link units of measurement of what is available with units of measurement of what is to be calculated. STEP 5: Set up an equation of factors using needed and available quantities and the conversion factors. STEP 6: Multiply the numerator. Multiply the denominator. Divide the numerator by the denominator. STEP 7: Reassess to determine if the amount makes sense. IV Flow Rates  To determine mL/hr when administering fluid via an IV pump, the process is the same as the ratio and proportion/desired over have methods.  When calculating gtt/min, follow these steps: o STEP 1: What is to be calculated?  What is the unit of measurement that is to be calculated?  gtt/min o STEP 2: What quantities are needed? Needed = desired  The quantity needed may be the prescribed dosage.  Volume (mL)/infusion time (min or hr) o STEP 3: What quantities are available? Available = have  Drop factor (gtt/mL) o STEP 4: Are conversion factors needed to find what is desired?  60 min = 1 hr o STEP 5: Set up an equation of factors using needed and available quantities and the conversion factors.  If minutes are available, the process is the same as the ratio and proportion/desired over have methods.  If hours are available:  IV flow rate(gtt/min) gtt/min= × ( ) ( ) ×  Cancel out identical units:  IV flow rate(gtt/min) gtt/min= × ( ) ( ) × o STEP 6: Multiply the numerator. Multiply the denominator. Divide the numerator by the denominator. o STEP 7: Reassess to determine if the amount makes sense.
21. 21. EXAMPLE Calculate the drip rate of 3000mls of 5% dextrose over 24hrs using an IV set with drop factor of 20drops/ml?  Collect data:  Drip rate (DR) =?  Volume (V) = 3000ml  Concentration ( C )= 5% dextrose = 5g dextrose in 100ml of 5% dextrose solution = 5g/100ml  Time (T) = 24hrs  Drop factor (DF) = 20drops/ml METHOD 1(SEQUENTIAL METHOD) STEP1: Identify the wanted variable (unknown variable/ what you are looking for) and its unit.  Drip rate drops/min Step2: Identify the given quantity (doctor‘s order) and its units.  3000ml in 24hrs Step 3: Identify known equivalent or conversion factors.  5% dextrose =5g/100mL,  20drops/min,  60min/hr Step 4: Draw the magic line  ---------------------------------- STEP 4a: Write the given quantity with its units at the beginning of the line making sure the numerator is above the line and denominator is below the line.  STEP4b: Write an equal to sign at the end of the magic line.  STEP4c: Write the units of the wanted variable after the equals-to sign making sure you leave some space between the equals to sign and the unit of the wanted quantity.  Step5: Place the equivalent or conversion factors so that the unwanted units cancel out until the wanted units similar to units of wanted quantities are left.  STEP6: Multiply all the numerators.  Multiply all the denominators  Divide the two values and record it in the space provided METHOD 2 (RANDOM METHOD)  Step 1: Unknown variable (what are you looking for- ‗wanted quantity‘) is drip rate (DR) and its unit is drops/min.
22. 22.  —―—―—―—― = drops/min Step 2: Write the given quantity with its units at the beginning of the line making sure the numerator is above the line and denominator is below the line.  Step 3a:insert all the conversion factors without order making sure all unnecessary units are cancelled out ie 1hr=60mins, 20drops=1ml  Step 3b: need conversion factor to covert hours to minutes and relationship of hours to minutes is 1hr=60min, i.e. 1hr/60min. DR (drops/min) = 20drops/min x 3000ml x 1/24hrs x 1hr/60min= 41.67drops/min=41drops/min  Our equation has now same units on both sides of the equation if we cancels like ones out hence we can now solve the equation.  Step 4; compute your answers by multiplying all the numerator and multiplying all the denominators then dividing the two results Question 19 below: A:  Data collection:  Concentration ( C ) = 1.5%=1.5g of glycine in 100ml of 1.5% glycine solution=1.5g/100ml  Flow rate (FR) = 80ml/min (doctor‘s order)  Gram (M) = ?  Time (T)=3hrs METHOD 3(SEQUENTIAL-ANOTHER WAY) STEP1: Identify the wanted variable (unknown variable/ what you are looking for) and its unit.  mass grams g Step2: Identify known variable with numerator unit as the wanted quantity.  1.5g/100ml Step 3: Identify known equivalent or conversion factors.  1.5% glycine= 1.5g of glycine in 100ml of 1.5% glycine solution= 1.5g/100ml  Time 3hours  60min=1hr Step 4: Draw the magic line  ---------------------------------- STEP 4a: Write the known variable with numerator the same as the wanted quantity at the beginning of the line making sure the numerator is above the line and denominator is below the line.  STEP4b: Write an equal to sign at the end of the magic line.  STEP4c: Write the units of the wanted variable after the equals-to sign making sure you leave some space between the equals to sign and the unit of the wanted quantity.  Step5: Place the equivalent or conversion factors so that the unwanted units cancel out until the wanted units similar to units of wanted quantities are left.  STEP6: Multiply all the numerators.
23. 23.  Multiply all the denominators  Divide the two values and record it in the space provided QUESTION: An IV of 1000ml of 5% D/0.9% NaCl is started at 8pm. The flow rate is 38drops per minute, and the drop factor is 10drops per milliliter. At what time will this infusion finish? ANSWER: SEQUENTIAL METHOD Given quantity: 1000ml (volume to be infuse) Known equivalences (conversion factors): 10gtt/ml (drop factor) 38gtt/min (flow rate) 1hr=60min Wanted quantity: hr? (Time) =4hrs 23min Time of finish will be 8pm + 4hr 23min= 12:23am EXAMPLE The prescriber writes an order for 1000ml of 5% D/W with 10units of Pitocin (oxytocin). Your patient must receive 3mU of this drug per minute. Calculate the flow rate in microdrops per minute. ANSWER SQUENTIAL METHOD Given quantity: 3mU/min (dosage rate) Known equivalences: 10units/1000ml (strength) 60gtt/ml (standard microdrop drop factor) 1unit=1000mU Wanted quantity:?mcgtt/min (flow rate) EXAMPLE Gynaecologist performing hysteroscopy uses 1.5% Glycine as distending medium. If the flow rate is 80ml/min, how many grams of glycine will the infusion into the uterus if the operation lasted for 3hrs? If the flow rate is change to 100ml/min what is the dose of glycine infusion? If the drop factor of the IV set is 10drops/ml what is the new drip rate? The assistant changes the giving set to give 10drops/sec in order to be able to give 150mg/min. what is the new flow rate in ml/min. what is the drop factor of the new IV set?
24. 24. SEQUENTIAL METHOD Given quantity =80ml/min (doctor‘s order) Wanted quantity (what am looking for) amount grams g Unit equivalencies: 1.5% glycine i.e. 1.5g/100ml Time 3hrs 60min=1hr Hence Unit path way SEQUENTIAL METHOD (OTHER WAY) Data collection: Concentration (C) = 1.5%=1.5g of glycine in 100ml of 1.5% glycine solution =1.5g/100ml Flow rate (FR) = 100ml/min (doctor‘s order) Dose (D) =? Dose (g/min) = ⁄ SEQUENTIAL METHOD ⁄ C: Data collection: Flow rate (FR) = 100ml/min Drop factor (DF) = 10drops/ml Drip rate (DR) =? Drip rate (drops/min) ⁄ SEQUENTIAL METHOD Wanted quantity drip rate drops/min Given quantity 100ml/min Unit equivalent drop factor 10drops =ml Unit path E: RANDOM METHOD Data collection: Concentration (C) = 1.5g of glycine in 100ml of 1.5% glycine solution =1.5g/100ml Dose (D) = 150mg/min Drip rate (DR) = 10drops/sec Flow rate (FR) =? Flow rate (ml/min) ⁄ Note because variable available is 1.5g/100ml and variable need should have ml as numerator hence the variable is inversed. Also changing gram to mg and to cancel both g and mg variable need is 1g/1000mg, i.e. 1g=1000mg : RANDOM METHOD Data collection:
25. 25. Concentration (C) = 1.5%=1.5g of glycine in 100ml of 1.5% glycine solution =1.5g/100ml Dose (D) = 150mg/min Drip rate (DR) = 10drops/sec Drop factor (DF) =? Drop factor (drops/ml) = ⁄ SQUENTIAL METHOD Given quantity dose=10drops/sec Wanted quantity drop factor drops/min Unit equivalent drip rate 150mg/min 1.5mg/100ml 1min=60sec 1g=1000mg ⁄ The physician has ordered 500mL D5W with 10units oxytocin intravenously. Begin at 1mU/min and then increase by 1mU/min every 30minutes until active labor is achieved. Maximum dose is 28mU/min. A: Calculate the IV rate (ml/hr) for the beginning infusion B: Calculate the IV drip rate for the beginning infusion. C: What is the maximum IV rate(ml/hr) the Pitocin infusion may be set for? D: What is the maximum IV drip rate the Pitocin infusion may be set for? A: data Given quantity; dose = 1mu/min Wanted quantity; flow rate = ml/hr Unit equivalents; 500ml=10unit, 1000mU=1unit, 60min=1hr Unit path: D: data Given quantity; dose =28mU/min Wanted quantity; drip rate = drops/min Unit Equivalent; 60gtt=ml, 10unit=500ml, 1000mU=1unit, Unit Path; Ratio: is the numerical relationship between two dimensions (units). It means part per part it can be express as A: B A/B Ratio can be converted into fraction which can be converted to decimals which can also be converted to percentages. Eg 1:2=1/2=0.5=50% Ratio 1:2 means 1part per 2parts e.g. 20mg/ml means 20mg of solute per ml of solution.
26. 26. 2: RATIO & PROPORTION A ratio is the same as a fraction: it indicates division. A ratio is used to express a relationship between one unit or part of the whole. A slash (/) or colon (:) is used to indicate division, and both are read as ―is to‖ or ―per.‖ The numerator (N) of the fraction is always to the left of the colon or slash, and the denominator (D) of the fraction is always to the right of the colon or slash. With medications, a ratio usually refers to the weight of a drug (e.g., grams) in a solution (e.g., mL). Therefore, 50 mg/mL = 50 mg of a drug (solute) in 1 mL of a liquid (solution). For the ratio of 1 part to a total of 2 parts, you can write 1:2 or 1/2. A proportion is two ratios that are equal. A proportion can be written in the fraction or colon format. In the fraction format, the numerator and the denominator of one fraction have the same relationship as the numerator and denominator of another fraction (they are equivalent). The equals symbol (=) is read as ―as‖ or ―equals.‖ In the colon format, the ratio to the left of the double colon is equal to the ratio to the right of the double colon. The double colon (::) is read as ―as.‖ You can also use an equals symbol (=). The first and fourth terms are called extremes and the second and third terms are called the means. Is the relationship between two ratios. It equates two ratios. There are two ways of expressing proportions. It use variables with one common unit and based on their units it relates them through proportion to find the unknown variable. It uses the common unit between the variable to find the unknown. It is commonly used to calculate drugs doses and injections. It may sometimes needs multiple steps before the final answer  PROPOTIONS EXPRESSED AS TWO RATIOS: This uses the relation of the various variables as proportion to one another. Its works on lot of logic deduction base on how one variable is related to the next base on their common unit. It is easier for use by those with poor mathematical skills. It does need the nurse to memorize any formula hence best for most nurse and health care worker. Example if drop factor 15drops/ml of drop rate is 45drops/min. flow rate in ml/min will be: the common unit between the two known variables is drops and the unit of the unknown variable is ml/min. Hence: 15drops :1ml=45drops : x  PROPORTION EXPRESSED AS TWO FRACTIONS: It is similar to proportion but put the units into fractions rather than proportion. 15drops/1ml = 45drops/x In proportion expressed as 15drops:1ml=45drops:3ml. The two inner values are called the ‗means‘ and the outer values are called the ‗extremes‘. The product of the means is equal to the product of the extremes. I.e. 1ml×45drops=15drops×3ml. A proportion consists of two ratios of equal value. The ratios are connected by a double colon (::), which symbolizes the word as. 2 : 3 :: 4 : 6 Read the above proportion: ―Two is to three as four is to six.‖ The first and fourth terms of the proportion are the extremes. The second and third terms are the means. 2 : 3 :: 4 : 6 2 and 6 are the extremes 3 and 4 are the means A helpful way to remember the correct location of the extremes and means is E = The end of the problem M = The middle of the problem
27. 27. In a proportion the product of the means equals the product of the extremes because the ratios are of equal value. This principle may be used to verify your answer in a proportion problem. 3 4 = 12, product of the means 2 6 = 12, product of the extremes If three terms in the proportions are known and one term is unknown, an x is inserted in the space for the unknown term. 2 : 3 :: 4 : x RATIO AND PROPORTIONS • Ratio is same as fraction  Use to express a relationship between two units or quantities  A slash (/) or colon (:) is use to indicate division and both are read as is to or per  With medication usually refers to weight of drug (i.e. gram) in a quantity of the solution ( i.e. cc‘s)  50mg/cc= 50mg of a drug (solute) in 1cc of a liquid (solution) • A proportion states that two ratios are equal  In fraction form where two fractions are equal1/3=3/9  Colon form e.g. 1:3 :: 3:9 • Frequently in dose calculation problems one quantity is known ( i.e. 100mg per mL = 100mg/1mL) and it is necessary to find an unknown quantity because the physician has ordered something different from what is available ( i.e. 75mg) In proportion problem the unknown quantity (? mL) to give 75mg is identify as x SOLVING A SIMPLE PROPORTION PROBLEM 1. Multiply the extremes. 2. Multiply the means. 3. Place the product that includes the x on the left of the equal sign and the product of the known terms on the right of the equal sign. 4. Divide the product of the known terms by the number next to x. The quotient will be the value of x. COLLECT ALL THE DATA FOR THE QUESTION Step 1: Identify the unknown variable Step 2: Identify a variable that has one of its unit similar to one of the unit of the unknown variable. Step 3: Identify a second known variable that has its numerator unit similar to the other unit of the selected variable. Step 4: Relate the two selected variables as a ratio or as a fraction inn order to help in finding the second unit of the unknown variable. Step 5: solve for the unknown. Pitocin (oxytocin) 10 units/1,000 mL RL, start at 0.5mIU/min increases by 1 mIU/min q20 minutes. What is the rate of flow in mL/h for the initial dose of Pitocin? The drop factor is 60mcgtt/ml. Calculate the flow rate in mcgtt/min.
28. 28. Data collection: Concentration (C) = 10units/1000ml Dose (D) = 0.5mIU/min at 1mIU/min Time (T) =20mins Flow rate (FR) =? Drop factor (DF) = 60mcgtt/ml Drip rate (DR) =? Step 1: unknown variable is flow rate (FR) and its unit is ml/min Step 2: variable 10unit/1000ml has one of its unit similar to the unknown variable flow rate. Step 3: variable 0.5mIU/min has one of its units similar to the identified variable 10IU/1000ml. Step 4: relate the two variables: 10000mIU: 1000ml :: 0.5mIU: x or 10000mIU ÷1000ml= 0.5mIU ÷ x Step 5: x= = 0.05ml Hence 0.05ml is given in one minute i.e. flow rate is 0.05ml/min. b. 60gtt:1ml::Xgtt:0.05ml 60gtt×0.05ml=1ml×Xgtt Xgtt = =3gtt Drip rate =3gtt/min 3: FORMULA METHOD This uses various formulas in the medication calculation. These formulas need memorization. It is faster and less tedious if the formula is remembered. In certain instances the nurse (health care worker) may forget the formula or even memorize the wrong one. This may lead to giving wrong amount of medication to the patient with detrimental effects First step is to calculate the flow rate, this value would then give you a crude idea as to whether to choose microdrop or macrodrop as your drop factor then second step is drip rate can be calculated by using the product of flow rate and the drop factor. Hence  STEP ONE: The flow rate is calculated either  by dividing the total volume (in millilitres) prescribed for the patient by the number of hours required for the delivery. This gives the flow rate in milliliters per hour (ml/hr).  ( ) ( )) ( )  or by dividing the dose of the medication by the final concentration into which the drug/ medication is prepared.  Flow RATE (FR)= ( ) ( )  Dose is amount per unit time. It is calculated by dividing amount of drug over by the time to give the drug.  ( ) ( ) ( )
29. 29.  Concentration is the amount of drug per unit volume of the solution. It is amount of drug divided by the total volume of the solution. ( ) ( ) ( ) • STEP TWO: The flow rate (ml/hr) is then multiplied by the drip factor of the selected, chosen or identified giving set(nominal number of drops per ml) to give the drip rate i.e. the total number of drops required per hour(Dougherty and Lister 2004): note if flow rate is less than 60ml/hr. a microdrip is chosen. • To obtain the number of drops required per minute, divide the number of drops per hour by 60 (number of minutes in 1 hour): • To calculate (flow rate) milliliters per hour you need two pieces of information • The total volume to be infuse in milliliters • The total time for infusion in hours • Use this standard formula ( ) ( ) ( Example: from question 1 of the problem below we are to give 1000ml D5/RL in 8hrs hence • To calculate the time of infusion you need • Total volume of infusion (milliliters) • Rate of infusion (milliliters/minute or hours) Use the formula ( ) ( ) ( ) Example If Doctor ordered that patient should be giving 2L of NS at a rate of 100ml/hr. • To calculate drops per minute (drip rate), you need • two pieces of information • Flow rate • Drop factor • Use the formula ( ) ( ) ( ) Note: variables should be converted to similar units before inserting into the formula. FOR FLUID INFUSION ( ) ( ) ( ) ( ) Other formula includes
30. 30. ―Desired Over Have Times Vehicle‖ Drug Formula - This formula is useful when solving problems that involve oral and injectable drugs. One must have the following information in the ―story problem‖ in order to use this formula: Dose Required = Desired = D Dose on Hand = Have = H Vehicle = How Drug is Supplied = V Give = What We Will Actually Give To Our Patient = G ( ) ( ) ( ) ( ) From the information that is provided in the problem to be solved, certain words or phrases can provide the reader with clues as to how to set up the problem. For example: The ―Desire‖ or ―Need‖ (what is ordered) in the problem is generally written as follows: - ―You have an order to give‖ - ―The doctor‘s order reads, give…‖ - ―The order reads‖ - ―You have an order for‖ - ―You are to give‖ - ―Your patient has an order for‖ - ―Amoxicillin 500 mg is ordered‖ - ―Gentamycin 50mg/kg is ordered‖ (must figure this calculation out to determine what the need or desire is) - ―The recommended dose of drug A is 200-400mg/kg/day‖ (must figure out the range of the recommended dose) The ―Have‖ (what you physically have in your hand) in the problem is generally written as follows: - ―On hand is…‖ - ―Available is…‖ - ―The medication is supplied as‖ - ―The vial reads‖ - ―Amoxicillin is available in…‖ - ―Your patient is receiving‖ - ―You have available‖ - ―The bottle reads‖ - ―Drug A comes in‖
31. 31. The ―Vehicle‖ (form the medication is supplied in) in the problem is generally written as follows: - tablets, capsules, mL, etc. The ―Give‖ is what you will actually give to the patient Remember, many drug calculations require a multi-step approach to solving. You may have to perform several conversions before you can actually set up the final problem to obtain the answer you are seeking. PERCENT • Percentage is Always a division of 100 • It means the ―hundredth part‖ • Has a symbol of % • In solution (combination of solute and solvent) the % means proportion of solute per portion of the solution. It is can be expressed as weight of solute per hundredth portion of the solution (weight/volume)or volume of solute per hundredth volume of solution (volume/volume) • grams of solute per 100ml or 100cc of solution‖ for (w/v) solutions • Millilitres of solute per 100ml or 100cc of solution‖ for v/v solutions  A 5% solution means 5grams of drug (solute) per 100cc (100ml) of solution. Another way of putting it is every 100ml of the 5% contains 5g od the solute  0.9% means 0.9g of solute per 100cc of the solution e.g. normal saline (100cc(100ml) of solution contains 0.9g of NaCl)  10% means 10g of solute per 100cc (100ml)of solution e.g. 10% glucose means every 100ml of 10% glucose contains 10g of glucose  20% means 20g of solute per 100cc (100ml) of solution e.g. 20% mannitol contains 20g of mannitol for every 100ml of the solution  50% means 50g of solute per 100cc (100ml) e.g. 50% MgSO4 means every 100ml 0f the 50% MgSO4 contains 50g of MgSO4. For example question 7 of problem below; The label on the vial of magnesium sulphate is 50% w/v means every 100ml of the 50% MgSO4 contains 50g of MgSO4.In other words 50g of MgSO4 are contain in100mls of the solution from the vial. RATIO STRENGTH The concentrations of weak solutions are frequently expressed in terms of ratio strength. Because all percentages are a ratio of parts per hundred, ratio strength is merely another way of expressing the percentage strength of solutions or liquid preparations (and, less frequently, of mixtures of solids). For example, 5% means 5 parts per 100 or 5:100. Although 5 parts per 100 designates a ratio strength, it is customary to translate this designation into a ratio, the first figure of which is 1; thus, 5:100 = 1:20. When a ratio strength, for example, 1:1000, is used to designate a concentration, it is to be interpreted as follows: For solids in liquids=1 g of solute or constituent in 1000 mL of solution or liquid preparation. • For liquids in liquids = 1 mL of constituent in 1000 mL of solution or liquid preparation. • For solids in solids = 1 g of constituent in 1000 g of mixture.