Mathematics in Anesthesia PPT.pptx

MATHEMATICS IN ANESTHESIA Ratios Ratios are a means of expressing a relationship between quantities, they the expression of a fraction using a different symbol. Example: The blood/gas coefficient for an anesthetic agent's solubility in blood as compared to gas maybe expressed as 2.3 which would i...

MATHEMATICS IN ANESTHESIA Ratios Ratios are a means of expressing a relationship between quantities, they the expression of a fraction using a different symbol. Example: The blood/gas coefficient for an anesthetic agent's solubility in blood as compared to gas maybe expressed as 2.3 which would indicate the agent is 2.3 times more soluble in blood than in gas, thus the ratio of the relationship would be 2.3:1 or 2.3/1 or 2.3. Miler, R.D., Eriksson, L.I., Fleisher, L. & Wiener-Kronish , J.P. (2010). Miler's anesthesia (7th ed.). Philadelphia: Churchil Livingstone/Elsevier. Ratio to MG/ML  Take the second number and divide into 1000  Ex: 1:10,000 = 1,1000/10,000= 0.1mg/ml  1:200,000= 1,000/200,000= 0.005 mg/ml Percent  Percent (%) expressions represent the expression of a quantity in terms of the parts per one hundred. A percent number is a fraction whose numerator is verbalized and whose denominator is assumed or understood to be one hundred.  Simple fractions can be changed to percent (%) by first converting it to a decimal fraction (example: 1/2 =.50) and then multiplying by one hundred and affixing the percent sign (example:.50 x 100 = ­50%). Percent in Pharmacology To convert from a % expression to a decimal, divide by 100. In pharmacology: % solution is expresses as grams / 1.0 milliliter a 100% solution = 1 gram / 1 milliliter Percent to MG/ML  Multiply the percent by 10 to get mg/ml  0.25% * 10 = 2.5mg/ml  5% * 10 = 50mg/ml Different Expression Examples  Propofol is a 1% solution  How many mg/ml?  What is the ratio expression?  Epinephrine is 1:1000  How many mg/ml?  What is the percent expression?  Rocuronium is 10mg/ml  What is the ratio expression?  What is the percent expression? Solute A solute is a substance dissolved in solvent to make a solution. A solute may be in the form of solid, liquid, or gas. A solute may be “pure” drug or a concentrated solution. Solvent A solvent is the component of a solution that is capable of dissolving another substance known as solute. Dissolve means to cause to pass into solution. Dilute means to thin or reduce the concentration of a solute or of a solution in solution to lessen the potency, strength, or purity of it my mixing it with more solvent (usually saline or water when used with drugs). A stock solution is a relatively concentrated solution from which a weaker solution can be made by diluting it with more solvent (usually saline or water when used with drugs). Drug calculation problem: You have a 1% solution of phenylephrine and you desire to make up a 500 cc (ml) bottle of 1:20,000 solution of phenylephrine in Lactated Ringer's. How would you mix up the solution? Given: 1% solution of phenylephrine 500 ml. of Lactated Ringer's Desire: 500 ml. of 1:20,000 phenylephrine in Lactated Ringer's Metric Units of Weight and Volume 1 Kilogram = 1,000 grams 1 liter = 1,000 milliliters or cubic centimeters 1 Gram = 1,000 milligrams 1/1000 gram = 1 milligram 1 milliliter = 1/1,000 liter Metric Terms Metric weight standard: This standard is based on the fact that 1 milliliter of pure water weighs 1 gram at 4 degrees centigrade. Using this standard and generalizing to other solutions, by definition 1 gram of solute with sufficient solvent to make 1 gram per cc of a solution equals 100% solution and the relationship of this may expressed as: 1 gram/cc = 100% solution or a 1:1 solution 1,000 mg/cc = 100% solution or a 1:1 solution Units Drug calculation problem: You have a 1% solution of phenylephrine and you desire to make up a 500 cc (ml) bottle of 1:20,000 solution of phenylephrine in Ringer's Lactate. How would you mix up the solution? Given: 1% solution of phenylephrine 500 ml. of Lactated Ringer's Desire: 500 ml. of 1:20,000 phenylephrine in Lactated Ringer's A General Approach to the Problem by Proportion Method 1. Determine the mg/ml concentration of the final solution 2. Determine the mass of drug to be placed into the 500 ml volume e.g., mass of drug needed = 500 ml x 0.05 mg/ml = 25 mg Problem You have on hand a 0.6 gram ampule of the powered form of drug “A”. How would you create a 0.4% solution of this drug? (You may use the IV fluid of your choice to create this mixture.) Problem You mix Drug A 2 grams in 100 milliliters of normal saline. What concentration of Drug A (expressed in %) have you created? Question You are going to administer a subarachnoid block (spinal anesthetic) and wish to administer 15 milligrams of bupivacaine. (For subarachnoid use, bupivacaine is prepared preservative free as a 0.75% concentration of bupivacaine in 8.25% dextrose.) What volume of bupivacaine must you administer to provide 15 milligrams of this drug? Question You are going to administer a subarachnoid block and wish to administer a solution of 80 milligrams of lidocaine which includes 0.15 milligrams of epinephrine. (For subarachnoid use, lidocaine is prepared preservative free as a 5.0% preparation in 7.5% dextrose.) The spinal anesthesia kit also contains a 1.0 milliliter ampule of epinephrine 1:1,000. What volumes of lidocaine and epinephrine will you administer?  Question The label reads: “Neosynephrine 1%”. How many milligrams per milliliter are in a 1% solution of any drug? For surgical hemostasis, a surgeon requests a 1:10,000 solution of neosynephrine. How many milligrams per milliliter would be in a 1:10,000 concentration of drug? Using your 1% neosynephrine supply, how would you create 20 milliliters of a 1:10,000 solution of neosynephrine? Your patient’s arterial blood has a pH of 7.40. What is pH? Describe its mathematical basis. PH pH the negative log of the hydrogen concentration or –log[H+] [ ] = moles per liter  What is a logarithm? Logarithm In mathematics, the logarithm is the inverse operation to exponentiation. That means the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. In simple cases the logarithm counts repeated multiplication. For example, the base 10 logarithm of 1000 is 3, as 10 to the power 3 is 1000; the multiplication is repeated three times. LOG LOG Henderson-Hasselbalch Equation  PH can be calculated with Bicarbonate and carbonic acid concentrations Question In what respect does oxygen (with a molecular weight of 32) = hydrogen (m.w. = 2) = water (m.w. = 18) = carbon (m.w. = 12) = carbon dioxide (m.w. = 44)? How can they all be compared? Avogadro (Amedeo) Avogadro’s hypothesis (1776-1856) the mole Avogadro Equal volumes of all gases contain equal numbers of molecules under conditions of fixed temperature and pressure. Therefore, 1 mole of oxygen (with a molecular weight of 32) = 1 mole of hydrogen (m.w. = 2) = 1 mole water (m.w. = 18) = 1 mole carbon (m.w. = 12) = 1 mole carbon dioxide (m.w. = 44)? mEq A liter of a particular intravenous solution contains, among other substances, 4.5 mEq · l-1 of potassium. What is a mEq?  Formula: mEq= mg/atomic weight * valence “Etiquette” SI Prefixes SI Prefixes The Seven Base Units of the SI MGHTextbook ofAnesthetic Equipment, The Warren S. Sandberg, Richard D. Urman, and Jesse M. Ehrenfeld Appendix, 381-384 Copyright © 2011 by Saunders, an imprint of Elsevier Inc Useful Conversions MGH Textbook ofAnesthetic Equipment, The Warren S. Sandberg, Richard D. Urman, and Jesse M. Ehrenfeld Appendix, 381-384 Copyright © 2011 by Saunders, an imprint of ElsevierInc Sandberg, W., Urman, R. & Ehrenfeld, J. (2011). The MGH textbook of anesthetic equipment. Philadelphia: Churchill Livingstone. Examples of SI-Derived Units with Special Names Sandberg, W., Urman, R. & Ehrenfeld, J. (2011). The MGHtextbook of anesthetic equipment. Philadelphia: Churchil Livingstone. SI Units with Compound Names Force 1 newton will accelerate a 1 kilogram mass at 1 meter per second per second. What is the force of gravity? What measurement are we going to talk about? Gravity  All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s  This does not account for air resistance Pressure  Pressure = force per unit area  Pressure in Anesthesia  The efficacy of the 3 cc syringe vs the 60 cc syringe in developing high pressure flow of fluid.  How to design an apparatus to allow for the delivery of oxygen from an E cylinder under 1800 psi pressure to a glass manometer?  The oxygen failure warning device.  Blood Pressure  Pipeline pressure  APL (Adjustable Pressure Limiting) https://www.facebook.com/kasey.hayley/videos/98443521 1621140/ Diagram of a generic two-gas anesthesia machine. (Modified with permission from Check-Out, a Guide for Preoperative Inspection of an Anesthesia Machine. Park Ridge, IL, American Society of Anesthesiologists, 1987.) (Modified with permission from Check-Out, a Guide for Preoperative Inspection of an Anesthesia Machine. Park Ridge, IL, American Society of Anesthesiologists, 1987.) Inhaled Anesthetic Delivery Systems Brockwell, Russell C., Miller's Anesthesia, 25, 667-718 Copyright © 2010 Copyright © 2010 by Churchill Livingstone, an imprint of Elsevier Inc. Pressure sensor shut-off valve. The valve is open in A because the oxygen supply pressure is greater than the threshold value of 20 psig. The valve is closed in B because of inadequate oxygen pressure. (Redrawn with permission from Bowie E, Huffman LM: The Anesthesia Machine: Essentials for Understanding. Madison, WI, Ohmeda, A Division of BOC Health Care, Inc., 1985.) (Redrawn with permission from Bowie E, Huffman LM: The Anesthesia Machine: Essentials for Understanding. Madison, WI, Ohmeda, A Division of BOC Health Care, Inc., 1985.) Inhaled Anesthetic Delivery Systems Brockwell, Russell C., Miller's Anesthesia, 25, 667-718 Copyright © 2010 Copyright © 2010 by Churchill Livingstone, an imprint of Elsevier Inc. Quiz: What do the following terms have in common: mmHg, psi, cmH2O, bars, mbars, torr, paschals, kPa?? Weather The weather forecast includes the following statement: “We have a high pressure system developing.” What is the weatherperson referring to?? How is atmospheric pressure measured? Torr What is a Torricelli tube? Pressure Units 760 mmHg ~ 760 torr ~ 14.7 psi ~ 100 kPa ~ 1 bar ~ 1000 mbars Question You have an oxygen E cylinder with a pressure gauge that registers 0 psi. Is there oxygen in that cylinder? Gauges What is gauge pressure (“psig”)? What is absolute pressure (“psia”)? What is a Bourdon gauge? The Bourdon gauge, representing a mechanical gauge that requires no power. The Bourdon tube is an evacuated compartment. Monitoring Ventilation Berry, James M., Anesthesia Equipment: Principles and Applications, Chapter 9, 223-242 Copyright © 2013 Copyright © 1993, 2013 by Saunders, an imprint of Elsevier Inc. Question An oxygen cylinder (full) contains 137 bars of pressure. How many psig is that?? How many kPa?? What is the psia? Question Patient A has a CVP of 10.2 cmH2O with a water manometer. Patient B has a CVP of 7.5 mmHg with a pressure transducer. Who has the higher CVP? The Hg Manometer  Hg is 13.6 times as dense as water  A pressure supporting a 7.5 mm column of Hg, therefore will support a 102 mm (10.2 cm) column of water 1 kPa supports a 7.5 mm column of Hg; 1 kPa = 7.5 “mmHg” Pressure units 1 kPa = 7.5 mmHg = 10.2 cm H2O Relevance  You are doing a craniotomy in a sitting position. The surgeon wants a CPP of 90 at all times.  What is the formula for CPP?  Where is your transducer? Altitude What is the difference between an FIO2 of 0.40 in Buffalo and Denver? Nitrous oxide, usually administers in a 50-70% concentration, can be expected to be equally effective at all atmospheric pressures. TRUE FALSE Why?  Describe the function of a water manometer. Why must / must not you hold a water manometer perpendicular to the plane of the floor? How do we measure blood pressure? BP Cuff Manometer NIBP Oscillometry (manual and automated) Radial artery compression Invasive techniques Fiberoptic catheter tip transducer Work = F x D Joule the force of 1 N over I meter The Work of Breathing Ventilator Work Cardiac Work A, The spontaneous breath progresses clockwise, starting at zero, with tidal volume (VT ) on the y-axis. B, Ventilator-initiated volume control pressure-volume loop. In this instance, positive end-expiratory pressure is 5 cm H2 O and cycles counterclockwise. (Modified from Lian JX: Understanding ventilator waveforms and how to use them in patient care. Nurs Crit Care 2009; 4:43-55.) (Modified from Lian JX: Understanding ventilator waveforms and how to use them in patient care. Nurs Crit Care 2009; 4:43-55.) Monitoring Ventilation Berry, James M., Anesthesia Equipment: Principles and Applications, Chapter 9, 223-242 Copyright © 2013 Copyright © 1993, 2013 by Saunders, an imprint of Elsevier Inc. Kenny et al. (2008) Kenny et al. (2008) The pressure – volume loop as an expression of work W=FxD and P = F / A, therefore F = PA and V = D x A, therefore, D = V / A So W = PA x V/A and W = PV Power – the rate of work Watt 1 joule per second per second