Formulas Flashcards
Henderson Hasselbalch
determines how lipid soluble something is at a given pH if pKa is known.
Log (protonated concentration/unprotonated concentration) = pKa - pH
The higher the pKa, the stronger the acid (the more dissociated it is)
Acids are more water-soluble in alkaline solution
Bases are more water-soluble in acidic solution
Acids are more lipid-soluble in acidic solution
Bases are more lipid-soluble in basic solution
Shunt fraction (Berggren equation)
Qs/Qt = (CcO2 - CaO2) / (CcO2 - CvO2)
Qs/Qt = shunt fraction (shunt flow divided by total cardiac output)
CcO2 = pulmonary end-capillary O2 content, same as alveolar O2 content
the oxygen content of pulmonary endcapillary blood, and it is assumed that it is equal to CtO2 (A), the alveolar oxygen content. This assumption is based on a two-compartment model, where this compartment is perfectly oxygenated (i.e. the arterial and alveolar oxygen content is the same)
CaO2 = arterial O2 content
the oxygen content of systemic arterial blood, which will be lower than the content of “perfect” endcapillary blood because it is mixed with the relatively hypoxic Qs
CvO2 = mixed venous O2 content
the oxygencontent of mixed venous blood, is a known variable, and it is return to the lungs at a flow rate equal to the cardiac output, Qt
The estimated shunt fraction (Fshunte) can be calculated if an assumed value is substituted for CvO2 in the Berggren equation
“True” shunt can be identified if the subject is made to breathe 100% FiO2
- this decreases the contribution from V/Q scatter
- with 100% FiO2, the measured shunt fraction is the “true” intrapulmonary shunt
- This technique does not separate “true” shunt from anatomical shunt (contribution from thebesian veins and bronchial veins) or cardiac defects
Cardiac output
Cardiac output is definied as the volume of blood ejected by the heart per unit time. It is usually presented as
Stroke volume x heart rate in L/min
The determinants of cardiac output are:
- heart rate: a higher heart rate increases cardiac output as it multiplies by stroke volume; an excessively high heart rate decreases cardiac output by decreasing preload
- stroke volume, which in turn determined by preload, afterload, and contractility
Preload:
- increased preload leads to an increase in the stroke volume
- preload is determined by:
intrathoracic pressure
atrial contribution (atrial kick)
central venous pressure (RA pressure)
mean systemic filling pressure which depends on total venous blood volume and venous vascular compliance
compliance of the ventricle and pericardium
duration of ventricular diastole
end-systolic volume of the ventricle
Afterload:
- ventricular radius (end-diastolic volume)
- ventricular wall thickness
- ventricular transmural pressure
intrathoracic pressure
ventricular cavity pressure
ventricular outflow impedance and aortic input impedance
arterial resistance
- vessel radius
- blood viscosity
- length of the arterial tree
- inertia of the blood column
- influence of reflected pressure waves
- arterial compliance
Cardiac contractility:
- increased contractility improves stroke volume at any given preload or afterload value
- affected by: heart rate (bowditch effect), afterload (anrep effect), preload (frank-starling mechanism), cellular and extracellular calcium concentrations, temperature
Summary:
- stroke volume increases with increased preload, up to a plateau, beyond which it begins to decrease again
- stroke volume decreased with increased afterload, in a fairly linear fashion
- stroke volume increases with increased contractility, for any given preload and afterload value
Oxygen delivery
DO2 = Qt x CaO2
Where Qt is the cardiac output in L/min
CaO2 is the oxygen content of whole blood
the oxygen content of whole blood is the fraction of dissolved O2 and the product of Hb (g/L) x 1.39 In mL) multiplied by the saturation of hemoglobin
Systemic vascular resistance
SVR = (80 x (MAP - mean right atrial pressure) / cardiac output
SVR is the resistance (pressure drop) generated in blood flowing through the whole arterial circulation. Normally the pressure gradient is constant, and the flow is regulated by changes in vascular resistance.
Factors that affect SVR are the parameters of the Hagen-Poiseuille equation (length of the vessel, viscosity of the blood, radius of the vessel); arterial baroreflex control, peripheral and central chemoreceptors, pulmonary baroreceptors, hormones, temperature, intrinsic myogenic regulation, metabolic regulation, flow/shear associated regulation, conducted vasomotor responses, local cooling, immunological modulation by inflammatory mediators.
Respiratory quotient
The respiratory quotient, also known as the respiratory ratio (RQ), is defined as the volume of carbon dioxide released over the volume of oxygen absorbed during respiration. It is a dimensionless number used in a calculation for basal metabolic rate when estimated from carbon dioxide production to oxygen absorption.
RQ = CO2eliminated / O2consumed
RQ typically is reported as a known 0.8
CVP waveform
generally measured at the junction of the superior vena cava and the right atrium. This is most commonly done via a central venous catheter placed through the right internal jugular vein.
A normal CVP waveform contains five components. These components include three peaks (a, c, v) and two descents (x, y). All of these components correspond to various aspects of the cardiac cycle.
The first peak is the a-wave, which immediately follows the p wave of the ECG waveform. The a-wave is a pressure increase that is due to atrial contraction at end-diastole. Shortly after the a-wave there is a second peak, the c-wave. The c-wave immediately follows the r wave of the ECG waveform. This is a pressure increase due to tricuspid bulging into the atrium as a result of isovolumic ventricular contraction (IVC). Note that the a and c-waves are split by the r wave of the ECG waveform. This is because the a-wave always represents end-diastole and the c-wave represents early ventricular systole.
Following the c-wave is the first major descent in the CVP waveform, the x-descent. The x-descent is a drop in atrial pressure during ventricular systole caused by atrial relaxation. At the trough of the x-descent there is an increase in atrial pressure as the atrium begins to fill during late systole. This is called the v-wave. The v-wave corresponds to the end of the t wave in the ECG waveform. The final aspect of the CVP waveform is the y-descent, which is due to an atrial pressure drop as blood enters the ventricle during diastole.
Waveform Component: a-wave Phase of the cardiac cycle: end diastole Mechanical Event: atrial contraction
Waveform Component: c-wave Phase of the cardiac cycle: early systole Mechanical Event: Tricuspid bulging (IVC)
Waveform Component: v-wave Phase of the cardiac cycle: late sytole Mechanical Event: systolic filling of the atrium
Waveform Component: x-wave Phase of the cardiac cycle: mid systole Mechanical Event: atrial relaxation
Waveform Component: y-wave Phase of the cardiac cycle: early diastole Mechanical Event: early ventricular filling
CaO2
(arterial oxygen content) CaO2 = (SaO2 x Hb x 1.37) + (PaO2 mmHg x 0.003)
Bohr’s dead space equation
Physiological dead space can be measured using the Bohr-Enghoff method
- The Bohr equation can be used to determine physiological dead space from the difference between the exhaled CO2 and alveolar CO2 but the latter is hard to measure
The equation is Vd/Vt = (PACO2 - PECO2) / PACO2
- the Enghoff modification of the Bohr equation uses arterial CO2 instead of alveolar CO2 and is, therefore, easier to measure, but it is influenced by multiple factors such as: dead space, intrapulmonary shunt, diffusion impairment, V/Q heterogeneity
Pulmonary vascular resistance
Factors which influence pulmonary vascular resistance:
- Pulmonary blood flow:
- increased blood flow results in decreased pulmonary vascular resistance in order for pulmonary arterial pressure to remain stable
- distension of pulmonary capillaries
- recruitment of previously collapsed or narrowed capillaries
- Lung volume
- the relationship between lung volume and PVR is “U”-shaped
- pulmonary vascular resistance is lowest at FRC
- at low lung volumes, it increases due to the compression of larger vessels
- at high lung volumes, it increases due to the compression of small vessels
- hypoxic pulmonary vasoconstriction
- a biphasic process (rapid immediate vasoconstriction over minutes, then a gradual increase in resistance over hours)
- mainly due to the constriction of small distal pulmonary arteries
- attenuated by: sepsis, pneumonia, hypothermia, iron infusion
- metabolic and endocrine factors
- catecholamines, arachidonic acid metabolites (thromboxane A2) and histamine increase PVR
- hypercapnia and (independently) academia also increase pVR
- alkalemia decreases PVR and suppresses hypoxic pulmonary vasoconstriction
- hypothermia increases PVR and suppresses hypoxic pulmonary vasoconstriction
- autonomic nervous system
- alpha1 receptors: vasoconstriction
- beta2 receptors: vasodilation
- muscarinic M3 receptors: vasodilation
- blood viscosity
- PVR increases with increasing hematocrit
- drug effects
- pulmonary vasoconstrictor: adrenaline, noradrenaline, and adenosine
- pulmonary vasodilators: nitric oxide, milrinone, levosimendan, sildenafil, vasopressin, bosantan/ambrisantan, prostacycline, and its analogs, calcium channel blockers and ACE-inhibitors
Boiling point
boiling point is defined as the temperature at which vapor pressure equals atmospheric pressure (760 mmHg). Boiling points are listed below (celsius):
Sevoflurane: 58.5
Desflurane: 22.8
Isoflurane: 48.5
Enflurane: 50.2
N2O: -88
(Desflurane: high volatility/moderate potency, requires the use of a special vaporizer for proper utilization of this gas. Desflurane vaporizers are heated to 39*C which increases the vapor
Heat of vaporization
In a closed container, molecules from a volatile liquid escape the liquid phase and become vapor. These gaseous molecules strike the wall of the container, exerting what’s known as vapor pressure. Vapor pressure is directly correlated with temperature. Increasing temperature will increase the ratio of gas:liquid molecules, thereby increasing vapor pressure.
Vapor pressure of volatile agents at 20 degrees C (mmHg):
- sevoflurane: 157
- desflurane: 669
- isoflurane: 238
- enflurane: 172
- halothane: 243
- N2O: 38,770
Saturated vapor pressure
Evaporation is the phenomenon by which molecules in the liquid phase (with high kinetic energy) escape from the surface of a liquid to enter the gas phase. Inside the vaporizer, molecules will enter the gas phase until the rate of vaporize molecules equals the rate of molecules returning to the liquid phase. This dynamic equilibrium is known as saturation. The pressure exerted by this gas is known as “saturated vapor pressure.” SVP increases in a non-linear fashion as the temperature of an anesthetic in the liquid phase increases and is independent of the barometric pressure. The SVP for all anesthetic gases is measured at 20*C and is a unique characteristic for each drug. (ex: iso SVP = 239 mmHg)
Specific heat
specific heat is the quantity of heat (calories) required to raise the temperature of a unit mass (grams) of a substance by 1*C. Heat must be supplied to the liquid anesthetic in the vaporizer to maintain the liquid’s temperature during the evaporation process, when heat is being lost.
Venous return
Venous return is the rate of blood flow into the heart form the veins. At a steady state, venous return and cardiac output are equal. Venous return can be expressed as:
VR = (MSFP - RAP) / VR where MSFP is mean systemic filling pressure and RAP is right atrial pressure and VR is the venous resistance
Factors which influence venous return include:
- factors which affect cardiac output: afterload, contractility
- factors which affect mean systemic filling pressure: total venous blood volume, venous smooth muscle tone
- factors which affect right atrial pressure: intrathoracic pressure (spontaneous v PPV), pericardial compliance, right atrial compliance, right atrial contractility, tricuspid valvular competence and resistance
- factors which affect venous resistance: mechanical factors (posture, intraabdominal pressure, skeletal muscle pump, obstruction to venous flow (pregnancy), hyperviscosity (polycythemia, hyperproteinemia)), neuroendocrine factors (autonomic tone, vasoactive drugs)
