Ohm's law
Demonstrates the relationship between current (I), resistance (R), and voltage (V) in an electrical circuit and can be expressed in three ways:
It can also be used to describe blood flow (cardiac output, Q), resistance (R), and pressure difference across vessels (∆) in the cardiovascular system.So blood flow is directly proportional to the pressure gradient across the vessel and inversely proportional to the resistance.The absolute pressure in the vessel is therefore less important than the ∆P across the vessel determining the flow.
Poiseuille's law (Hagan‐Poiseuille)
Gives the relationship between resistance to flow and vessel dimensions and is analogous to Ohm's Law.
It applies to laminar flow of incompressible uniformly viscous fluids (described as “Newtonian Fluids”) in uniform vessels.
The law does not apply to pulsatile flow.
Its main application is in peripheral vessels where flow is almost steady.
The Poiseuille equation can be derived by inserting the factors which affect resistance (R) into Ohm's Law. (for laminar flow in a vessel of length l, radius r and blood viscosity η)So, with substitution,
Significance of Poiseuille's Law:Because r in this equation is raised to the fourth power, slight changes in vessel diameter (radius) cause tremendous changes in flow.An increase in viscosity (e.g., with dehydration) will contribute to a decrease in blood flow.
Laplace's law
States that for any given pressure (P), the tension (T) developed by the ventricular wall increases as the radius (R) of the cylinder increases.For a cylindrical vessel T = P × R.For a spherical vessel T = (P × R)/2.So for any given radius and internal pressure, a spherical vessel will have half the wall tension of a cylindrical vessel.
In the case of the heart, the left ventricle has a much greater radius than the right ventricle and thus is able to develop greater tension (or force).
Starling's law (Frank‐Starling mechanism, see Table 3.1)
Describes the intrinsic capability of the heart to increase its force of contraction in response to an increase in venous return.This response occurs in isolated hearts indicating that it is independent of humeral and neural factors.
Preload directly determines cardiac output when the HR is constant.
An increase in preload, up to a certain point, increases cardiac output.
At the end‐diastolic volume, cardiac output will not increase further and may actually decrease.
F Tissue oxygen delivery
As stated, the ultimate responsibility of the cardiovascular system is to provide adequate oxygen to the working cells.
CaO2 = ([Hb] × SaO2% × 1.36) + (PaO2 × 0.003)[Hb] = concentration of hemoglobin in the blood in gr/dlSaO2 = percent saturation of hemoglobin with oxygen1.36 = a constant (Hüfner's) describing the amount of oxygen bound by 1 g of HbPaO2 = the partial pressure of oxygen in arterial blood0.003 = the solubility coefficient of oxygen in blood (ml/mmHg of oxygen/dL of blood)
Note: The effect of decreases in [Hb] and SaO2 on CaO2 are shown in Box 3.1.
Box 3.1 Effects of Decreases in [Hb] and SaO2 on CaO2
Normal [Hb](15 g/dl) and normal SaO2 (SaO2 98%, PaO2 95 mmHg):
Normal [Hb](15 g/dl) and decreased SaO2 (SaO2 85%, PaO2 60 mmHg):
Decreased [Hb] (6 g/dl) and normal SaO2 (SaO2 98, PaO2 95 mmHg):
Comment: Although adequate Hb saturation with O2 is important, a critical mass of circulating red cells is imperative for tissue oxygenation.
VII Anesthesia
A Effects of anesthetic drugs (see Table 3.3)
Most drugs used for sedation/tranquilization and anesthesia cause some degree of dose‐dependent cardiovascular changes which may manifest as changes in HR, preload, afterload, contractility or a combination of these factors.
Regardless of which drugs are used, drug dosages in compromised patients should almost always be reduced.Most adverse effects, like the cardiovascular depression caused by inhalational anesthetic gases, are dose‐dependent.A greater percentage of administered drug may reach the brain (see below).
B Effects of cardiovascular disease
Depending on the severity of the cardiovascular disease, changes in HR, preload, afterload and contractility can range from barely noticeable to life threatening.
SV decreases due to decreased contractility and increased afterload.
Decreased contractility due to:Direct effects of the disease (e.g. myofibril damage from ischemia).Indirect effects of electrolyte imbalance (e.g. decreased ionized calcium), acid–base imbalance, or sepsis.
Increased afterload due to:A hypotension‐mediated increase in sympathetic activity, which results in excessive vasoconstriction in an attempt to maintain BP in the face of decreased cardiac output.A hypotension‐mediated decrease in arterial baroreceptor inhibition of autonomic centers in the brain stem, which stimulates the release of renin, which increases vascular resistance and promotes salt and water retention through release of aldosterone.
Decreased SV due to decreased contractility and increased afterload.This causes cardiac output to become more HR dependent.HR generally increases, thereby increasing myocardial O2 consumption.
Increased preload due to reduced SV, accumulated venous return and an increase in fluid retention secondary to activation of the renin/angiotensin system.Table 3.3 Cardiovascular effects of some commonly used anesthetic drugs.Source: Adapted from Muir (1998).DrugHeartHeart rhythmPre‐loadAfter‐loadContractilityCardiacrateoutputAcepromazine↑−↓↓− or ↓↑or ↓Alpha2 agonists↓↓+↑↑− or ↓↓Benzodiazepines−−−−−−Opioids− or↓−↓−− or ↓− or ↓Thiopental↑+↓↓↓↓Ketamine and Tiletamine↑+↑↑↑
