Bohr equation

frac{VD}{VT}  =  frac{PaCO2-PECO2}{PaCO2}

This describes the amount of physiological dead space in the lungs, it’s given as a ratio and a typical value is 0.2 – 0.35.


All expired carbon dioxide (FE) must, by definition, come from alveolar gas (VA x FA) not dead space gas (VD).

Therefore to derive the Bohr equation (explanatory notes in brackets):

VT  x  FE  =  VA  x  FA

VT  x  FE  =  (VT-VD)  x  FA   (As VA=VT-VD)

VT  x  FE  =  VT  x  FA  –  VD  x  FA  (Multiply out brackets)

VD  x  FA  =  VT  x  FA  –  VT  x  FE  (Rearrange)

VD  x  FA  =  VT  x  (FA-FE)  (Simplify)

frac{VD}{VT}  =  frac{(FA-FE)}{FA}  (Divide by VT and FA)

The fraction of CO2 in the alveoli (FA) can’t realistically be measured, so the partial pressure of CO2 in the blood is used as it is virtually identical. The fraction of expired CO2 can easily be measured as a partial pressure with a capnometer.

frac{VD}{VT}  =  frac{PaCO2-PECO2}{PaCO2}


Dead space

The volume within the respiratory system that does not participate in gas exchange.

Anatomical dead space
The volume of the conducting airways (~150mls)

Physiological dead space
Volume of alveoli that do not eliminate carbon dioxide, plus the anatomical dead space volume


In health the anatomical dead space volume is the same as the physiological dead space volume, however in lung disease and other clinical situations the physiological dead space may get larger.

Measuring alveolar ventilation

Because no gas exchange occurs in the anatomical dead space all carbon dioxide in expired gases must come from alveolar gas.

VCO2 = VA  x  FCO2

Therefore VA  =   frac{VCO2}{FCO2}

The partial pressure of carbon dioxide in the alveoli is proportional to the fraction of carbon dioxide (FCO2) multipled by K, a constant.

VA  =  frac{VCO2}{PCO2}  x  K

This is the alveolar ventilation equation. The alveolar ventilation is inversely proportional to the partial pressure of carbon dioxide.

The Bohr equation is used to calculate the fraction of dead space in the lungs.

Fick’s law of diffusion

The rate of transfer of a gas through a sheet of tissue is proportional to the tissue area and the difference in gas partial pressures between the two sides, and inversely proportional to tissue thickness.

Vgas  alpha  frac{A}{T}  x  D  x  (P1-P2)

Where D is the diffusion constant (Graham’s law), stating that diffusion is proportional to solubility but inversely proportional to the square root of the molecular weight (or density).

D  alpha  frac{Solubility}{sqrt{MW}}

Carbon dioxide diffuses around twenty times more rapidly than oxygen does due to increased solubility despite a higher molecular weight.


The rate of diffusion through a tissue is proportional to the cross sectional area but inversely proportional to the thickness.

The rate of diffusion is proportional to the pressure differential between either side of the tissue.

The more soluble a substance is the more rapidly it will diffuse, but the larger it’s molecular weight the slower it will diffuse.


Fick principle

The Fick principle is commonly applied to cardiac output calculations. It essentially states that blood flow to an organ can be calculated from a marker substance if the following is known:

  1. Amount of marker substance taken up by organ per unit time
  2. Concentration of marker in arterial blood supplying organ
  3. Concentration of marker in venous blood leaving the organ

This can be applied to the measure cardiac output where the marker substance is oxygen.

In other words the amount of a substance taken up by an organ per unit time is equal to the arterial concentration minus the venous concentration, divided by the production or uptake.

CO  =  frac{VO2}{CaO2-CvO2}

Therefore the cardiac output is inversely proportional to the arteriovenous difference of the marker substance.

CO  alpha  frac{1}{a-v}

In reality this method is cumbersome and rarely used as measuring oxygen uptake is difficult in a clinical situation. The Fick determination is a derived version of the Fick principle where a standard oxygen uptake is used based on the assumption that the oxygen consumption is 125ml of O2 per minute perm² of body surface area. The average body surface area for an adult male is 2m², giving a rough oxygen consumption of 250mls per minute.

This method can also be used to estimate renal blood flow, but instead of oxygen a marker such as para-aminohippuric acid or inulin is used.

Receptor subtypes

A receptor is a molecule that receives chemical signal from outside the cell to cause a particular action.

There are four main types in the body.

  1. Ligand gated ion channel
  2. G protein coupled receptor
  3. Tyrosine kinase
  4. Intranuclear

Ligand gated ion channels

These are widespread throughout the body. In general these are pentameric ion pores composed of five subunits, each unit traverses the membrane four times. The binding of a particular ligand changes the channel’s permeability to particular ions, which can then flow down a concentration gradient.


Nicotinic acetylcholine receptor


This is a non-selective cation channel, though it is mainly sodium that passes through it when open. These receptors are found at the neuromuscular junction and are important for transmission of action potentials to cause muscle contraction.

The five subunits are: two alpha, one beta, one epsilon and one gamma. Binding of acetylcholine causes opening of the ion pore and increased membrane permeability to sodium. Sodium enters the cell down it’s concentration gradient which causes depolarisation of the muscle sarcolemma and contraction. These receptors are targeted by muscle relaxants used during tracheal intubation and anaesthesia.

GABAa receptor


Gamma-amino-butyric acid receptors are widespread throughout the central nervous system. They are pentameric ion channels with two alpha, two beta and one gamma subunits. The two main binding sites are the general anaesthetic binding sites located between the alpha and beta subunits and the benzodiazepine binding site located between the alpha and gamma subunits.

When GABA binds to the receptor the central chloride channel is opened, increasing the membranes permeability to chloride. Chloride enters the cell down a concentration gradient. This reduces the membrane potential and increases the stimulus required to reach a threshold to depolarise the nerve cell. Therefore these receptors have an inhibitory effect on the central nervous system.

G protein coupled receptors

These consist of a single polypeptide chain which crosses the membrane seven times, they are often described as serpentine because of this. The polypeptide has two ends; a C (carboxy) end which is in the cytoplasm and an N (amino) end which is outside the cell and the site of ligand binding.

Common examples of these in the body are the adrenoceptors (alpha and beta), muscarinic acetylcholine receptors and GABAb receptors.


The binding of a ligand to the N- end of the polypeptide chain causes a conformational change of the protein. This change causes G protein to dissociate into it’s subunits, and it is the alpha subunit that causes an effect. It is known as G protein because in order to dissociate it binds GTP.

There are three subtypes of the G protein coupled receptor; Gs, Gi and Gq.

Gs e.g. Beta-1 adrenoceptor


Gs causes stimulation of adenylate cyclase to increase cyclic AMP production. This increases calcium release from the sarcoplasmic reticulum of the myocyte, which has positive chronotropic and inotropic activity. Review the cardiac myocyte structure and function here.

Gi e.g. Muscarinic acetylcholine receptor

Essentially the opposite of Gs, they decrease activation of adenylate cyclase which reduces levels of cyclic AMP within the cell.

Gq e.g. Alpha-1 adrenoceptor


Gq receptors cause the activation of phospholipase C. This increases levels of mediators such as IP3 and DAG which lead to increase calcium entry into the cell. This promotes smooth muscle contraction in the vessel wall and leads to vasoconstriction.

Tyrosine Kinase


Examples of this type of receptor are the insulin receptors, as well as receptors for cytokines and growth hormone. The ligand binds to the receptor which is related to tyrosine kinase within the cytoplasm. Activation of tyrosine kinase causes a cascade of a variety of processes that are crucial to normal cell function, e.g. gene transcription.



These receptors are within the nucleus of the cell. The ligand therefore has to be lipid soluble in order to be able to get into the cell nucleus. The ligand binds to the receptors which then have a direct effect on target genes increasing or decreasing protein synthesis. An example of these would by thyroxine and steroids.

Control of the circulation

This is essential to ensure adequate blood flow reaches tissues to supply their metabolic demand, an important part of homeostasis. There are multiple control mechanisms which can be grouped into local (intrinsic) or systemic (extrinsic).

  • Circulatory control of the heart and brain are mainly intrinsic to maintain flow independant of systemic circulation
  • Circulation of the skin and gut is largely extrinsically controlled

Resistance vessels
Increasing or decreasing the tone of smooth muscle within arterioles varies the perfusion pressure across a capillary bed. Vascular smooth muscle is primarily innervated by sympathetic fibres that maintain a baseline level of tone.

Capacitance vessels
Increasing or decreasing the tone here varies intravascular volume as veins contain >60% of blood volume. This has no effect on vascular resistance.

Local mechanisms controlling blood flow


This is the most important as it determines the balance of oxygen supply and demand for tissues. Exposure of tissues to hypoxia or injury causes release of factors that cause vasodilatation independant of systemic control. This varies in spectrum from localised erythema to reperfusion syndrome.

  • CO2 and H+ ions: Cause arteriolar vasodilatation. Lactic and pyruvic acid lower pH and have a similar effect.
  • Serotonin: Released from platelets at site of mechanical injury, causes vasoconstriction.
  • Adenosine, ATP, ADP and AMP: Strong vasodilatory effects. Adenosine dilates hepatic arteries in response to decreased portal blood flow.

Mechanical response

Myogenic mechanism: Vascular smooth muscle contracts or relaxes depending on transmural pressure. This means when perfusion pressure varies the flow can remain constant.

Endothelial mechanism: Increases in flow velocity are associated with vasodilalation, probably due to endothelium derived nitric oxide.

Endothelial factors

Prostacyclin and Thromboxane A2: Arachidonic acid derivatives dependent on cyclo-oxygenase. Prostacyclin is a vasodilator that inhibits platelet aggregation by increasing cyclic AMP preventing vesicular release of thromboxane A2 and von Willebrand factor. Thromboxane A2 is a potent vasoconstrictor which promotes platelet aggregation. These two substances are in balance in health, regular aspirin causes prostacyclin effects to predominate.

Nitric oxide (NO): Potent vasodilator. Synthesised from arginine by NO-synthase and inactivated by haemoglobin. The release from the endothelium can be trigged by substances such as bradykinin and acetylcholine.

Systemic control can be humoral or neurological

Systemic humoral control of blood flow


The most powerful agents responsible for humoral control. Adrenaline is released from the adrenal medulla, with primary effects of the heart. Noradrenaline is released from the adrenal medulla and sympathetic post-ganglionic nerve endings and is a powerful vasoconstrictor.


Otherwise known as anti-diuretic hormone (ADH), this is released from the posterior pituitary in response to increased osmolarity sensed by the osmoreceptors in the hypothalamus. It’s primary action is on the kidney collecting ducts to cause retention of free water, but at supranormal doses it causes systemic vasoconstriction and increased blood pressure.

V1 receptors: Vasoconstriction
V2 receptors: Renal effects
V3 receptors: Modulates secretion of ACTH
NB. Vasopressin is a non-selective V receptor agonist, Terlipressin is a selective V2 agonist.

Angiotensin II

Formed from angiotensin I in the lungs by angiotensin converting enzyme (ACE). The central effects are to cause the sensation of thirst and release of aldosterone from the adrenal cortex. It is also a powerful peripheral vasoconstrictor.

Atrial Natriuretic Peptide (ANP)

Released from the atria in response to atrial stretch. It causes natriuresis and subsequent loss of free water, lowering blood pressure. It inhibits vasopressin secretion and there is increasing evidence it causes shedding of the endothelial glycocalyx.


Produced in the central nervous system, gastric mucosa and mast cells. Potent vasodilator, it’s release can be inhibited by H1, H2 and H3 receptor antagonism.

Kinins e.g. Bradykinin

Produced from exocrine glands e.g. pancreas, salivary and sweat glands. Vasodilators. ACE is a kinase, which can explain some side effects of ACE-inhibitors e.g. angioedema, cough.

Systemic neurological control of blood flow

All blood vessels except capillaries and venules have smooth muscles in their walls which are supplied by sympathetic motor fibres. These fibres have a normal firing rate or resting tone than can be increased or decreased. Vascular smooth muscle is supplied by noradrenergic sympathetic fibres which increased activity causes vasoconstriction, whereas skeletal muscle is supplied by cholinergic sympathetic fibres in which increased activity causes vasodilatation.

Vasomotor control centres in the CNS

These are located in areas of the reticular formation in the medulla and pons.
Pressor region: Maintains a tonic output to keep a background level of vasomotor tone. It is capable of increasing the heart rate, vascular tone and myocardial contractility.
Depressor region: Inhibits the pressor region.

Efferent – Project directly to preganglionic neurones in the intermediolateral (IML) grey columns of the spinal cord. Preganglionic fibres pass from the IML to the paravertebral sympathetic chain. Post-ganglionic fibres carry sympathetic outflow to effector sites.

Afferent – Baroreceptors in carotid sinus and chemoreceptors in carotid body feed afferent impulse to CNS via the nerve of Herine, a branch of the glossopharyngeal nerve (cranial nerve IX). Aortic baroreceptors relay impulses via the vagus nerve (X). These synapse in the medulla at the nucleus tractus soliatrius (NTS).



Peripheral: Carotid and Aortic bodies
Respond primarily to a reduction in oxygen tension, also senstivie to increase pCO2 and changes in pH. Main effects are on the respiratory centre, though have some minor effects on the pressor region.

Central: Vasomotor centres respond directly to pCO2 and pH.
This central control predominates over peripheral effects. The central receptors are not sensitive to hypoxia.

The cardiac cycle

Aortic pressure-volume loop

This diagram summaries the mechanical performance of the heart.



The cardiac cycle starts at the end diastolic point (EDP) when the mitral valve closes.

Isovolumetric contraction then occurs causing a vertical ascending segment, ending at the opening of aortic valve marking the beginning of systole. Ejection ends at the end systolic point (ESP) when the aortic valve closes.

Isovolumetric relaxation ends when the mitral valve opens allowing ventricular filling to begin again.

The area of this loop is called the stroke work.

Aortic vs Ventricular pressure


Coronary anatomy

Sinoatrial node: At the junction of the SVC and right atrium on the posterolateral surface.

Atrioventricular node: Lies in atrial septum above coronary sinus.

Left coronary artery arises from the posterior aortic sinus, and the right coronary artery arises from the anterior aortic sinus. The sinuses of valsalva (also known as the aortic sinuses) are shaped to encourage equal bilateral flow.

Coronary arteries

  • Right Coronary Artery (RCA):  Supplies the  RA, RV, and interatrial septum.  It usually supplies both the SA and AV nodes.
  • Posterior Descending Artery (PD):  Supplies the inferior portion of the LV and the posterior septum.  The PD arises from the RCA in 70% of cases and the CFX in the remaining 20%.
  • Left Main Coronary Artery (LCA):  Gives rise to the LAD and CFX.
  • Left Anterior Descending artery (LAD):   Supplies the LV, RV, and interventricular septum.  Arises from LCA.  May also be called the anterior interventricular artery.
  • Circumflex artery (CFX):  Supplies the LA and LV.  Arises from the LCA and anastamoses with the RCA.

Schematic of coronary arteries


The right coronary artery supplies to SA node in 60% of people, and it supplies the AV node in 90% of people.

Dominance refers to which side supplies the posterior interventricular artery (also called the posterior descending artery). 70% of people are right side dominant, 20% co-dominant and 10% left side dominant.


Coronary perfusion pressure

CPP = aortic pressure – intraventricular pressure

Left ventricle:

Systole: [SBP-LVESP] = 120-120 = 0mmHg

Diastole: [DBP-LVEDP] = 70-10 = 60mmHg

In the right ventricle flow occurs throughout the cardiac cycle.

Cardiac myocyte



Troponin I inhibits binding of myosin to actin. Calcium binds to troponin C causing a conformational change, this moves troponin I allowing actin to bind to myosin. Increased stretch of sarcomere increases the affinity of troponin C for calcium, therefore increasing contractility.