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.


The Larynx

The larynx is a functional sphincter at the beginning of the respiratory tree. It protects against foreign bodies and is used for phonation. It is lined with ciliated columnar epithelium.




Internal brand of superior laryngeal nerve: Above the cords.
Recurrent laryngeal nerve: Below the cords.

Recurrent laryngeal nerve: All muscles except the cricothyroid muscle which is innervated by the external brand of the superior laryngeal nerve.

Of note is the different sensory innervations affected during tracheal intubation and the haemodynamic effects these can have. The valeculla has sensory supply from the glossopharyngeal nerve, whereas beneath the epiglottis has sensory innervation from the vagus nerve. Using a standard Macintosh blade seated in the valeculla produces a sympathetic response both due to nociception and due to the glossopharyngeal nerve’s connection to the nucleus tractus solitarius and subsequent effects on heart rate and blood pressure (see Control of circulation). However when a Miller blade is used this stimulates the sensory afferents of the vagus nerve which can in turn produce vagal stimulation and bradycardia. This is particularly evident in children who do not have a high sympathetic resting tone.

Blood supply

Arterial supply from the laryngeal branches of superior and inferior thyroid arteries. Venous drainage from laryngeal brances of superior and inferior thyroid veins.

Laryngeal muscles


There are three extrinsic and six intrinsic muscles.


  1. Sternothyroid – Arises from manubrium, inserts into thyroid cartilage lamina. Functions as a depressor of the larynx.
  2. Thyrohyoid – Connects thyroid lamina to greater horn of hyoid. Functions as an elevator of the larynx.
  3. Inferior constrictor – Constricts laryngeal inlet. Propofol relaxes these muscles very effectively and so aids placement of a laryngeal mask airway.


These are all paired muscles, except transverse arytenoid which is a midline structure.

  1. Cricothyroid – Anterior horn of cricoid to inferior horn of thyroid cartilage. Contraction tilts cricoid upwards, moving arytenoids posteriorly and therefore tensing the vocal cords.
  2. Posterior cricoarytenoid – Posterior cricoid to muscular surface of arytenoid. Contraction externally rotates arytenoids causing abduction of the cords.
  3. Lateral cricoarytenoid – Outer cricoid to muscular surface of arytenoid. Contraction adducts vocal cords.
  4. Transverse arytenoid – Posterior surface of both arytenoids. Contraction narrows distance between the two arytenoids, constricting glottis.
  5. Aryepiglottic – Causes a minor constriction of laryngeal inlet.
  6. Thyroarytenoid – Thyroid lamina to anterior arytenoid. Contraction pulls arytenoid anteriorly relaxing the cords.


Abductors Adductors Tenses cords Relaxes cords
Posterior cricoarytenoids Lateral cricoarytenoids Cricothyroids Thyroarytenoids
Transverse arytenoid

Recurrent laryngeal nerve injury

This is a problem because all intrinsic muscles except the cricothyroid muscles are supplied by these nerves. Therefore the only muscle with any tone after a RLN injury is a muscle that moves the arytenoids posteriorly and tenses the cords. A bilateral RLN injury can therefore cause upper airway obstruction.

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.

Malposition of central lines

Central venous access is a core skill in Critical care, useful for when peripheral access is impossible, to infuse phlebitic drugs or for rapid correction of electrolytes. Sites of access are the internal jugular veins, subclavian veins and femoral veins.

Ultrasound has helped make the procedure safer by reducing the incidence of arterial puncture and failed insertion than the traditional landmark technique. However a frustrating and potentially dangerous complication of central line insertion is malposition of the catheter which is not necessarily prevented by ultrasound. The ideal position for the catheter tip is within the superior vena cava, above its junction with the right atrium and lying parallel with the vessel walls. On a chest radiograph catheter tip placement over 10mm below the carina has a high risk of intracardiac placement. Despite the optimum placement being common knowledge there is a large variation in catheter tip placement¹.

Internal jugular vein

The commonest malposition associated with internal jugular vein cannulation is the catheter ending up in the ipsilateral subclavian vein. This can be detected with a post-insertion chest x-ray. The incidence of this is felt to be higher with a left sided cannulation (4.9% in one study² compared to 1.1% on the right). The incidence of vessel wall perforation is also felt to be higher with a left sided approach. Other potential routes of malposition are the azygous vein, thymic vein, contralateral subclavian vein and even the contralateral internal jugular vein.

Malposition of an IJV central venous catheter into the ipsilateral subclavian vein

Malposition of an IJV central venous catheter into the ipsilateral subclavian vein

Subclavian vein

The most common malposition associated with subclavian vein cannulation is malposition into the ipsilateral internal jugular vein. This is more common when a right sided approach is undertaken. Redirecting the central line into the superior vena cava requires interventional radiology assistance and the use of fluoroscopy. On chest x-ray a catheter that enters the left side of the heart should immediately raise concerns about inadvertent arterial cannulation.

Femoral vein

Aside from inadvertent arterial puncture, malposition of femoral lines are uncommon. The use of large bore haemodialysis lines presents the problem if vessel wall injury as described in a case report where a retroperitoneal haematoma occurred due to iliac artery perforation.

But does this cause a problem?

The problems associated with malposition of a CVC are theoretically increased risk of local thrombosis, risk of vessel wall perforation and inaccurate measurement of the central venous pressure (for whatever that’s worth).

However these risks might be a lot lower than expected. In one cohort study of 1619 patients over three years (Pikwer et al, 2008) a malposition rate of 3.3% was recorded. The right subclavian vein had the highest rate of malposition (9.1%) and the right internal jugular vein had the lowest (1.4%), and only 6 of the 53 malpositioned catheters were removed or adjusted. No case of malposition was associated with localised thrombosis, vessel wall perforation or cerebral complications.

Personally I would argue that catheter malposition can be divided into three categories, all of which have very different implications.

  1. Venous malposition: Probably not as a big a deal as we think, unless the line is being used for high volume fluid administration or large amounts of phlebitic drugs. The inadvertently cannulated vein should have it’s area of venous drainage (e.g. the arm for subclavian vein) monitored closely for signs of swelling and there should be a good reason not to re-site the central line when possible.
  2. Arterial malposition: A very serious complication with potentially debilitating or fatal consequences. Arterial puncture should be recognised immediately from pressure of blood flow, and ideally the guidewire should be confirmed within the target vein with ultrasound prior to dilatation.
    In one particularly terrifying case series the importance of not simply pulling out an arterial central venous catheter manually is highlighted. In the case series, of the patients who had the catheter immediately removed and manual pressure applied 47% had a serious complication including neurological injury and 2 out of 17 patients died. The patients who underwent immediate surgical exploration with removal by a vascular surgeon in the operating theatre had much better outcomes, with no serious complications or deaths.
  3. Extravascular malposition: Potentially serious complication depending where the catheter tip ends up. This should be recognised by inability to aspirate blood from all lumens and the lack of a CVP trace, and if not then by chest x-ray. Administering through these lines can have disastrous complications.

How to avoid central venous catheter malposition?

The safe use of ultrasound is now seen as standard of care. After vessel puncture and the guidewire is inserted the vessel should be scanned again with the ultrasound probe to ensure the guidewire is seen within the vessel. Using a longitudinal view you can also make sure the wire is passing down the vein and isn’t sticking in the posterior wall.

The J tip of the guidewire could theoretically be angled to ensure the guidewire passes down the vein and towards the right atrium. For subclavian vein cannulation the J tip should be angled so the tip faces caudad to encourage a turn towards the right atrium. Inserting the guidewire with the needle bevel facing down could also potentially encourage the guidewire to enter the brachiocephalic vein and subsequently the SVC. For internal jugular vein cannulation the J tip could be angled to the tip faces medially, to discourage the wire from turning into the ipsilateral subclavian vein. However in reality controlling the direction of the guidewire tip is almost impossible without fluoroscopic guidance.

For internal jugular vein cannulation one potential tip would be to use ultrasound to image the subclavian vein after insertion of the guidewire to ensure it is hasn’t entered there instead of the SVC. This is relatively simple to do and involves first imaging the subclavian vein in the short axis to distinguish it from the artery and then rotating the probe 90 degrees to see the vein in long axis and allowed guidewire visualisation.

Unfortunately the literature suggests that operator skill and patient position make no difference in the rates of venous malposition. The important aspect then becomes recognition, which is why post-insertion chest x-rays are important. Your institution may have a policy on the management of malpositioned central lines, ensure you are familiar with it and follow it’s advice.


Venous malposition may not be as bad as we think, however other types of malposition (arterial and extravascular) can be disastrous. Simple measures can reduce the risk and increase recognition of malposition:

  1. Use ultrasound and be competent in it’s use.
  2. Visualise the guidewire within the target vein prior to dilatation.
  3. Transduce the catheter to check a venous pressure waveform (or send a blood gas to ensure a venous sample).
  4. Get a post-insertion chest x-ray.
  5. Your institution may have a departmental policy on management of malpositioned central venous catheters.



  1. Tizard K, Welters I. Central venous catheter placement: where is the end of the line? Critical Care 2012, 16(Suppl 1):P208.
  2. Muhm M, Sunder-Plassmann G, Apsner R et al. Malposition of central venous catheters. Wien Klin Wochenschr. 6; 109(11):400-5, 1997.
  3. Malhotra D, Gupta S, Gupta S, Kapoor B. Malposition of internal jugular vein cannula into ipsilateral subclavian vein in reverse direction – Unusual case report. Intern J Anesthesiol. 2009;22:1
  4. Pikwer A, Bååth L, Davidson B, Perstoft I, Akeson J. The incidence and risk of central venous catheter malpositioning: a prospective cohort study in 1619 patients. Anaesth Intensive Care. 2008 Jan;36(1):30-7.

Transverse section through the neck at C6

Landmarks in relation to the cervical vertebrae

  • At C1, base of the nose and the hard palate
  • At C2, the teeth of a closed mouth
  • At C3, the mandible and hyoid bone
  • At C4, the common carotid artery bifurcates
  • From C4-5, the thyroid cartilage
  • From C6-7, the cricoid cartilage

Transverse section through C6


The thyroid covers the 2nd to 4th tracheal rings. When performing a surgical tracheostomy the isthmus of the thyroid is general displaced downwards by blunt dissection, through if this is not possible it may need to be divided. When performing a percutaneous dilatational tracheostomy the space between the 2nd and 3rd tracheal ring is usually chosen. Tracheostomy higher than this increases the risk of tracheal stenosis. The use of ultrasound to select puncture site to avoid aberrant midline vessels can make the procedure safer, but the use of bronchoscopic guidance is essential for a percutaneous approach.

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.