The relationship between bacterial growth and time is a tear-away exponential. The mathematical relationship between y and x in this case is:

y = ex

Where: the power is x, and the base is e.

Euler’s number (e) is a mathematical constant that is the base for all logarithms occurring naturally. Its value is 2.718.

The statement X increasing with an increase in Y is proportional to Y refers to the change in y in terms of x when considering any exponential relationship.

This is not a build-up exponential, and that is mathematically stated as y = 1-e-kt.

The negative x axis being a horizontal asymptote and the y intercept being 0, 1 are examples of tearaway exponentials , but do not describe an exponential process.

Sevoflurane is highly fluorinated methyl isopropyl ether widely used as an inhalational anaesthetic. It is suggested that sevoflurane preconditioning occurs via the opening of mitochondrial Potassium ATP dependent channel similar to that of Ischemic Preconditioning protection.

The anterior tibial artery originates from the distal border of the popliteus. In the posterior compartment, it passes between the heads of the tibialis posterior and the oval aperture of the interosseous membrane to reach the anterior compartment.

On entry into the anterior compartment, it runs medially along the deep peroneal nerve.
The upper third of the artery courses between the tibialis anterior and extensor digitorum longus muscles, while the middle third runs between the tibialis anterior and extensor hallucis longus muscles.

At the ankle, the anterior tibial artery is located approximately midway between the malleoli. It continues on the dorsum of the foot, lateral to extensor hallucis longus, as the dorsalis pedis artery.

To begin, one must determine the child’s approximate weight. There are a variety of formulas to choose from. It is acceptable to use the advanced paediatric life support formula:

(Age + 4) 2 = Weight

A 5-year-old child will weigh around 18 kilogrammes.

10 mcg/kg (0.1 ml/kg of 1 in 10 000 adrenaline) = 180 mcg is the appropriate dose of intravenous or intraosseous adrenaline.

The correct energy level to deliver is 4 J/kg, which equals 72 joules.

The pad size that is appropriate for this patient is 8-12 cm. For an infant, a 4.5 cm pad is appropriate.

To allow adequate separation in infants and small children, the pads should be placed anteriorly and posteriorly on the chest.

When using a bag and mask to ventilate, take two breaths for every 15 chest compressions. If chest compressions are being applied intubated and without interruption, a ventilation rate of 10-20 breaths per minute should be given.

Chest compressions should be done at a rate of 100-120 per minute, the same as an adult.

Dabigatran template is a prodrug and its active metabolite is a direct thrombin inhibitor. It is a synthetic, reversible, non-peptide thrombin inhibitor. This inhibition of thrombin results in a decrease of fibrin and reduces platelet aggregation.

Drugs like warfarin act by inhibiting the activation of vitamin K-dependent clotting factors. These factors are synthesized by the liver and activated by gamma-carboxylation of glutamate residues with the help of vitamin K. Hydroquinone form of vitamin K is converted to epoxide form in this reaction and regeneration of hydroquinone form by enzyme vitamin K epoxide reductase (VKOR) is required for this activity. Oral anticoagulants prevent this regeneration by inhibiting VKOR, thus vitamin K-dependent factors are not activated. These factors include clotting factors II, VII, IX, and X as well as anti-clotting proteins, protein C and protein S.

The standard error of the mean (SEM) is a measure of the spread expected for the mean of the observations – i.e. how ‘accurate’ the calculated sample mean is from the true population mean. The relationship between the standard error of the mean and the standard deviation is such that, for a given sample size, the standard error of the mean equals the standard deviation divided by the square root of the sample size.

SEM = SD / square root (n)

where SD = standard deviation and n = sample size

Approximately 20% of halothane and 0.02% desflurane undergo hepatic biotransformation. Desflurane, halothane, and isoflurane are metabolised in the liver by cytochrome p450 to trifluoroacetate. Through an immunological mechanism involving trifluoroacetyl hapten formation, trifluoroacetate is thought to be responsible for hepatotoxicity.

Potency of inhaled anaesthetic agents is measured using the minimal alveolar concentration (MAC). The MAC of halothane is 0.74% while that of desflurane is 6.3%. The potency can also be compared using the oil: gas partition coefficient (224 and 18.7 for halothane and desflurane respectively).

Onset of action of volatile agents depends on the blood:gas partition coefficient. A lower blood:gas partition coefficient and insolubility in blood means faster onset and offset of action. The blood gas coefficient for halothane is 2.4 while that of desflurane is 0.42. Desflurane is less soluble than halothane in blood. Halothane has a pungent smell that can irritate the airway which limits its use for a gaseous induction especially in paediatric anaesthesia. desflurane is not pungent.

Desfluranes boiling point is only slightly above normal room temperature (22.8°C) making it extremely volatile while the boiling point of halothane is approximately 50.2°C.

Half life (T½) is the time required to change the amount of drug in the body by one-half (or 50%) during elimination. The time course of a drug in the body will depend on both the volume of distribution and the clearance.

Extrapolating the values from the plasma concentration vs time:

Plasma concentration at 0 hours = 800 mcg/mL
Plasma concentration at 2 hours = 400 mcg/mL
Plasma concentration at 4 hours = 200 mcg/mL
Plasma concentration at 6 hours = 100 mcg/mL
Plasma concentration at 8 hours = 50 mcg/mL
Plasma concentration at 10 hours = 25 mcg/mL
Plasma concentration at 12 hours = 12.5 mcg/mL
Plasma concentration at 14 hours = 6.25 mcg/mL

Adenosine receptors are expressed on the surface of most cells.
Four subtypes are known to exist which are A1, A2A, A2B and A3.

Of these, the A1 and A2 receptors are present peripherally and centrally. There are agonists at the A1 receptors which are antinociceptive, which reduce the sensitivity to a painful stimuli for the individual. There are also agonists at the A2 receptors which are algogenic and activation of these results in pain.

The role of adenosine and other A1 receptor agonists is currently under investigation for use in acute and chronic pain states.

Arrhythmias and/or hypotension are the most common causes of death from tricyclic antidepressant (TCA) overdose.

The quinidine-like actions of tricyclic antidepressants on cardiac tissues are primarily responsible for their toxicity. Conduction through the His-Purkinje system and the myocardium slows as phase 0 depolarisation of the action potential slows. QRS prolongation and atrioventricular block are caused by slowed impulse conduction, which also contributes to ventricular arrhythmias and hypotension.

Arrhythmias can also be caused by abnormal repolarization, impaired automaticity, cholinergic blockade, and inhibition of neuronal catecholamine uptake, among other things.

Acidaemia, hypotension, and hyperthermia can all exacerbate toxicity.

The anticholinergic effects of tricyclic antidepressants, as well as the blockade of neuronal catecholamine reuptake, cause sinus tachycardia. Sinus tachycardia is usually well tolerated and does not require treatment. It can be difficult to tell the difference between sinus tachycardia and ventricular tachycardia with QRS prolongation.

A QRS duration of more than 100 milliseconds indicates a higher risk of arrhythmia and should be treated with systemic sodium bicarbonate.

The tricyclic is dissociated from myocardial sodium channels by serum alkalinization, and the extracellular sodium load improves sodium channel function.

Insulin is secreted from the β cells of the pancreas. It consists of 51 amino acids arranged in two chains. It interacts with cell surface receptors (not the nuclear receptors and thus mechanism of action is not similar to steroids).
Since insulin can pass from plasma to interstitium and lymphatics, it can be measured in lymph but the concentrations here can be up to 30% less than that of plasma.

It decreases blood glucose by stimulating the entry of glucose in muscle and fat (by increasing the synthesis of Glucose transporters)

Oxytocin is structurally similar to Antidiuretic Hormone (ADH) and thus oxytocin cause water intoxication (due to ADH like action)

Oxytocin is secreted by the posterior pituitary along with ADH. It increases the uterine contractions with complete relaxation in between. It increases the contraction of the upper segment (fundus and body) of the uterus whereas the lower segment is relaxed facilitating the expulsion of the foetus

Antidiuretic hormone (ADH) also called vasopressin is released from the posterior pituitary in response to hypertonicity and increases fluid reabsorption from the kidney.

The adrenal medulla comprises chromaffin cells (pheochromocytes), which are functionally equivalent to postganglionic sympathetic neurons. They synthesize, store and release the catecholamines noradrenaline (norepinephrine) and adrenaline (epinephrine) into the venous sinusoids.
The majority of the chromaffin cells synthesize adrenaline.

The inferior mesenteric artery arises from the abdominal aorta at the level of the L3 vertebrae and supplies blood to the final third of the transverse colon, the descending colon, the sigmoid colon and the uppermost part of the rectum.

It is the artery most likely to affect the left colon.

Cardiac conduction

Phase 0 – Rapid depolarization. Opening of fast sodium channels with large influx of sodium

Phase 1 – Rapid partial depolarization. Opening of potassium channels and efflux of potassium ions. Sodium channels close and influx of sodium ions stop

Phase 2 – Plateau phase with large influx of calcium ions. Offsets action of potassium channels. The absolute refractory period

Phase 3 – Repolarization due to potassium efflux after calcium channels close. Relative refractory period

Phase 4 – Repolarization continues as sodium/potassium pump restores the ionic gradient by pumping out 3 sodium ions in exchange for 2 potassium ions coming into the cell. Relative refractory period

Atrial natriuretic peptide (ANP) is secreted mainly from myocytes of right atrium and ventricle in response to increased blood volume.
It is secreted by both the right and left atria (right >> left).

It is a 28 amino acid peptide hormone, which acts via cGMP
degraded by endopeptidases.

It serves to promote the excretion of sodium, lowers blood pressure, and antagonise the actions of angiotensin II and aldosterone.

The Mapleson A (Magill) and coaxial version of the Mapleson A system (Lack circuit) are more efficient for spontaneous breathing than any of the other Mapleson circuits. The fresh gas flow (FGF) required to prevent rebreathing is slightly greater than the alveolar minute ventilation (4-5 litres/minute). This is delivered to the patient through the outer coaxial tube and exhaust gases are moved to the scavenging system through the inner tube. In the Lack circuit, the expiratory valve is located close to the common gas outlet away from the patient end. This is the main advantage of the Lack circuit over the Mapleson A circuit.

The Mapleson E circuit is a modification of the Ayres T piece and the FGF required to prevent rebreathing is 1.5-2 times the patient’s minute volume.

The Bain circuit is the coaxial version of the Mapleson D circuit.

The FGF for spontaneous respiration to avoid rebreathing is 160-200 ml/kg/minute.

The FGF for controlled ventilation to avoid rebreathing is 70-100 ml/kg/min.

The anterior cerebral artery supplies the midline portion of the frontal lobe and the superior medial parietal lobe of the brain. It also supplies the front four-fifths of the corpus callosum and provides blood to deep structures such as the anterior limb of the internal capsule, part of the caudate nucleus, and the anterior part of the globus pallidus.

The cerebral hemispheres are supplied by arteries that make up the Circle of Willis. The Circle of Willis is formed by the anastomosis of the two internal carotid arteries and two vertebral arteries.

Clinically, the internal carotid arteries and their branches are often referred to as the anterior circulation of the brain. The anterior cerebral arteries are connected by the anterior communicating artery. Near their termination, the internal carotid arteries are joined to the posterior cerebral arteries by the posterior communicating arteries, completing the cerebral arterial circle around the interpeduncular fossa, the deep depression on the inferior surface of the midbrain between the cerebral peduncles.

The middle cerebral artery supplies part of the frontal, temporal and parietal lobes.

The posterior cerebral artery supplies the occipital lobe.

Sugammadex is a modified cyclodextrin that works as an aminosteroid neuromuscular blocking (nmb) reversal agent. By encapsulating each molecule in the plasma, it rapidly reverses rocuronium and, to a lesser extent, vecuronium-induced neuromuscular blockade. Consequently, a  concentration gradient favours the movement of these nmb agents away from the neuromuscular junction.  Pancuronium-induced neuromuscular blockade at low levels has also been reversed.

By inhibiting voltage-dependent calcium channels at the neuromuscular junction, antibiotics in the aminoglycoside group potentiate neuromuscular blocking agents. This can be reversed by giving calcium but not neostigmine or sugammadex.

Sugammadex will not reverse the effects of mivacurium, which belongs to the benzylisoquinolinium class of drugs.

A phase II or desensitisation block occurs when the motor end-plate becomes less sensitive to acetylcholine as a result of an overdose or repeated administration of suxamethonium. The use of neostigmine has been shown to be effective in reversing this weakness.

The α-2 adrenoceptor has three subtypes (2a, 2b and 2c). The receptors are generally presynaptic, meaning they prevent noradrenaline from being released at nerve endings. Both the central and peripheral nerve systems are affected by the α-2 agonists. α-2 agonists cause drowsiness, analgesia, and euphoria centrally in the locus coeruleus (in the brainstem), lower the MAC of volatile anaesthetic drugs, and are used to treat acute withdrawal symptoms in chronic opioid addicts.

The most common impact of α-2 agonists on heart rate is bradycardia. The adrenoreceptors α-1 and α-2 are blocked by phenoxybenzamine.

Clonidine is a selective agonist for the α -2 receptor, having a 200:1 affinity ratio for the α-2: α-1 receptors, respectively.

Tizanidine is similar to clonidine but has a few key variances. It has the same sedative, anxiolytic, and analgesic characteristics as clonidine, although for a shorter period of time and with less effect on heart rate and blood pressure.

Dexmedetomidine, like clonidine, is a highly selective α-2 adrenoreceptor agonist having a higher affinity for the α-2 receptor. In the case of α-2: α-1 receptors, the affinity ratio is 1620:1. It has a biphasic blood pressure impact and induces a brief rise in blood pressure and reflex bradycardia (activation of α-2b subtypes of receptors in vascular smooth muscles), followed by a reduction in sympathetic outflow from the brainstem and hypotension/bradycardia.

A prodrug is methyldopa. It blocks the enzyme dopa-decarboxylase, which converts L-dopa to dopamine (a precursor of noradrenaline and adrenaline). It is also converted to alpha-methyl noradrenaline, a centrally active agonist of the α-2 adrenoreceptor. These two processes contribute to its blood pressure-lowering effect. Without a rise in heart rate, cardiac output is generally maintained. The heart rate of certain patients is slowed.

Phentolamine is a short-acting antagonist of peripheral α-1 and α-2 receptors that causes peripheral vascular resistance to reduce and vasodilation to increase. It’s used to treat hypertensive situations that aren’t life threatening (e.g. hypertension from phaeochromocytoma).

A baroreceptor reflex commonly causes reflex tachycardia when systemic vascular resistance drops.