Convergent Series in Medicine

There were 160,000 deaths from cardiovascular causes in the UK in 2016. If the number of deaths decreases by 5% every year, year after year, indefinitely, what is the total number of people that would have succumbed to cardiovascular causes?

This is an example of a convergent geometric series.

In general, the sum of a geometric series is given by S= a (1-r^n)/1-r, where S is the sum of the first n numbers, a is the first number in the sequence, and r is the common ratio of the sequence (the factor by which each successive number increases or decreases).

Now, can you predict what would be the sum of the series if n was infinite? Would the sum S be finite or infinite?

The answer is that it depends on the value of r, the common ratio. If r is between -1 & 1, the sum S would be a finite (convergent series), while if r is <-1 or >1, the sum would be infinite (divergent series).

If r is a fraction, the limit of the equation S= a (1-r^n)/1-r, as n approaches infinity, is S = a/1-r.

In the above example, r=0.95, as the death rate falls by 5% every year, the total number deaths in infinite number of years would be 160,000/0.05=32,00,000.

The sum of this geometric series is finite, hence it's a convergent series.

Alcohol, The Herald

Take a look at the following two situations, and see what you make of them.

In the first, a 33-year old man complains of severe left shoulder pain after drinking alcohol. He's lost weight and has night sweats.

Elsewhere, a 30 year old man has rhinorrhoea, breathlessness and wheezing every time he drinks alcohol.

The first man had Hodgkin's lymphoma. The second had Aspirin Exacerbated Respiratory Disease (AERD).

Musculoskeletal pain can be triggered by alcohol in many cancers. In one series, 40% of these were due to Hodgkin's lymphoma.

Similarly, although the usual trigger for upper & lower respiratory symptoms in AERD is aspirin or Cox 1 inhibiting NSAIDs, alcohol is a common trigger as well. The mechanism is not known.

What's Common to McLeod Syndrome & Glycerol Kinase Deficiency?

McLeod syndrome was first described in a trainee dentist, after whom the condition is named. In most cases it occurs due to truncation of the XK gene, present on Xp21. As the protein occurs on red cell membrane as a heterodimer, linked to the Kell antigen, the condition can sometimes be picked up by the Blood Bank due to the absence or attenuation of the Kell blood group antigen.

Mcleod syndrome shares many features with choreo-acanthocytosis, an autosomal recessive condition caused by defects in a protein called chorein. However, the latter does not have the blood group phenotype of McLeod syndrome- i.e. reduced or absent Kell antigen and absent XK antigen (also called Kx antigen).

McLeod Syndrome can occur alone, or as part of the contiguous gene deletion syndrome affecting neighbouring genes on the short arm of X-chromosome, leading to congenital adrenal hypoplasia, Duchenne Muscular Dystrophy (DMD), X-linked Retinitis Pigmentosa, or combinations thereof.

All documented men with McLeod syndrome have a raised CK between 400-4000 IU/l. It happens even in subjects without contiguous gene deletion, and cannot therefore be attributed to DMD.

Here's where it gets interesting. Similar elevations in CK can be seen in subjects with Glycerol Kinase deficiency, which is also coded on Xp21. This has infantile, juvenile and adult forms, and most with the adult form are asymptomatic except for 2 findings- hypertriglyceridaemia and raised CK. The infantile and occasionally, the juvenile form presents with abdominal pain, non-ketotic hypoglycemia and seizures, much like the carnitine disorders presented elsewhere in this blog.

The hypertiglyceridaemia seen in subjects with glycerol kinase deficiency is actually a pseudo-phenomenon. These subjects in fact have markedly raised serum glycerol, which tests positive in assays for triglycerides. Think of this condition when you see raised CK and high triglycerides in an adult male who is otherwise well.

Nobody knows why these two disparate conditions arising from gene defects on Xp21 should have raised CK. This is currently unexplained.

Curiously, subjects with choreo-acanthocytosis due to reduction in chorein also have a raised CK. However, this is an autosomal recessive condition and therefore cannot be attributed to the X-chromosome.

Unusual Pulmonary Function Tests- "The Non-Specific" and "Complex Restrictive" Patterns

So you thought you knew all about lung function tests, right? Well, try these two scenarios.

In the first, both FEV1 and FVC are low, and the FEV1/FVC ratio is normal. You suspect restriction. You request a TLC by whole body plethysmography, and to your surprise, the TLC is normal.

In another patient, the FEV1 and FVC are again low, the FEV1/FVC ratio is normal, and the TLC is low. However, the FVC is disproportionately reduced compared with TLC when measured against what is considered normal.

The first pattern is called the "Non-specific pattern", while the second is termed "the complex restrictive pattern".

The non-specific pattern is not uncommon- in fact, it crops up in around 10% of PFTs. These subjects were originally thought to have airway obstruction, but it's now clear that obstruction is present in only 60% of such subjects. The other 40% are due to chest wall disorders such as obesity, or neuromuscular disorders, or due to poor technique.

These two categories need differentiating with further tests such as repetition of spirometry after administration of a bronchodilator. This will identify the cohort with obstruction. A chest Xray should pick up a lung mass or pleural effusion. Obesity should be self evident, while Maximal Inspiratory Pressure, Maximal Expiratory Pressure and Maximal Ventilation Volume should identify those with neuromuscular weakness.

Fully two-thirds of subjects with the "non-specific" pattern continue to display this pattern over the years. Only a minority evolve into a frankly obstructive or restrictive phenotype on PFT.

The other pattern, called "Complex Restriction" is much more unusual, and probably accounts for less than 2% of PFTs. Here, the FVC is disproportionately reduced in relation to the TLC, with a discrepancy of >10% in relation to normal values. This pattern occurs relatively frequently in young females. It is associated with atelectasis, diaphragmatic paralysis, mosaic air trapping on imaging, bronchiectasis, BMI>40 or <18.5 and neuromuscular weakness. The term "Complex Restriction" differentiates this group from "Simple Restriction", where the FEV1 and FVC are reduced as well, but the TLC is reduced by proportionately the same extent as the FVC. While subjects with simple restriction are likely to have ILD, those with complex restriction usually do not have ILD. An excellent account can be found in the latest edition of Mayo Clinic Proceedings: https://www.mayoclinicproceedings.org/article/S0025-6196(18)30282-9/pdf

Perineural Spread of Tumour- Beware That Trigeminal Neuralgia

Perineural spread of tumours is a phenomenon that is often subtle, unobtrusive until very late and below the radar for most physicians, including oncologists. Perineurium is the second of the three nerve covers, and under the perineurium lies a potential space, where tumors can spread freely, unimpeded by immune calls, often spreading centripetally towards the brainstem, and less commonly towards the periphery. One should perhaps start by explaining the difference between perineural spread (PNS) and perineural invasion (PNI).

PNI is of two types- one that is only picked up on miscroscopic examination of the resected tumour specimen, and one that is obvious clinically or radiologicaly (usually on MRI). The former is called microscopic PNI, while the latter is called clinical PNI, named nerve PNI, or PNS.

Therefore PNS can be a clinically manifest phenomenon, presenting with numbness or paralysis, or silent, but radiologically obvious on MRI. PNS, by definition, affects large nerves.

Where does PNS crop up most often? In the head and neck, typically in territories supplies by the cranial nerves V & VII, which tend to be the most commonly affected by PNS.

Cutaneous squamous cell cancer (SCC) is the most common malignancy that leads to PNS. The second most common, in terms of ratio, is adenoid cystic carcinoma of the salivary gland. Other predisposing tumours, albeit less common, include basal cell carcimoma, salivary ductal carcinoma, ex-pleomorphic adenoma, and rarely melanoma. Mucosal (head and neck) SCC is a distinctly uncommon source of PNS.

In most cases, the tumour, usually a SCC, has been removed in the remote past, ranging from a few months to few years ago. There are no signs of metastases anywhere else in a third of cases, just in the perineural space.

One must suspect PNS when a subject with a remote history of treated SCC presents with numbness, or paresthesiae in one or more divisions of the trigeminal nerve. The most commonly affected is the maxillary branch. Symptoms are often attributed to trigeminal neuralgia. Men are affected 5 times more commonly as women. Similarly, the facial nerve may be involved, often partially. Upon exiting the stylomastoid foramen, the VII nerve splits into two divisions which then give rise to 5 branches. Usually one or more such branches are involved, for example giving rise to weakness of muscles of mastication. When the entire VII nerve is involved, an erroneous diagnosis of Bells palsy is often made. However, it is worth remembering that Bells palsy occurs acutely while VII nerve involvement in PNS occurs gradually over months.

The median interval between removal of the primary tumour and manifestation of PNS is 16 months, but can be years. Six out of 7 patients have a previous history of cancer, while around 7.5% have no previous history. In a third of cases there is no evidence of PNI in the excised original tumour. The original tumour may have been unclassifiable, treated early with radiotherapy or cryotherapy or not biopsied at all, and thus a definite history of a preceding primary may be difficult to establish, with the only evidence of the same being sun damaged skin.

MRI with neural imaging is better at diagnosis than CT, and should be used when available. Normal nerves appear isointense to the surrounding tissue on T1- and T2-weighted MRIs, but upon injury the nerves become hyperintense and thus visible on T2-weighted MRI. Survival at 5 years is 50-64%. Most patients are treated with a combination of surgery and radiotherapy.

Read the following article for a more comprehensive review.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4846401/

Phaeochromocytoma/Paragangliomas Arise Against a Background of Chonic Hypoxia

Phaeochromocytomas/paragangliomas (Pheo/PGL) are tumours of the neuroendocrine system. Roughly a third of these tumours are inherited, driven by genes such as VHL, EPAS-1, EGLN-1, SDH A, SDH B, SDH C, SDH D, SDH AF, RET, and a couple of others. Several of these genes, epitomised by Hypoxia Inducing Factor (HIF), are activated in response to hypoxia. HIF-beta is constitutive, while HIF-alpha is inducible. Several of the SDH genes are also "turned on" by hypoxia. When these genes are constitutively activated in the absence of hypoxia, say due to a mutation, they are said to mimic "pseudohypoxia".

In the 1960s, it became apparent that pheo/PGL was more common in subjects with chronic hypoxia, specifically in two subgroups- in subjects with congenital cyanotic heart disease (CCHD) and in subjects living at high altitudes. Subjects with CCHD in particular, have a much higher incidence of pheo/PGL than the general population. The incidence of pheo/PGL in subjects with non-cyanotic congenital heart disease such as VSD, PDA, ASD and bicuspid aortic valve is no different than the general population.

Similarly subjects living at high altitudes have a higher risk of paragangliomas.

In the latest issue of New England Journal of Medicine, Vaidya and colleagues found that activating somatic mutations in EPAS-1, which codes for HIF-2 alpha, were present in 4 out of 5 subjects with CCHD presenting with pheo/PGL. To put this in perspective, the incidence of EPAS-1 activating mutations in subjects with pheo/PGL who do not have CCHD is only 5-6%.

In developed countries, most subjects with CCHD would have had surgical corrections such as Fontan's procedure in childhood. While the duration of uncorrected CCHD correlates positively with the risk of pheo/PGL, corrective procedures do not ameliorate risk. These tumors can arise many decades later.

Most of these subjects have striking polycythaemia. The latter is of course seen in tumours other than pheo/PGL. For example germ line mutations in VHL lead to the Von Hippel Lindau syndrome, with a higher risk of haemangioblastomas and renal cancer. Somatic mutation in VHL leads to a higher risk of renal cell cancer, and can again be associated with polycythaemia.

It is tempting to hypothesise that the hypoxia inducible genes, when chronically activated by hypoxia itself, through the agency of EPAS-1, as in CCHD, or constitutively (and inappropriately) activated by germline and somatic mutations in genes such as VHL, lead to increased risk of tumours- pheo/PGL in the case of CCHD, pheo/PGL & renal cell cancer with germline VHL mutations, and renal cell cancer in somatic VHL mutations.

It is worth clarifying here that VHL is an inbuilt inhibitor of HIF-alpha. When VHL is mutated (with inactivation), HIF-alpha becomes disinhibited and is free to act as a growth promoting gene (new blood vessels, pheo/PGL, renal cell cancer).

There is no suggestion that acquired causes of hypoxia in adulthood such as heavy smoking or chronic lung disease lead to a higher risk of pheo/PGL. It appears that the drive from hypoxia must start very early in life, such as with CCHD, in order to lead to activating mutations such as in EPAS-1, that would in turn increase the risk of pheo/PGLs.

Since many of the symptoms of CCHD mimic pheo/PGL (tachycardia, palpitation, headache, fatigue), physicians dealing with such patients should have a high index of suspicion for pheo/PGL.

Interestingly the profile of secreted catecholamines in pheo/PGL arising in CCHD is very similar to those where pheo/PGLs arise as part of an inherited syndrome due to "pseudohypoxia" mimicking mutations (VHL, SDH-x). Such subjects have high levels of noradrenaline and normetanephrines and almost normal levels of adrenaline and metanephrines.

More Snow for Britain?

Does weather fascinate you? It certainly grips me. Perhaps because I live in a smallish island (by American standards) buffeted by Atlantic currents from the West and Siberian drifts from the East. Westerly currents mean rain and warmer temperatures, while flow from the East and North is chilly. Simple, you'd think?

Well, weather forecasting is difficult, even for the best in the business. Weather patterns are stochastic, influenced by lots of different variables changing constantly, and it takes a helluva job to get it right most of the time.

So can you make money out of calling the weather right? In February 2018, BBC ditched their £3 million annual contract with the UK's venerable Met Office, which had stood for some 95 years. Instead they plumped for a private weather forecasting company called Meteo Group, founded by a Dutch meteorologist in the 1980s, now headquartered in London. There were howls of protest from traditionalists when BBC's familiar weather pages were replaced by strange charts and symbols from the pan-European group, but the BBC stood its ground.

The irony is that Meteo Group- the private company, takes its raw data from the Met Office....it then puts that data into its own models and comes up with a bespoke prediction.

Well, here's the interesting bit. This coming week, the two agencies- Met Office and Meteo Group- BBC's erstwhile and current weather Gurus- are about to go head to head. Meteo Group are predicting more snow leading up to Easter, on the premise that Siberian winds are going to linger over Britain, much to a runner's chagrin, while the Met Office are predicting cold weather, but no snow, based on their view that the Easterly stuff will work its way through but not tarry. As you can imagine, I am firmly rooting for the latter.

We shall find out soon. Who would have thought there would be so much riding on a bit of forecast?