Some days ago, David Systrom offered an overview of his work on cardiopulmonary testing in ME/CFS during a virtual meeting hosted by the Massachusetts ME/CFS & FM Association and the Open Medicine Foundation. In this blog post, I present an introduction to the experimental setting used for Systrom’s work (paragraph 1), a brief presentation of his previous findings (paragraph 2), and an explanation of his more recent discoveries in his cohort of patients (paragraph 3). In paragraph 4 you’ll find a note on how to support his research.
1. Invasive Cardiopulmonary Exercise Testing
It is a test that allows for the determination of pulmonary, cardiac, and metabolic parameters in response to physical exertion of increasing workload. It is, mutatis mutandis, the human equivalent of an engine test stand. A stationary bike with a mechanical resistance that increases by 10 to 50 Watts for minute is usually employed for assessing the patient in a upright position, but a recumbent bike can also be used in some instances. Distinguishing between these two different settings might be of pivotal relevance in ME/CFS and POTS. I shall now briefly describe some of the measurements that can be collected during invasive cardiopulmonary exercise testing (iCPET) and their biological meaning. For a more accurate and in-depth account, please refer to (Maron BA et al. 2013), (Oldham WM et al. 2016). I have used these papers as the main reference for this paragraph, unless otherwise specified.
Gas exchange. A face mask collects the gasses exchanged by the patient during the experiment and allows for monitoring of both oxygen uptake per unit of time (named ) and carbon dioxide output (), measured in mL/min. Gas exchange is particularly useful for the determination of the anaerobic threshold (AT), i.e. the point in time at which the diagram of in function of displays an abrupt increase in its derivative: at this workload, the patient starts relying more on her anaerobic energy metabolism (glycolysis, for the most part) with a build-up of lactic acid in tissues and blood (see Figure 1).
Oxygen uptake for unit of time at AT (called max) can be considered an integrated function of patient’s muscular, pulmonary, and cardiac efficiency during exercise. It is abnormal when its value is below 80% of what predicted according to patient’s age, sex, and height. Importantly, according to some studies there might be no difference in max between ME/CFS patients and healthy controls, unless the exercise test is repeated a day after the first measure: in this case the value max for patients is significantly lower than for controls (VanNess JM et al. 2007), (Snell CR and al. 2013).
Another measure derived from the assessing of gas exchange is minute ventilation (VE, measured in L/min) which represents the total volume of gas expired per minute. The link between VE and is as follows:
Maximum voluntary ventilation (MVV) is the maximum volume of air that is voluntarily expired at rest. During incremental exercise, a healthy person should be able to maintain her VE at a value ∼0.7 MVV and it is assumed that if the ratio VE/MVV is above 0.7, then the patient has a pulmonary mechanical limit during exercise. If VE is normal, then an early AT suggests an inefficient transport of oxygen from the atmosphere to muscles, not due to pulmonary mechanics, thus linked to either pulmonary vascular abnormalities or muscular/mitochondrial abnormalities. It is suggested that an abnormally high derivative of the diagram of VE in function of and/or a high ratio VE/ at AT (these are measures of how efficiently the system gets rid of ) are an indicator of poor pulmonary vascular function.
Respiratory exchange ratio (RER) is a measure of the effort that the patient puts into the exercise. It is measured as follows:
and an RER>1.05 indicates a sufficient level of effort. In this case the test can be considered valid.
Arterial catheters. A sensor is placed just outside the right ventricle (pulmonary artery, Figure 2) and another one is placed in the radial artery: they allow for measures of intracardiac hemodynamics and arterial blood gas data, respectively. By using this setting, it is possible to indirectly estimate cardiac output (Qt) by using Fick equation:
where the is measured by the radial artery catheter and the venous one is measured by the one in the pulmonary artery (ml/L). An estimation for an individual’s predicted maximum Qt (L/min) can be obtained by dividing her predicted max by the normal maximum value of during exercise, which is 149 mL/L:
If during iCPET the measured Qt max is below 80% of the predicted maximum cardiac output (as measured above), associated with reduced max, then a cardiac abnormality might be suspected. Stroke volume (SV), defined as the volume of blood ejected by the left ventricle per beat, can be obtained from the Qt according to the following equation:
where HR stands for heart rate. One obvious measure from the pulmonary catheter is the mean pulmonary artery pressure (mPAP). The right atrial pressure (RAP) is the blood pressure at the level of the right atrium. Pulmonary capillary wedge pressure (PCWP) is an estimation for the left atrial pressure. It is obtained by the pulmonary catheter. The mean arterial pressure (MAP) is the pressure measured by the radial artery catheter and it is a proxy for the pressure in the left atrium. RAP, mPAP, and PCWP are measured by the pulmonary catheter (the line in red) which from the right atrium goes through the tricuspid valve, enters the right ventricle, and then goes along the initial part of the pulmonary artery (figure 2).
Derived parameters. As seen, Qt (cardiac output) is derived from actual direct measures collected by this experimental setting, by using a simple mathematical model (Fick equation). Another derived parameter is pulmonary vascular resistance (PVR) which is obtained using the particular solution of the Navier-Stokes equations (the dynamic equation for Newtonian fluids) that fits the geometry of a pipe with a circular section. This solution is called the Poiseuille flow, and it states that the difference in pressure between the extremities of a pipe with a circular cross-section A and a length L is given by
where is a mechanical property of the fluid (called dynamic viscosity) and Q is the blood flow (Maccallini P. 2007). As the reader can recognize, this formula has a close resemblance with Ohm’s law, with P analogous to the electric potential, Q analogous to the current, and analogous to the resistance. In the case of PVR, Q is given by Qt while . Then we have:
where the numeric coefficient is due to the fact that PVR is usually measured in and 1 dyne is Newton while 1 mmHg is 1333 N/m².
2. Preload failure
A subset of patients with exercise intolerance presents with preload-dependent limitations to cardiac output. This phenotype is called preload failure (PLF) and is defined as follows: RAP max < 8 mmHg, Qt and max <80% predicted, with normal mPAP (<25 mmHg) and normal PVR (<120 ) (Maron BA et al. 2013). This condition seems prevalent in ME/CFS and POTS. Some of these patients have a positive cutaneous biopsy for small-fiber polyneuropathy (SFPN), even though there seems to be no correlation between hemodynamic parameters and the severity of SFPN. Intolerance to exercise in PLF seems to improve after pyridostigmine administration, mainly through potentiation of oxygen extraction in the periphery. A possible explanation for PLF in non-SFPN patients might be a more proximal lesion in the autonomic nervous system (Urbina MF et al. 2018), (Joseph P. et al. 2019). In particular, 72% of PLF patients fits the IOM criteria for ME/CFS and 27% meets the criteria for POTS. Among ME/CFS patients, 44% has a positive skin biopsy for SFPN. One possible cause for damage to the nervous system (both in the periphery and centrally) might be TNF-related apoptosis-inducing ligand (TRAIL) which has been linked to fatigue after radiation therapy; TRAIL increases during iCPET among ME/CFS patients (see video below).
3. Latest updates from David Systrom
During the Massachusetts ME/CFS & FM Association and Open Medicine Foundation Fall 2020 Event on Zoom, David Systrom reported on the results of iCPET in a set of ME/CFS patients. The max is lower in patients vs controls (figure 3, up). As mentioned before, max is an index that includes contributions from cardiac performances, pulmonary efficiency, and oxygen extraction rate in the periphery. In other words, a low max gives us no explanation on why it is low. This finding seems to be due to different reasons in different patients even though the common denominator among all ME/CFS patients of this cohort is a low pressure in the right atrium during upright exercise (low RAP, figure 3, left). But then, if we look at the slope of Qt in function of (figure 3, right) we find three different phenotypes. Those with a high slope are defined “high flow” (in red in figure 3). Then we have a group with a normal flow (green) and a group with a low flow (blue). If we look then at the ability to extract oxygen by muscles (figure 3, below) expressed by the ratio
we can see that the high flow patients reach the lowest score. In summary, all ME/CFS patients of this cohort present with poor max and preload failure. A subgroup, the high flow phenotype, has poor oxygen extraction capacity at the level of skeletal muscles.
Now the problem is: what is the reason for the preload failure? And in the high flow phenotype, why the muscles can’t properly extract oxygen from blood? As mentioned, about 44% of ME/CFS patients in this cohort has SFPN but there is no correlation between the density of small-fibers in the skin biopsies and the hemodynamic parameters. Eleven patients with poor oxygen extraction (high flow) had their muscle biopsy tested for mitochondrial function (figure 4) and all but one presented a reduction in the activity of citrate synthase (fourth column): this is the enzyme that catalyzes the last/first step of Krebs cycle and it is considered a global biomarker for mitochondrial function. Some patients also have defects in one or more steps of the electron transport chain (fifth column) associated with genetic alterations (sixth column). Another problem in high flow patients might be a dysfunctional vasculature at the interface between the vascular system and skeletal muscles (but this might be true for the brain too), rather than poor mitochondrial function.
The use of an acetylcholinesterase inhibitor (pyridostigmine) improved the ability to extract oxygen in the high flow group, without improving cardiac output, as measured with a CPET, after one year of continuous use of the drug. This might be due to better regulation of blood flow in the periphery. This paragraph is an overview of the following video:
The trial on the use of pyridostigmine in ME/CFS at the Brigham & Women’s Hospital by Dr. David Systrom is funded by the Open Medicine Foundation (R). This work is extremely important, as you have seen, both for developing diagnostic tools and for finding treatments for specific subgroups of patients. Please, consider a donation to the Open Medicine Foundation to speed up this research. See how to donate.
The equations of this blog post were written using .
When I got sick, about 20 years ago, for the first time I started thinking about diseases and loss of health. And I remember coming to the conclusion of how fortunate I was, from a physical standpoint. Not of how fortunate I had been in the past (that was obvious), when I could conquer mountains, running on rocks with my 15 Kg bike on the shoulders; no, of how fortunate I was in that very moment, while confined at home, mostly lying horizontally. I was fortunate, I could still move my hands, I had still all my body, even if I couldn’t use it in the outside world, even if most of the usual activities of a 20 years old man were far beyond reaching, I realized how fortunate I was. And after 20 years I still say that, as for the physical functioning, I am a very lucky man. There are even some years, during the core of the summer, in which I can run for some minutes in the sun. I am blessed.
I am aware that this might offend some patients, but I think that those who have ME/CFS in the vast majority of cases are fortunate too, from a physical standpoint. Yes, it is annoying to need help from others for so many things, but with assistance and some arrangements, you can go on with a productive life… unless you have cognitive impairment.
Actually, I never felt fortunate concerning my cognitive functioning. That has been a true tragedy, I have lost my entire life because of the cognitive damage, by any means because of the limitations of my body. I would have had a meaningful life (according to any standard) even with physical limitations way worse than mine if I had had a functioning brain. But I lost it when I was 20 before I could get the best from it and that is the only real tragedy.
As an example of what I am saying, consider a person like Stephen Hawking: he has been a prolific scientist, he had a stellar career (literally), he shaped our culture with his books for the general public, he was a father of three, and so forth. And yet for most of his life, while he was doing all these things, his physical functioning was way worse than the one of the average ME/CFS patient (worse even of a very severe patient, probably). For many years he could use only the muscles of the head. That’s it. Think about that. Was he missing or invisible? Definitely not!
Was he a disabled man? Yes, technically speaking he was, but in fact, he has never really been disabled, if we judge from his accomplishments. He once said that the disease somehow even helped him in his work, because he could concentrate better on his quantum-relativistic equations¹.
So what I am saying is that if we consider the physical functioning in ME/CFS, it is a negligible problem in most of the cases. The only thing that matters is the impairment in cognition (in the cases in which it is present), especially if it starts at a young age (consider that after you reach your thirties there is very little chance that your brain will give a significant contribution to humanity, even if you are perfectly healthy, so it is not a big loss if you get sick after that age). That is disastrous and there is no wheelchair you can use for it. For all the other symptoms you can find a way to adjust, just as Hawking did in a far worse situation.
This might be one of the reasons for the bad reputation of ME/CFS: there isn’t awareness about cognitive issues, no one talk about them (and in some cases, they are in fact not present at all). But I am pretty sure that the real source of disability in these patients, the lack of productivity, is due to their cognitive problems (when present). Also because in a world like ours, you can work even without using most of your muscles. It is not impossible, I would say it is the rule for a big chunk of the population.
The following one is an interview with Norwegian neurologist Kristian Sommerfelt, in which he points out some analogous considerations. He has done some research on ME/CFS with the group of Fluge and Mella, including the well-known study on pyruvate dehydrogenase. From the subtitles of the video (minute 3:38):
“This [the cognitive problem] is a very typical ME symptom and some of what I believe causes the main limitation. I don’t think the main limitation is that they’re becoming fatigued and exhausted by moving around, walking, running, or having to sit still. If it were just that, I think many ME-patients could have had a much better life. But the problem is that just actively using the mind leads to problems with exactly that, using the mind. It comes to a stop, or slow down, depending on how ill they are.”
¹ It seems that Stephen Hawking had a very unusual presentation of Amyotrophic Lateral Sclerosis (ALS): one half of those with this disease die within 30 months from the first symptom; moreover one out of two ALS patients has a form of cognitive impairment which in some cases can be diagnosed as frontotemporal dementia [R]. So, Stephen Hawking was somehow lucky, in his tragedy, and he doesn’t represent the average ALS patient. I mentioned his case as an example of a person with very severe physical impairment and no apparent cognitive decline, not as an example of the average ALS patient.
The purpose of the following analysis is to search for the viral epitopes that elicited – in a ME/CFS patient – IgGs against a set of 6 peptides, determined thanks to an array of 150.000 random peptides of 16 amino acids each. These peptides were used as query sequences in a BLAST search against viral proteins. No human virus was found. Three phages of bacterial human pathogens were identified, belonging to the classes Actinobacteria and γ-Proteobacteria. One of these bacteria, Serratia marcescens, was identified in a similar study on 21 ME/CFS cases.
Scientists have been speculating about an infectious aetiology of ME/CFS for decades, without ever being able to link the disease to a specific pathogen. The idea that the disease might be triggered and/or maintained by an infection is due to the observation that for most of the patients the onset occurs after an infectious illness (Chu, L. et al. 2019). It has also been observed that after a major infection (whether parasitic, viral or bacterial) about 11% of the population develops ME/CFS (Mørch K et al. 2013), (Hickie I. et al. 2006).
In recent years, the advent of new technologies for pathogen hunting has given renewed impulse to the search for ongoing infection in this patient population. A 2018 study, investigating the genetic profile of peripheral blood for prokaryotic and eukaryotic organisms reported that most of the ME/CFS patients have DNA belonging to the eukaryotic genera Perkinsus and Spumella and to the prokaryotic class β-proteobacteria (alone or in combination) and that these organisms are statistically more present in patients than in controls (Ellis J.E. et al. 2018). Nevertheless, a previous metagenomic analysis of plasma by another group revealed no difference in the content of genetic material from bacteria and viruses between ME/CFS patients and healthy controls (Miller R.R. et al. 2016). Moreover, metagenomic analysis pursued in various samples from ME/CFS patients by both Stanford University and Columbia University has come empty (data not published, R, R).
2. Immunological methods
Another way of investigating the presence of current and/or past infections that might be specific of this patient population is to extract the information contained in the adaptive immune response. This can be made in several ways, each of them having their own limits. One way would be to collect the repertoire of T cell receptors (TCRs) of each patient and see if they have been elicited by some particular microorganism. This is a very complex and time-consuming method that has been developed in recent years and that I have described in details going through all the recent meaningful publications (R). The main limitation of this method is that, surprisingly, TCRs are not specific for a single epitope (Mason DA 1998), (Birnbaum ME et al. 2014), so their analysis is unlikely to reveal what agent selected them. On the other hand, the advantage of this method is that T cell epitopes are linear ones, so they are extremely suited for BLAST searches against protein databases. An attempt at applying this method to ME/CFS is currently underway: it initially gave encouraging results (R), then rejected by further analysis.
Another possible avenue for having access to the information registered by adaptive immunity is to investigate the repertoire of antibodies. The use of a collection of thousands of short random peptides coated to a plate has been recently proposed as an efficient way to study the response of B cells to cancer (Stafford P. et al. 2014), infections (Navalkar K.A. et al. 2014), and immunization (Legutki JB et al. 2010). This same method has been applied to ME/CFS patients and it has shown the potential of identifying an immunosignature that can differentiate patients from controls (Singh S. et al. 2016), (Günther O.P. et al. 2019). But what about the antigens eliciting that antibody profile? Given a set of peptides one’s antibodies react to, a possible solution for interpreting the data is to use these peptides as query sequences in a BLAST search against proteins from all the microorganisms known to infect humans. This has been done for ME/CFS, and the analysis led to several matches among proteins from bacteria, viruses, endogenous retroviruses and even human proteins (in fact, both this method and the one previously described can detect autoimmunity as well) (Singh S. et al. 2016). There are several problems with this approach, though. First of all, the number of random peptides usually used in these arrays is not representative of the variety of possible epitopes of the same length present in nature. If we consider the paper by Günther O.P. and colleagues, for instance, they used an array of about 10^5 random peptides with a length of 12 amino acids each, with the number of all the possible peptides of the same length being 20^12 ∼ 4·10^15. This means that many potential epitopes one has antibodies to are not represented in the array. Another important limitation is that B cell epitopes are mainly conformational ones, which means that they are assembled by the folding of the proteins they belong to (Morris, 2007), the consequence of this being that the subset of random peptides one’s serum react to are in fact linear epitopes that mimic conformational ones (they are often called mimotopes) (Legutki JB et al. 2010). This means that a BLAST search of these peptides against a library of proteins from pathogens can lead to completely misleading results.
Recently an array of overlapping peptides that cover the proteins for many know viruses has been successfully used for the study of acute flaccid myelitis (AFM). This technology, called VirScan, has succeeded in linking AFM to enteroviruses where metagenomic of the cerebrospinal fluid has failed (Shubert R.D. et al. 2019). This kind of approach is probably better than the one employing arrays of random peptides, for pathogen hunting. The reason being that a set of only 150.000 random peptides is unlikely to collect a significant amount of B cell epitopes from viruses, bacteria etc. Random peptides are more suited for the establishment of immunosignatures.
3. My own analysis
I have recently got access to the results of a study I was enrolled in two years ago. My serum was diluted and applied to an array of 150.000 peptides with a length of 16 random amino acids (plus four amino acids used to link the peptides to the plate). Residues Threonine (T), Isoleucine (I) and Cysteine (C) were not included in the synthesis of peptides. Anti-human-IgG Ab was employed as a secondary antibody. The set of peptides my IgGs reacted to has been filtered with several criteria, one of them being subtracting the immune response common to healthy controls, to have an immune signature that differentiates me from healthy controls. The end result of this process is the set of the following six peptides.
Table 1. My immunosignature, as detected by an array of 150.000 random peptides 20-amino-acid long, four of which are used for fixing them to the plate and are not included here.
The purpose of the following analysis is to search for the viral epitopes that elicited this immune response. To overcome the limitations enumerated at the end of the previous paragraph I have decided to search within the database of viral proteins for exact matches of the length of 7 amino acids. Why this choice? A survey of a set of validated B cell epitopes found that the average B cell epitope has a linear stretch of 5 amino acids (Kringelum, et al., 2013); according to another similar work, the average linear epitope within a conformational one has a length of 4-7 amino acids (Andersen, et al., 2006). To filter the matches and to reduce the number of matches due to chance, I opted for the upper limit of this length. I excluded longer matches to limit the number of mimotopes for conformational epitopes. Moreover, I decided to look only for perfect matches (excluding the possibility of gaps and substitutions) so to simplify the analysis. It is worth mentioning that a study of cross-reactive peptides performed for previous work (Maccallini P. 2016), (Maccallini P. et al. 2018) led me to the conclusion that cross-reactive 7-amino-acid long peptides might often have 100% identity.
So, to recap, I use the following method: BLAST search (blastp algorithm) against viral proteins (taxid 10239), a perfect match (100% identity) of at least 7-amino-acid peptides (≥43% query cover), max target sequences: 1000, substitution matrix: BLOSUM62.
Table 2 is a collection of the matches I found with the method described above. You can look at figure 1 to see how to read the table.
Table 2. Collection of the matches for the BLAST search of my unique set of peptides against viral proteins (taxid 10239). HP: human pathogen. See figure 1 for how to read the table.
There are no human viruses detected by this search. There are some bacteriophages and three of them have as hosts bacteria that are known to be human pathogens. Bacteriophages (also known as phages) are viruses that use the metabolic machinery of prokaryotic organisms to replicate (figure 2). It is well known that bacteriophages can elicit specific antibodies in humans: circulating IgGs to naturally occurring bacteriophages have been detected (Dąbrowska K. et al. 2014) as well as specific antibodies to phages injected for medical or experimental reasons (Shearer WT et al. 2001), as reviewed here: (Jonas D. Van Belleghem et al. 2019). According to these observations, one might expect that when a person is infected by a bacterium, this subject will develop antibodies not only to the bacterium itself but also to its phages.
If that is the case, we can use our data in table 2 to infer a possible exposure of our patient to the following bacterial pathogens: Stenotrophomonas maltophilia (HP), Serratia marcescens (HP), Mycobacterium smegmatis mc²155 (HP). In brackets, there are links to research about the pathogenicity for humans of each species. M. smegmatis belongs to the class Actinobacteria, while S. maltophila and S. marcescens are included in the class γ-Proteobacteria.
Interesting enough, Serratia marcescens was identified as one of the possible bacterial triggers for the immunosignature of a group of 21 ME/CFS patients, in a study that employed an array of 125.000 random peptides (Singh S. et al. 2016). This bacterium accounts for rare nosocomial infections of the respiratory tract, the urinary tract, surgical wounds and soft tissues. Meningitis caused by Serratia marcescens has been reported in the pediatric population (Ashish Khanna et al. 2013).
The next step will be to perform a similar BLAST search against bacterial proteins to see, among other things, if I can find matches with the six bacteria identified by the present analysis. A further step will be to pursue an analogous study for eukaryotic microorganisms and for human proteins (in search for autoantibodies).
What is happening with the CCI-hypothesis in the ME/CFS community closely resembles what happened in Italy (mainly, but not only) with the CCVI-hypothesis of Multiple Sclerosis (MS). There was this new avenue, completely unexpected and very fascinating (to me, at least), that linked MS to a defect in the venous system of the neck, named Chronic cerebrospinal venous insufficiency (CCVI) by the Italian researcher Paolo Zamboni . Several MS patients underwent surgery to correct one or more veins of the neck and described themselves as cured of MS thanks to this surgery. Among them also a prominent patient advocate, Pavarotti’s wife, who gave enormous publicity to this kind of technique .
The diagnosis of CCVI was somehow subjective, and only CCVI-literate doctors could do it properly. The same applied for the surgery. Several surgeons in private practice started doing the surgery on MS patients, earning a lot of money in a very short period of time.
Does this seem familiar?
After a decade and several well-designed studies, no correlation between CCVI and MS has been demonstrated , .
I am not saying that there is no correlation between CCI and ME/CFS. We don’t know yet. I personally find interesting these new hypotheses about the effect of abnormal mechanical strains on the functioning of the brainstem and the possible link to ME/CFS-like symptoms and I am trying to study this new field (see this blog-post), among all the other hypotheses about the aetiology of ME/CFS.
What I would like to point out with this post is that it is perfectly possible that several patients improve with this kind of surgery even in the absence of any link between CCI and ME/CFS. This is a weird (and fascinating) phenomenon that we have already seen in other diseases. It always has the same pattern: a somehow subjective diagnosis that only a few physicians can do, a surgery or a drug that many physicians are warning against, a huge amount of patients who say that they have recovered after the intervention.
Nei giorni scorsi mi è stato chiesto di scrivere un breve discorso da pronunciare davanti al ministro Giulia Grillo, in una delle tante occasioni in cui la aristocrazia contemporanea concede la voce alle istanze degli elettori. Non ho mai considerato i politici degli interlocutori interessanti, per due ordini di ragioni, collegate fra loro: la prima è che non li ritengo artefici della storia, la seconda è che, in media e con qualche proverbiale eccezione a suffragio della regola, si tratta di persone mediocri.
Del resto una persona in gamba di certo non si dedica alla politica, non ne avrebbe il tempo né la motivazione. Immaginate se Fancis Crick, anziché prendere d’assalto la struttura del DNA a colpi di funzioni di Bessel, si fosse dedicato alla amministrazione delle piccolezze pubbliche: che perdita, che delitto contro l’umanità! Euclide, che da solo ha prodotto il volume che è secondo per diffusione solo alla Bibbia (che però vanta decine di autori tra evangelisti e profeti, oltre il Creatore dell’Universo), ci avrebbe lasciati orfani della spina dorsale della nostra formazione se, anziché donarsi alla matematica, si fosse fatto traviare dall’agone politico. Se Newton si fosse perso in dibattiti sulla cosa pubblica, la prima equazione differenziale della storia avrebbe dovuto attendere forse decenni, ma non sarebbe mai stata così bella. I ministri passano senza lasciare traccia, le persone grandi – magari travestite da miserabili (si pensi a Van Gogh o a Srinivasa Ramanujan) – cambiano il mondo per sempre e sempre per il meglio.
Insomma, gli individui di talento non devono occuparsi di politica, è umiliante. E altrettanto umiliante è, a mio avviso, cercare di interloquire con gli amministratori della polis. Ciò nonostante, poiché mi è stata fatta questa richiesta accorata, ho scritto quanto segue, controvoglia e consapevole di aver compiuto un passo ulteriore nel mio personale cammino verso l’inferno.
Illustre Ministro e gentili convenuti,
attraverso queste poche righe apprenderete della esistenza di una patologia a cui è associato un livello di disabilità non inferiore a quello della sclerosi multipla, dell’artrite reumatoide o dell’insufficienza renale  e la cui prevalenza nella popolazione generale è superiore a quella della sclerosi multipla . Di questa malattia non avete probabilmente mai sentito parlare ma è possibile che ciascuno di voi abbia conosciuto almeno una volta nella vita una persona che ne è afflitta: un’amica, o il figlio di un collega; individui produttivi fino a un certo momento della loro esistenza, poi inspiegabilmente scomparsi dalla scuola o dal lavoro, per un male che non riescono a chiamare per nome.
Si stima che 240 mila italiani ne soffrano, circa lo 0.4% della popolazione . Di questi, l’80% non è in grado di svolgere una attività lavorativa  e il 25% è costretto in casa o a letto dalla severità dei sintomi . Il loro funzionamento fisico e mentale sarà compromesso per sempre – solo il 5% dei pazienti guarisce  – e la loro vita sarà ridotta in molti casi a una sopravvivenza improduttiva.
Riuscite a ricordare la vostra peggiore influenza? Una fatica prepotente vi costringe a letto, la mente diventa incapace di formulare pensieri, è necessaria assistenza anche per piccoli gesti quotidiani. Ecco, in prima approssimazione è possibile affermare che le persone affette da questa condizione sperimentino quel tipo di compromissione tutti i giorni, dal momento dell’esordio della patologia. E la caratteristica dei pazienti, il sintomo patognomonico della condizione, è che qualunque tentativo di evadere dalla cattività fisica e mentale peggiora i sintomi. Ogni sforzo, anche il più triviale, acuisce la patologia. L’età media di insorgenza della malattia è 33 anni, ma sono documentati casi di esordio a meno di 10 anni di vita e a più di 70 . E naturalmente, più precoce è l’esordio e maggiori sono i danni nella vita del paziente: i ragazzi perderanno l’istruzione, lo sport, gli amici e il futuro; gli adulti dovranno rinunciare al lavoro e alla famiglia.
Chiunque di voi o dei vostri congiunti può sviluppare la malattia domani. In quel caso malaugurato, al termine di un percorso annoso tra vari ospedali e specialisti, dopo aver speso i risparmi in cerca di una risposta, scoprireste che nessuna cura potrà restituirvi la salute. Non conta quanto talentuosi foste prima, quante risorse avete a disposizione, non conta la vostra posizione sociale: la vita sarà rovinata per sempre.
Tutti coloro che professionalmente si occupano di questi pazienti, dai ricercatori ai medici, si riferiscono alla patologia con la sigla ME/CFS, un nome con una lunga storia, troppo lunga da raccontare qui.
Non spetta a me parlare delle anomalie immunitarie, metaboliche e neurologiche documentate in questi pazienti negli ultimi 30 anni, ma fornirò al Ministro, e a chiunque sia interessato, la documentazione scientifica raccolta sin qui sulla ME/CFS, tra cui in particolare una revisione della letteratura ad opera della prestigiosa National Academy of Medicine, la quale nel 2015 ha definito la ME/CFS “una malattia multisistemica, seria, cronica che limita drammaticamente la vita di chi ne è colpito” (7).
Ad oggi non è possibile salvare queste persone, ma c’è una comorbidità che le affligge su cui si può e si deve intervenire: la cronica mancanza di fondi per la ricerca e di assistenza sanitaria ed economica. C’è bisogno di ambulatori dedicati, di consapevolezza diffusa e di ricercatori che indirizzino i loro sforzi verso questo problema. In Italia abbiamo tutta la tecnologia e le competenze scientifiche per giocare un ruolo di primo piano nella corsa alla ricerca di una cura, ricerca che attualmente vede impegnati alcuni gruppi sparsi nel pianeta, con risorse umane ed economiche tragicamente troppo modeste. Con una sua decisione, Ministro, si può cambiare il corso di queste vite lasciate fino ad oggi sole ad affrontare lo iato muto della loro esistenza.
Falk Hvidberg, M, et al. The Health-Related Quality of Life for Patients with Myalgic Encephalomyelitis / Chronic Fatigue Syndrome (ME/CFS). PLoS One. . 6 Jul 2015, Vol. 10, 7.
Jason, LA, et al. Differentiating Multiple Sclerosis from Myalgic Encephalomyelitis and Chronic Fatigue Syndrome. Insights Biomed. 12 Jun 2018, Vol. 2, 11.
Jason, LA, et al. A community-based study of chronic fatigue syndrome. Arch Intern Med. 11 Oct 1999, Vol. 159, 18, p. 2129-37.
Klimas, N e Patarca-Montero, R.Disability and Chronic Fatigue Syndrome: Clinical, legal, and patient perspectives. Binghamton : Routledge, 1998. p. 124.
Pendergrast, T, et al. Housebound versus nonhousebound patients with myalgic encephalomyelitis and chronic fatigue syndrome. Chronic Illn. Dec 2016, Vol. 12, 4, p. 292-307.
Cairns, R e Hotopf, M. A systematic review describing the prognosis of chronic fatigue syndrome. Occup Med (Lond). . Jan 2005, Vol. 55, 1, p. 20-31.
Beyond Myalgic Encephalomyelitis/Chronic Fatigue Syndrome: Redefining an Illness. Institute of Medicine. Washington (DC) : National Academies Press (US), 2015.
Nel 2014, un gruppo di esponenti del mondo biomedico e associativo italiano, riuniti dalla Agenzia Nazionale per i Servizi Sanitari Regionali (Agenas), ha prodotto un volume sulla Sindrome da Fatica Cronica (CFS) (R) i cui contenuti includono uno studio epidemiologico della patologia in Italia basato sulla analisi delle schede di dimissione ospedaliera (SDO) tra il 2001 e il 2010 e una revisione della letteratura scientifica internazionale sulla patologia. Gli scopi del documento sono quelli di educare medici, pazienti e loro familiari sulla CFS. Questo lavoro presenta scopi e metodi simili a quelli di un lavoro del 2015 che ha visto impegnati negli Stati Uniti un gruppo di esperti riuniti dalla prestigiosa Academy of Medicine (già Institute of Medicine) (R), con la differenza che in quest’ultimo caso il processo di revisione della letteratura ha anche partorito un nuovo criterio diagnostico per la patologia.
In 224 pagine, divise in 14 capitoli, sono affrontate non solo le anomalie genetiche, immunitarie, neuroendocrinologie e cognitive di questa popolazione di pazienti, ma sono riportati anche dati inediti sulla prevalenza della patologia nel nostro paese; non prima di avere fornito una panoramica sui diversi criteri diagnostici disponibili e senza trascurare i possibili interventi terapeutici. Tuttavia, dal confronto del documento Agenas con il volume della Academy of Medicine emergono almeno due differenze (vedi tabella) che li pongono, a mio modesto parere, in contraddizione fra loro.
Academy of Medicine
Fattori psicologici e/o psichiatrici
La CFS è una condizione medica, non è una malattia psichiatrica né psicologica.
La componente somatica e quella psicologica hanno lo stesso peso nella genesi dei sintomi.
I disturbi cognitivi nei pazienti con CFS/ME sembrano essere collegati con disagi di natura psicologica, specie nel sesso femminile.
Differenze nelle metodologie, nelle misure dei risultati, nei criteri di selezione dei soggetti e altri fattori rendono difficile trarre conclusioni circa l’efficacia di questi interventi.
Discreto successo per aumentare l’attività dei pazienti.
Esercizio aerobico graduale
Questo tipo di intervento è efficace nelle donne affette da CFS/ME.
Si osserva infatti che se gli esperti d’oltreoceano sanciscono fin dall’abstract che la CFS “è una condizione medica, non è una malattia psichiatrica né psicologica”, il documento nostrano dedica il capitolo 12 alle comorbità psichiatriche nei pazienti CFS e conclude che in questa patologia “componenti somatiche e aspetti psicologici si embricano in maniera complessa”, volendo con questa espressione ricercata significare che le due componenti menzionate hanno pari peso nella eziologia dei sintomi. Gli Autori italiani incoraggiano a non trascurare l’ambito psicologico perché “Escludere una delle due componenti, se può portare dei vantaggi a breve termine, a lungo termine rischia di privare il paziente di un trattamento personalizzato ed integrato” (pag. 189). In particolare, il documento Agenas non esclude un fattore causale della componente psicologica sui deficit cognitivi affermando che “I disturbi cognitivi nei pazienti con CFS/ME sembrano essere collegati con disagi di natura psicologica, specie nel sesso femminile” (Cap. 8, pag. 115).
Altra asimmetria fra i due documenti si ravvisa nelle raccomandazioni sui trattamenti. Il documento Agenas apre il capitolo sui trattamenti riconoscendo il valore terapeutico della terapia cognitivo comportamentale (CBT) (un tipo di psicoterapia) e dell’esercizio aerobico graduale (graded exercise therapy, GET) (cap. 12). Gli Autori stranieri, dal canto loro, concludono in Appendice C che “I lavori di Taylor e Kielhofner (2005), coerentemente con le conclusioni della revisione sistematica di Ross e colleghi (2002, 2004), non hanno fornito alcuna prova per quanto riguarda l’efficacia riabilitativa della CBT e/o della GET. Differenze nelle metodologie, nelle misure dei risultati, nei criteri di selezione dei soggetti e altri fattori rendono difficile trarre conclusioni circa l’efficacia di questi interventi”.
In tabella sono riassunte le contraddizioni rilevate fra i due documenti.
A.V.Determinanti della salute della donna, medicina preventiva e qualità delle cure: Chronic Fatigue Syndrome “CFS”. Roma : Age.na.s., 2014.
Beyond Myalgic Encephalomyelitis/Chronic Fatigue Syndrome: Redefining an Illness. Institute of Medicine. Washington (DC) : National Academies Press (US), 2015.
Recently there have been some anecdotal reports of patients with a diagnosis of ME/CFS who met the criteria for a diagnosis of craniocervical instability (CCI). After surgical fusion of this joint, they reported improvement in some of their symptoms previously attributed to ME/CFS (R, R). After some reluctance, given the apparently unreasonable idea that there could be a link between a mechanical issue and ME/CFS, I decided to look at this avenue. So here I am, with this new blog post. In paragraph 2, I introduce some basic notions about the anatomy of the neck. In paragraph 3, I describe three points that can be taken from the middle slice of the sagittal sections of the standard MR study of the brain. These points can be used to find four lines (paragraph 4) and these four lines are the basis for quantitative diagnosis of craniocervical instability (paragraph 5-10). In paragraph 11, I describe CCI. In paragraph 12, I discuss the possible link between craniocervical instability and ME/CFS. In paragraph 13, there is a collection of measures from the supine MRIs of some ME/CFS patients. In the last paragraph, I propose an alternative definition of CCI, with the introduction of Euler’s angles.
2. Basic anatomy
The craniocervical (or craniovertebral) junction (CCJ) is a complex joint that includes the base of the skull (occipital bone, or occiput), the first cervical vertebra (atlas or C1), the second cervical vertebra (axis or C2), and all the ligaments that connect these bones (Smoker WRK 1994). This joint encloses the lower part of the brainstem (medulla oblongata) and the upper trait of the spinal cord, along with the lower cranial nerves (particularly the tenth cranial nerve, the vagus nerve). Since the CCJ is included in the series of sagittal sections of every MR study of the brain, its morphology can be easily assessed (figure 1, left). It is worth mentioning that the CCJ is the only joint of the body that encloses part of the brain. The atlas and the axis are represented with more detail in figure 1 (right), where their reciprocal interaction has been highlighted. From a mechanical point of view, these two bones make up a revolute joint, with the rotation axis going through the odontoid process. This is only a simplification, though, because while it is true that the atlantoaxial joint provides mainly axial rotation, there are also 20 degrees of flexion/extension and 5 degrees of lateral bending, which means that spherical joint would be a more appropriate definition. Other degrees of freedom are provided at the level of the occipital atlantal joint, where 25 degrees of motion are provided for flexion/extension, 5 degrees of motion are provided for one side lateral bending and other 10 degrees are provided for axial rotation (White A. & Panjabi M.M. 1978).
The measurement of the Grabb’s line and of the clival-canal angle is based on a simple algorithm which starts with the identification of three points on the midline sagittal image of a standard MRI scan of the head (figure 2). In order to find this particular slice, search for the sagittal section where the upper limit of the odontoid process reaches its highest and/or the slice with the widest section of the odontoid process. This algorithm is mainly taken from (Martin J.E. et al. 2017). In looking at T1-weighted images, always keep in mind that cortical bone (and cerebrospinal fluid too) gives a low signal (black strips) while marrow bone gives a high signal (bright regions) (R).
Clival point (CP). It is the most dorsal extension of the cortical bone of the clivus at the level of the sphenooccipital suture. This suture can’t be seen clearly in some cases (figure 3 is one of these cases). So another definition can be used for CP: it is the point of the dorsal cortical bone of the clivus at 2 centimetres above the Basion (see next point).
Basion (B). It is the most dorsal extension of the cortical bone of the clivus. This is the easiest one to find!
Ventral cervicomedullary dura (vCMD). This is the most dorsal point of the ventral margin of the dura at the level of the cervicomedullary junction. I find this point the most difficult to search for and somehow poorly defined, but this is likely due to my scant anatomical knowledge.
Posteroinferior cortex of C-2 (PIC2). It is the most dorsal point of the inferior edge of C2.
Connecting the three points found in the previous paragraph allows us to define four lines (figure 3) that will be then used to calculate the Grabb’s measure and the clival-canal angle.
Clival slope (CS). It connects CP to vCMD. It is also called the Wackenheim Clivus Baseline (Smoker W.R.K. 1994).
Posterior axial line (PAL). It connects vCMD to PIC2.
Basion-C2 line (BC2L). It connects B to PIC2.
Grabb’s line (GL). It is the line from vCMD that is orthogonal with BC2L.
We now know all we need in order to take two of the most important measures for the assessment of craniocervical junction abnormalities.
5. The clival-canal angle and its meaning
The clival-canal angle (CXA) is the angle between CS and PAL. The value of this angle for the individual whose scan is represented in figure 4 is 142°. This angle normally varies from a minimum of 150° in flexion to a maximum of 180° in extension (Smoker WRK 1994). Ence, what we should normally see in a sagittal section from an MR scan of the brain is an angle between these two values. A value below 150° is often associated with neurological deficits according to (VanGilder J.C. 1987) and it is assumed that a CXA below 135° leads to injury of the brainstem (Henderson F.C. et al. 2019). A clival canal angle below 125° is considered to be predictive of CCI according to (Joaquim A.F. et al. 2018). In a study on 33 normal subjects employing standard MRI, CXA was measured in the sagittal section of each subject: this group had a mean value of 148° with a standard deviation of 9.88°; the minimum value was 129° and the maximum one was 175° (Botelho R.V. et al. 2013). The reader may have noted that the mean CXA in this study is below the cutoff for neurological deficits according to the 1987 book. This might be due to the fact that there is a difference between the measure taken on an MRI sagittal section and the one taken on radiographic images.
It has been demonstrated with a mathematical model that a decrease in the clival-canal angle produces an increase in the Von Mises stress within the brainstem and it correlates with the severity of symptoms (Henderson FC. et al. 2010). Von Mises stress gives an overall measure of how the state of tension applied to the material (the brainstem in this case) causes a change in shape. For those who are interested in the mathematical derivation of this quantity (otherwise, just skip the equations), let’s assume that the stress tensor in a point P of the brainstem is given by
Then it is possible to prove that the elastic potential energy due to change in shape stored by the material in that point is given by
where E and ν are parameters that depend on the material. Since in monoaxial stress with a module σ the formula above gives
by comparison, we obtain a stress (called Von Mises stress) that gives an idea of how the state of tensions contributes to the change of shape of the material:
In the brainstem, this parameter – as said – appears to be inversely proportional to the clival-canal angle and directly proportional to the neurological complaints of patients, according to (Henderson FC. et al. 2010). For a complete mathematical discussion of Von Mises stress, you can see chapter 13 of my own handbook of mechanics of materials (Maccalini P. 2010), which is in Italian though.
6. The Grabb’s measure and its meaning
The Grabb’s measure is the length of the segment on the Grabb’s line whose extremes are vCMD and the point in which the Grabb’s line encounters the Basion-C2 line. In figure 4 this measure is 0.8 centimetres. This measure has been introduced for the first time about twenty years ago with the aim of objectively measuring the compression of the ventral brainstem in patients with Chiari I malformation. A value greater or equal to 9 mm indicates ventral brainstem compression (Grabb P.A. et al. 1999). In a set of 5 children with Chiari I malformation and/or basal invagination (which is the prolapse of the vertebral column into the skull base) a high Grabb’s measure was associated with a low clival canal angle (Henderson FC. et al. 2010). When using MRI, it is assumed that values above 9 mm is abnormal (R) but I have not been able to find statistical data on this measure in MRIs of healthy individuals. Moreover, the study by Grabb was mainly on a pediatric population (38 children and two adults) with Chiari malformation. So it is unclear if these measures can be used to assess the CCJ in adults. The measure was made on sagittal sections of MRIs.
The CXA only takes into account osseous structures (it depends on the reciprocal positions between the body of the axis and the clivus), so it can potentially underestimate soft tissue compression by the retro-odontoid tissue. This problem can be addressed with the introduction of the Grabb’s measure (Joaquim A.F. et al. 2018). Nevertheless, we can assume that they both measure the degree of ventral brainstem compression, and if you look at figure 3 you realize that as the angle opens up, the Grabb’s measure becomes shorter. Points and lines described in these paragraphs for two more patients are represented in figure 4.
7. Horizontal Harris measure
Another measure that has been introduced to check the anatomical relationship between the skull and the Atlas is the distance between PAL and point B (figure 5). This measure has been introduced in (Harris J.H. e al. 1993) where it was performed in 400 adults and with a normal cervical spine and in 50 healthy children. In the first group, 96% of the individuals had a distance of the basion from PAL longer than 1-4 mm and shorter than 12 mm. All the children had a distance below 12 mm. This measure has been used recently to assess craniocervical instability in hypermobile patients (Henderson F.C. et al. 2019), along with the Grabb’s measure and the clival-canal angle. We will refer to this measure as HHM. It is important to mention that the study by Harris was based on radiographs, so it is unclear if they can be used for a comparison of measures taken from MRI sagittal sections. Yet a measure below 12 mm was considered normal in a study employing MRI (Henderson F.C. et al. 2019).
8. Distance between Chamberlain’s line and the odontoid process
Another measure that has been introduced to determine whether occipitovertebral relationship is normal or not is the distance between the Chamberlain’s line and the closest point of the tip of the odontoid process (also called dens) (figure 6). The Chamberlain’s line extends between the posterior pole of the hard palate and the posterior margin of the foramen magnum (called opisthion) (Smoker W.R.K. 1994). In a study on 200 healthy European adults employing standard MRI, this measure was taken from the T1 weighted sagittal section of each subject. Measures start from the cortical bone, i.e. from the dark signal. The mean was -1.2 mm with a standard deviation SD = 3 mm (Cronin C.G. et al. 2007). The minus before the number indicates that the mean position of the selected point of the dens is below the line.
9. Distance between McRae’s line and the odontoid process
McRae’s line is drawn from the anterior margin of the foramen magnum (basion) to its posterior border (opisthion). It was introduced in 1953 to assess normality at the level of the CCJ (McRae D.L. et Barnum A.S. 1953). The distance between McRae’s line and the closest point of the tip of the dens can be used, as in the case of Chamberlain’s line, to assess abnormality of the CCJ along the z-axis (figure 7). In a study on 200 healthy European adults employing standard MRI, this measure was taken from the T1 weighted sagittal section of each subject. Measures start from the cortical bone, i.e. from the dark signal. The mean was -4.6 mm with a standard deviation SD = 2.6 mm (Cronin C.G. et al. 2007). The minus before the number indicates that the mean position of the selected point of the dens is below the line. In normal individuals, the dens is always below the McRae’s line (McRae D.L. et Barnum A.S. 1953), (Cronin C.G. et al. 2007).
10. Distance between basion and odontoid process
It is the distance between the basion and the tip of the dens. It is also called basion-dental interval (BDI) and it has been proposed that a value greater of 10 mm is abnormal and predicts occipito-atlantal instability. Moreover, the average value is 5 mm, according to (Handerson F. 2016). I have not been able to find statistical data for BDI measured in MRI sagittal sections of healthy subjects. Moreover, I do not have a cutoff for the minimum value.
11. Craniocervical instability
According to some authors, the craniocervical junction is considered to be unstable (craniocervical instability, CCI) in the case of “any anomaly that leads to neurological deficits, progressive deformity, or structural pain”. A clival canal angle below 125° and/or a Grabb’s measure above 9 mm are considered to be predictive of CCI (Joaquim A.F. et al. 2018). Craniocervical instability has been described in congenital conditions like Down syndrome (Brockmeyer D 1999), Ehlers-Danlos syndrome (Henderson F.C. et al. 2019), and Chiari malformation (Henderson FC. et al. 2010) as well as in rheumatoid arthritis (Henderson F.C. et al. 1993).
In one study on craniocervical junction stabilization by surgery in five patients with Chiari I malformation or basal invagination (Henderson FC. et al. 2010), inclusion criteria, beside abnormal Grabb’s measure and CXA, were:
signs of cervical myelopathy (sensorimotor findings, hyper-riflexia);
signs of pathology at the level of the brainstem, collected in this table;
severe head and/or neck pain, improved by the use of a neck brace for at least a 2 weeks period.
The same inclusion criteria were adopted in another similar study on patients with hereditary hypermobile connective tissue disorders (Henderson F.C. et al. 2019).
Several mechanisms are believed to play a role in the genesis of the clinical picture described in CCI: stretch of the lower cranial nerves (vagus nerve is among them) and of the vertebral arteries; deformation of the brainstem and of the upper spinal cord (Handerson F. 2016).
12. Craniocervical instability and ME/CFS
CCI has been described in Ehlers-Danlos syndrome hypermobile type (Henderson F.C. et al. 2019), although the prevalence of CCI in EDSh has not been established, yet (to my knowledge). At the same time, an overlapping between EDSh and ME/CFS has been reported in some studies: most of EDSh patients met the Fukuda Criteria, according to (Castori M. et al. 2011) and it has been proposed that among patients with ME/CFS and orthostatic intolerance, a subset also has EDS (Rowe P.C. et al. 1999), (Hakim A. et al. 2017). So, it might seem not unreasonable to find CCI in a subgroup of ME/CFS patients.
Moreover, both in CCI and in ME/CFS there is an involvement of the brainstem. Briefly, hypoperfusion (Costa D.c: et al. 1995), hypometabolism (Tirelli U. et al. 1998), reduced volume (Barnden L.R. et al. 2011), microglial activation (Nakatomi Y et al. 2014), and loss of connectivity (Barnden L.R. et al. 2018) have been reported in the brainstem of ME/CFS patients. Basal ganglia dysfunction has also been documented in ME/CFS (Miller AH et al. 2014), and this could be an indirect measure of midbrain abnormal functioning, given the connection between substantia nigra (midbrain) and basal ganglia, via the nigrostriatal tract. It is worth mentioning here that vagus nerve infection has been proposed as a feasible cause of ME/CFS (VanElzakker MB 2013) and vagus nerve (the tenth cranial nerve) has its origin in the lower part of the brainstem. Recently, brainstem pathology in ME/CFS (midbrain serotoninergic neurons alteration, in particular) has been theorized as part of a mathematical model on disrupted tryptophan metabolism (Kashi A.A. et al. 2019), (R). So, one might argue that CCI could in some cases lead to a clinical picture similar to the one described in ME/CFS because in both these conditions there is a pathology in the same anatomical district (figure 8).
We know that in most of the cases ME/CFS starts after an infection (Chu L. et al. 2019). That said, how could CCI be linked to this kind of onset? The presence of CCI in rheumatoid arthritis (Henderson F.C. et al. 1993) might be a clue for a causal role of the immune system in this kind of hypermobility. In fact, a link between hypermobility and the immune system has been found also in a condition that is due to the duplication/triplication of the gene that encodes for tryptase (a proteolytic enzyme of mast cells) (Lyons JJ et al. 2016).
A piece of evidence against a link between CCI and ME/CFS is perhaps represented by the results of a study on EDSh patients with CCI who underwent surgery for their craniocervical junction abnormalities. Before surgery, all the 20 patients reported fatigue among their symptoms and two years after surgery the improvement in this symptom was not statistically significant, despite improvement in the craniocervical joint measures (CXA and Grabb’s measure) and improvement in overall functioning (Henderson F.C. et al. 2019). This seems to be a clue against the role of CCI in fatigue, at least in this patient population.
13. Craniocervical measures in a few ME/CFS patients
I have collected standard MRIs of the head of seven ME/CFS patients and I have performed the measures described in this article, using the sagittal section of T1 weighted series. Data are collected in table 1.
GM stands for Grabb’s measure and the cutoff for this value has been taken from an MRI study on children with Chiari malformation (Grabb P.A. et al. 1999). I have not been able to find a study on adult normal subjects, so I don’t have any reliable statistical data on that measure. Yet, the reported cutoff of 9 mm is what is commonly indicated for GM (R), (Handerson F. 2016), (Joaquim A.F. et al. 2018). HHM stands for horizontal Harris measure and the cutoff was deduced from (Henderson F.C. et al. 2019), but again, I have not found statistical data on this measure from MRIs sagittal sections of an adult healthy population. BDI is the basion-dens interval and the cutoff comes from (Handerson F. 2016) and no statistical data available on a suitable population. CDD and MDD are the distances of the tip of the dens from the Chamberlain’s line and the McRae’s line, respectively and I got the statistical data from an MRI study on adult healthy subjects (Cronin C.G. et al. 2007). CXA is the clival-canal angle: statistical data were from an MRI study on 33 healthy adults (Botelho R.V. et al. 2013), while the cutoff was indicated in (Henderson F.C. et al. 2019).
The only abnormal values found are the distance between the tip of the dens and both Chamberlain’s line and McRae’s line in P2 and the Grabb’s measure in P7, with the caveat that I don’t have suitable statistical data for comparison, in the latter case. And of course, I don’t know what the meaning of these slightly abnormal values is. Of notice, none of these patients would fit the criteria proposed in (Henderson F.C. et al. 2019) for surgery of the craniocervical junction.
Patient 4 should probably be excluded from this table: she had a documented B12 deficiency at the onset of her disease; she was treated with vitamin B12 injections. After some months she has substantially improved. So it might have been a case of vitamin B12 deficiency. She also has a problem with iron, which tends to be low and has to be supplemented; since vitamin B12 and iron are both absorbed in the small intestine, this patient may have some pathology in that area. In fact, signs of inflammation were found in a sample of her duodenum, but it was not possible to define a specific diagnosis (celiac disease was ruled out, as well as Crohn’s disease). Interesting enough, this patient had a diagnosis of POTS (by tilt table test) and vitamin B12 deficiency has been linked to POTS (Öner T. et al. 2014). As mentioned, she is in remission now.
Let’s try now a statistical analysis for the values of the clival canal angle reported in Table 1, using as control group the one published in (Botelho R.V. et al. 2013). We can use Cantelli’s inequality (see Eq. 2, paragraph 15) and extend it to a random vector. We get for the p value:
In our case m = 8, µ = 148, σ = 9.88. By using the following very simple code we calculate a p value < 0.03, which is statistically significant. The problem here is that the measure of the CXA in the control group has been made by someone else than me, so this might be a source of error. Moreover, the sample is very small. All that said, a tendency towards a reduction of the clival canal angle among ME/CFS patients might be further proof of increased mobility of the cranio-cervical joint in this patient population, in agreement with previous studies on other joints (Rowe P.C. et al. 1999), (Hakim A. et al. 2017).
mu = 148
ds = 9.88
m = 8
p = 1.;
x = [142, 146, 142, 142, 135, 140, 140, 139];
p = p*( 1/( 1 + ( ( (mu-x(i))/ds )^2 ) ) );
14. Craniocervical instability and Euler’s angles
A more sound definition of CCI might perhaps be obtained with the introduction of the angles that are used to describe the orientation of a rigid body with respect to a fixed coordinate system. To simplify our analysis, we assume here that atlas (C1) and axis (C2) are fixed one to the other. Then, consider the coordinate system (O; x, y, z) in figure 1 to be fixed to C1-C2 and then let’s introduce a second coordinate system (Ω; ξ, η, ζ), fixed to the skull. The orientation of (Ω; ξ, η, ζ) with respect to (O; x, y, z) is given by the angles ψ, φ, θ, called Euler’s angle (figure 7). The angle θ is the one between z and ζ. In order to define the other two angles, we have to introduce the N axis, known as line of nodes, which is the intersection between plane xy and plane ξη. That said, ψ is the angle between x and N, while φ is the angle between ξ and N.
All that said, craniocervical hypermobility may be defined as follows.
Def. We have CCI when there is an increase in the physiological range of Euler’s angles and/or when |ΩO|≠0.
In this definition, we have assumed that in physiological conditions the length of the vector ΩO is nought. The length of ΩO is indicated as |ΩO|. The condition |ΩO|≠0 means that at least one of the components of ΩO along the axises x, y, z is different from zero.
The reader can easily recognize now that:
the clival-canal angle is a measure of instability in the angle θ; we can also say that clival-canal angle measures instability around N;
Grabb’s measure and Horizontal Harris measure both indicate instability along the x-axis; they are a measure of the x component of vector ΩO;
Chamberlain’s line gives a measure of instability along the z-axis; the same applies to McRae’s line and to BDI.
15. Cantelli’s inequality
To assess the statistical significance of the experimental data in Table 1 we have used Cantelli’s inequality, also known as one-tailed Chebyshev’s inequality. Given the random variable X whose distribution has mean E[X] and variance Var[X], then Cantelli’s inequality states that:
for any η>0. The importance of these two inequalities is that they are true whatever the distribution is. In the case of our patient’s MRS data, we only knew mean values and standard deviations (which is the square root of variance) of the distributions of the metabolic values of the control group. So one way to assess significance was to use this inequality (the other way would be to use the less precise Chebyshev’s inequality). To prove Eq. 1 and Eq. 2 we have first to prove Markov’s inequality, which states that
for any a>0. In order to prove that, consider that for the probability on the left of the inequality we can write
At the same time, the expectation (or mean) of the distribution can be written
Thus we have
and Markov’s inequality is proved. Let’s now come back to the proof of Cantelli’s inequality. If we consider the random variable Y = X – E[X] we have that P(Y≥η) = P(Y+t≥η+t) and assuming that η+t > 0 we have
That said, Markov’s inequality gives
For the expectation on the right we have
and knowing that E[Y²] = Var[X] and that E[Y] = 0, we can write
The function on the right of the inequality is represented in Figure 4. It is easy to recognize that it assumes its lower value for t = Var(X)/η and this proves Eq. 1. The other inequality (Eq. 2) can be proved in the same way, considering the random variable Z = E[X] – X.
In this article, I report on the results from two research groups in which different experimental settings were used to measure electric impedance in blood samples from ME/CFS patients vs healthy controls. One of these studies comes from Stanford University and has been just published in PNAS: it is freely available here. The other one has been presented by Alan Moreau during the NIH conference on ME/CFS, and it is unpublished (R). In paragraph 2 I introduce the definition of impedance, in paragraph 3 you will learn something about the electric behaviour of cells, in paragraph 4 there is a description of the device used by the Stanford University group, in paragraph 5 there are the results of the experiment from Stanford University, in paragraph 6 there is a discussion of these results, in paragraph 7 the results from the other group are reported, and these two studies are compared in paragraph 8. In paragraph 9 I reported on two drugs that have shown the promise to be of therapeutic use in ME/CFS. Other notes follow in the last two paragraphs. If you are not interested in technical details on impedance (or if you don’t need them), go directly to paragraph 5.
In this paragraph, I try to give a very simple and short introduction to circuits in a sinusoidal regime in general, and to impedance in particular. The main definition that we need, for that purpose, is the so-called Steinmetz transform for a sinusoidal function. Let’s consider the sinusoid
where A is called amplitude and is the maximal value that the function can reach, ω is the angular frequency (also called pulsatance) which is an indication of how fast the value of the function changes in time, α is the phase and it gives the indication of what the value of the function a(t) was for t = 0. The Steinmetz transform consists of the univocal association of the sinusoid a(t) with the complex number
also called phasor (which stands for phase vector), where j=√(-1) is the imaginary unity. A complex number can then be easily represented as a vector in the complex plane (see figure 1).
Let’s now consider the elementary circuit in figure 2 (which is also a simplified model of the device in the study by Ron Davis), where a generator of electrical potential is linked to another circuit (depicted as a box in the figure, on the left) that in our case is represented by the sample of peripheral blood white cells incubated in plasma. But it could be an arbitrarily complex net made up of conductors and what follows would still hold. Let’s assume that the electric current and the voltage of the generator are given respectively by
We can associate to these sinusoids their respective phasors with the Steinmetz transform, which gives
That said, we define impedance of the sample, the complex number that we obtain dividing the phasor of u(t) by the phasor of i(t):
Impedance describes several physical properties of the box in figure 2. Without going into details (this is beyond the scope of this article) just consider what follows.
The real part of impedance represents the resistance of whatever is inside the box of figure 2, which can be seen as its ability to transform electric energy into heat, i.e. kinetic energy at a molecular level. The higher the value of the resistance, the more the ability to generate heat.
The imaginary part of the impedance (called reactance) can be positive or negative. When it is positive it indicates the ability of whatever is inside the box to translate a magnetic field into voltage. The higher the positive reactance, the more its ability to generate a voltage from a magnetic field. A positive reactance is also called inductive reactance.
When reactance is negative, it means that whatever is inside the box, it has the ability to store energy in an electric field: the higher the absolute value of the reactance, the more the energy stored in an electric field within the box. A negative reactance is also called capacitive reactance.
No matter how complex the system in the box is, its external electrical behaviour is completely characterized by its impedance, which means that the system can also be simplified in a series of an electrical component whose only relevant property is a resistance equal to the real component of impedance, and a second component completely characterized by a reactance with a value equal to the imaginary component of impedance (figure 2, on the right).
3. Impedanceof cells
The study of the impedance of cellular cultures is a field that started probably in the early nineties. In a paper from the Rensselaer Polytechnic Insititute (NY), it was demonstrated that the measure of electrical impedance of a single cell layer was more sensitive than optical microscopy for the measure of changes of nanometers in the cell diameter or subnanometer changes in the distance between the cell layer and the electrodes (Giaever I. & Keese CR. 1991). In that pivotal paper, a mathematical model for the impedance of a layer of cells was also proposed and solved, but it is beyond the scope of this article. A simplified electrical model of a cell layer is provided by a parallel of a capacitance due to dielectric properties of the cell membrane, and a resistance due to the cell membrane, to the cytoplasm and to the layer between cells (Voiculescu I. et al. 2018). We can add a resistance for the solution in which cells are incubated and we obtain the circuit in figure 3.
Remember now that the only electrical property that we can directly measure is the total impedance (both the real component and the imaginary one). So we have to find the relationships between these two components and the physical parameters introduced in figure 3. For the equivalent impedance of the sample (see the last paragraph for the mathematical passages) we have:
The dependence of the real part of and of its imaginary component to and can be got from figure 4. The absolute value of is represented in figure 5.
The capacitance in this formula is due – as said – to the dielectric properties of the plasma membrane. We can see a cell as a spherical capacitor, where two conductive layers (one in the cytoplasm and the other one in the extracellular space) are separated by the outer membrane. The insulating portion of a phospholipid membrane is of about 4.5 nm and it has been found that the capacitance per square cm of the cell membrane is one μF (Matthews GG, 2002). Since the permittivity constant ε is known, we can calculate the dielectric constant κ of a lipid membrane quite easily (see the last paragraph), and we find κ=5.
4. The nanoneedle
The device used for the measurement of the impedance of blood samples from ME/CFS patients is an array of thousands of sensors. Each sensor is made up of two conductive layers, separated by a dielectric material (figure 6). Each sensor is a sinusoid circuit that operates at a frequency of 15 kHz and at a voltage with an amplitude of about 350 mV. In figure 6, I have added the electric scheme for the circuit made up by the sensor itself and the sample, according to what seen in the previous paragraph. I have added some resistances and capacitors for the electrodes, according to (Esfandyarpour R et al. 2014).
As you can see from the picture, one of the dimensions of the sensor is below one micron, while the other is of about 3 microns. Keep in mind that the diameter of the average white blood cell is of about 15 microns… To me, such a small size makes it difficult the application to this system of both the electrical model by Ivar Giaever and Charles Keese and of the simplified one presented in the previous paragraph, which have been designed to describe the behaviour of a layer of cells that grow above an electrode that can harbour many cells on its surface. And in fact, in their paper, Esfandyarpour R. and his colleagues have sketched a different model (R, B), even though they haven’t used it to draw any conclusion or interpretation from the experimental data, yet.
5. The experiment
The measurement of the impedance of samples from ME/CFS patients and controls has been made with an array of thousands of electrodes, each one like the one in figure 6. The system took 5 measures of impedance for second and the experiment on each sample lasted for about 3 hours. The researchers measured, for each point in time, both the real and the imaginary component of the impedance of the sample. They also measured the module of the impedance.
Each sample consisted of peripheral blood mononuclear cells (PBMC) incubated in patient’s own plasma (plasma is blood without erythrocytes, platelets and white blood cells), at a concentration of 200 cells per μL. It might be useful to remember that PBMCs are basically all the white blood cells that are present in peripheral blood but granulocytes, which have multi-lobed nuclei and, as such, are not “monuclear”.
The researchers drew blood from 5 severe patients, 15 moderate patients (diagnosed by a physician according to the Canadian Consensus Criteria) and 20 healthy controls, with 5 of them age- and gender-matched to 5 of the ME/CFS patients.
About 20 minutes were required for the impedance to reach a steady state (the baseline level, characterized by swings in impedance below 2% of its value). The measures for each sample have been divided by the value of impedance at the baseline. This is the reason why the baseline has a value of 1 in the diagrams. After the steady state was reached, the researchers added 6 μL of NaCl to the samples. After a transient reduction in impedance, the samples from healthy controls returned to the baseline value. In samples from patients, the initial reduction in impedance after NaCl introduction was followed by a dramatic change in both the real component and the imaginary component of impedance. The normalized real part, in particular, had an increase of 301.67% ± 3.55 (see figure 7 and R).
6. What does it mean?
In the experiment by Stanford University, they added NaCl to the samples and this likely led to the activation of the sodium-potassium pump that requires a molecule of ATP in order to transport 3 Na ions outside the cells (and two K ions inside). This would be the only way for these cells to maintain the correct intracellular concentration of sodium, pumping out those Na ions that found their way to the cytoplasm from the plasma. This is like putting a cell on a stationary bike. What the experiment says is that this effort made by the cells to maintain homeostasis leads to huge changes in the electrical properties of the samples from ME/CFS patients, while producing virtually no changes in the samples from healthy controls. But what is the origin of the change in impedance?
If we consider the electrical model that I have proposed in figures 3 and 6 and looking at figure 4 (left), we might hypothesise that the change comes from a reduction in the capacitance which is due to the dielectric properties of cell membranes. A change in composition in these membranes could lead to a reduction in and thus to the observed increase in the real component of the total impedance. This might perhaps be linked to the reduction in the metabolism of the main components of the plasma membrane (sphingolipid, phospholipid and glycosphingolipid) in patients vs controls previously reported in a metabolomic study (Naviaux R et al. 2016). A reduction in the dielectric properties of cell membranes could also explain the increase in the module of impedance observed in this study (see figure 5). But it is worth noting again that the model I used for the description of the electrical properties of the sample is a hugely simplified version of the one proposed in (Giaever I. & Keese CR. 1991) and it has been developed for electrodes that are many times larger than the one used by Esfandyarpour R and colleagues. As said elsewhere, the authors have proposed a different, more complex, electric circuit (R, B) and they wrote that the process of using it to interpret the experimental data is currently on-going. But they did note that a change in plasma membrane composition might be responsible for the observed change in impedance, in one point of the article, among other possible explanations.
A release of molecules (cytokines?) from the PBMCs into the plasma might also be the cause of the change in impedance, but if we assume that our model in figure 3 is reliable, these molecules would only change the value of , so the imaginary component of the impedance would not be affected, while we know that there is a change in that component too. But again, our model is a very simplistic one.
A change in the shape or size of the cells would lead to a change in . But the authors observed the samples in standard live microscopy imaging and they were not able to record any significant cell size difference in samples from ME/CFS patients vs samples from healthy controls.
7. Canadian impedance
During the NIH conference on ME/CFS, the Canadian group led by Alan Moreau, presented, at the end of a speech about microRNAs, a measure of impedance on immortalized T cells incubated with plasma from healthy controls, plasma from ME/CFS patients, and plasma from patients with idiopathic scoliosis (figure 8) and, as you can see, there is an increase in impedance with the increase in plasma concentration only in the second group (R). This measure has been made with the CellKey system, after stimulation of cells with G-coupled protein receptors agonists (Garbison KE et al. 2012). It is also worth mentioning that this impedance is the one due to the flow of charges in the extracellular space and that it seems to be the module of impedance, rather than the real or the imaginary part.
Alan Moreau also noted that if we subgroup ME/CFS patients according to differences in circulating microRNA, we find that plasma from two of these groups leads to an increase in impedance while plasma from three other groups induces a decrease in impedance, if compared with T cells incubated with plasma from healthy controls (figure 9).
8. The X factor
Even though the Canadian experiment is not directly comparable to the one from the Stanford University group, nevertheless it is a partial confirmation of that result. Moreover, since in the Canadian experiment the cells are the same for all the groups (it is a line of immortalized T cells) and what changes is only the plasma they are incubated in, we can say that the origin of the electrical shift in these samples is something that is present in the plasma of patients (an X factor) and it might be due to the interaction between this X factor and cells. This interpretation is in agreement with a previous observation from a Norwegian group who incubated muscular cells in serum from 12 patients and from 12 healthy donors: they found an increase in oxygen consumption and in lactic acid production in cells incubated with sera from patients vs cells incubated with sera from healthy controls. This experiment was performed using the Seahorse instrument (Fluge et al. 2016). It is worth noting that in this case only serum was used, and serum is plasma without clotting factor.
The idea of an X factor present in plasma (or serum) of patients is even more suggestive if we take into account the unpublished result presented by Ron Davis during the NIH conference, called the “plasma swap experiment”, performed with the nanoneedle device (R). As you can see from figure 10, the increase in impedance happens only when cells are incubated with plasma from ME/CFS, no matter whether the cells are from healthy controls or from ME/CFS patients.
It is extremely important here to note that several filtrations of the plasma from patients have been made by the Stanford Group in order to discover what the X factor is: they have concluded that it is neither a metabolite nor a cytokine. Alan Moreau noted also that it is probably not an antibody. It turned out that it might be an exosome, a vesicle released by cells which contains – among other molecules – microRNA molecules. As Ron Davis said: “I guess that the signal is coming from damaged mitochondria, but it is only a guess” (R).
9. Drug testing
The authors of the study on the nanoneedle device are interested in using it for drug testing. Ron Davis reported during the last Emerge Australia conference (R) that two compounds are able to reduce the alteration in impedance seen in PBMCs incubated with plasma from patients: Copaxone, a peptide currently used in the treatment of multiple sclerosis, and SS31, a molecule not available yet, that can scavenge mitochondrial reactive oxygen species (ROS), thereby promoting mitochondrial function (Escribano-Lopez I. et al. 2018), (Thomas DA et al 2007).
10. Limitations of the study from Stanford University
Even though the differences observed in the electric properties of the samples from ME/CFS patients vs controls, after the addition of the osmotic stressor, are striking, there are some potential limitations that ought to be mentioned.
Only 5 of the 20 healthy controls were age and gender-matched to 5 ME/CFS patients. So the difference observed might be due, at least in part, to age or gender.
The difference in impedance might be due to some consequence of the disease, like deconditioning, since the healthy control was not a sedentary one.
I presented the content of this blog post after the screening of Unrest in Turin (Italy) in May 2019 (video in Italian).
11. Mathematical notes
The calculation of the impedance of the sample (figure 3) is as follows:
Then you have to add the resistance to the real part and you obtain . In order to calculate the dielectric constant of the lipid membrane just follow these passages:
In order to choose the range of variation for and in the diagrams in figures 4 and 5, I calculated the capacitance of a cell, assuming a spheric shape, a radius of 5 μm, a capacitance for square cm of 1 μF, a thickness of the plasma membrane of 4.5 nm, and a dielectric constant κ=5. This gives for a value of Farad. I then found the value of the imaginary component of the impedance of a culture of yeast cells measured by the nanoneedle, which is 800 kΩ and I set the angular frequency at 2π·15 kHz (which is the frequency of the generator of voltage of the nanoneedle). Then we have a reference value for resistance too: 1.9·. The simple code (Matlab) that I used to plot the diagrams in figure 4 and 5 is the following one.
% file name = impedance
% date of creation = 4/05/2019
% we define the angular frequency
w = 2*pi*15*(10^3)
% we register the array of the capacitance axis (pico Farad)
c_span = 4.;
delta_c = c_span/30.;
n_c = c_span/delta_c;
% we register the array
c(1) = 0.;
for i = 2:30+1
c(i) = c(i-1) + delta_c;
% we define the array of resistance (mega Ohm)
r_span = 9.;
delta_r = r_span/30.;
n_r = r_span/delta_r;
r(1) = 0.;
for i = 2:30+1
r(i) = r(i-1) + delta_r;
% we register the array of the real part and of the imaginary part of impedance and its module
Rcl = r(j)*(10^6);
Ccl = c(i)*(10^(-12));
Z_r (i,j) = Rcl/( 1 + ( (Rcl^2)*(w^2)*(Ccl^2) ) );
Z_i (i,j) = (-1)*( w*Ccl )/( ( 1/(Rcl^2) ) + (w*Ccl)^2 );
Z_m (i,j) = sqrt( (Z_r (i,j)^2)+(Z_i (i,j)^2) );
% we plot the real part of the impedance
mesh(r(1:n_r), c(1:n_c), Z_r(1:n_c,1:n_r));
ylabel('capacitance (pico Farad)');
xlabel('resistance (Mega Ohm)');
legend('Real part of Impedance',"location","NORTHEAST");
% we plot the imaginary part of the impedance
mesh(r(1:n_r), c(1:n_c), Z_i(1:n_c,1:n_r));
ylabel('capacitance (pico Farad)');
xlabel('resistance (Mega Ohm)');
legend('Imaginary part of Impedance',"location","NORTHEAST");
mesh(r(1:n_r), c(1:n_c), Z_m(1:n_c,1:n_r));
ylabel('capacitance (pico Farad)');
xlabel('resistance (Mega Ohm)');
legend('Module of Impedance',"location","NORTHEAST");
La versione in inglese di questo articolo è disponibile qui.
Molti dei miei lettori sono probabilmente a conoscenza dei tentativi attualmente fatti per simulare matematicamente il metabolismo energetico dei pazienti ME/CFS, integrando i dati metabolici con i dati genetici.In particolare, il dr.Robert Phair ha sviluppato un modello matematico delle principali vie metaboliche coinvolte nella conversione dell’energia, dall’energia immagazzinata nei legami chimici di grandi molecole come glucosio, acidi grassi e amminoacidi, all’energia immagazzinata nell’adenosina trifosfato (ATP), pronta per l’uso. Phair, che è un ingegnere, ha determinato le equazioni differenziali che regolano questa enorme quantità di reazioni chimiche e le ha adattate al profilo genetico trovato nei pazienti ME/CFS. Ma già alcuni anni fa due fisici pubblicarono un interessante modello matematico del metabolismo energetico durante e dopo l’esercizio, nei pazienti ME/CFS (Lengert N. et Drossel B. 2015). In quanto segue descriverò questo modello e le sue previsioni e vedremo da vicino queste equazioni differenziali.
Le vie metaboliche che sono state analizzate
Il modello di Lengert e Drossel estende due sistemi di equazioni differenziali precedentemente pubblicati che descrivono il comportamento della glicolisi, del ciclo di Krebs (enormemente semplificato come una singola reazione!), della catena di trasporto degli elettroni mitocondriale (descritta in dettaglio), del sistema della creatina chinasi e della conversione di adenosina difosfato (ADP) in ATP, nei muscoli scheletrici (Korzeniewski B. et Zoladz JA. 2001), (Korzeniewski B. et Liguzinski P. 2004). Gli autori hanno aggiunto equazioni per l’accumulo di lattato e il suo efflusso fuori dalla cellula, per la sintesi de novo di inosina monofosfato (IMP) durante il recupero, per la degradazione dell’adenosina monofosfato (AMP) in IMP, per la degradazione di IMP in inosina e ipoxantina. Tutte le vie coinvolte sono raccolte nella figura 1. Queste reazioni sono descritte da 15 equazioni differenziali e la soluzione è un insieme di 15 funzioni del tempo che rappresentano la concentrazione dei principali metaboliti coinvolti (come il lattato, il piruvato, l’ATP, ecc.). Diamo ora uno sguardo più da vicino a una di queste equazioni e alla struttura generale dell’intero sistema di equazioni.
Figura 1. Questa è una rappresentazione schematica dei percorsi metabolici descritti dal modello matematico sviluppato da Lengert e Drossel. In dettaglio: sintesi citosolica e degradazione di ADP, AMP e IMP (a sinistra), via della protein chinasi e glicolisi (centro), catena di trasporto degli elettroni e ciclo TCA (a destra). Da Lengert N. et Drossel B. 2015.
Equazioni differenziali per reazioni chimiche
Consideriamo l’equazione utilizzata dagli autori per la reazione catalizzata dalla lattato deidrogenasi (la trasformazione del piruvato in lattato, figura 2) dove si è anche tenuto conto dell’efflusso di lattato dal citosol. L’equazione differenziale è la seguente:
dove i tre parametri sono determinati sperimentalmente e i loro valori sono
Il primo descrive l’attività dell’enzima lattato deidrogenasi: più questo parametro è elevato, più l’enzima è attivo. Il secondo descrive la reazione inversa (dal lattato al piruvato). Il terzo è una misura di quanto lattato la cellula è in grado di trasportare al di fuori della sua membrana. Forse il lettore si è reso conto che l’equazione del lattato è una equazione differenziale ordinaria del primo ordine. Si dice “primo ordine” perché nell’equazione compare solo la derivata prima della funzione che dobbiamo determinare (lattato, in questo caso); “ordinario” si riferisce al fatto che il lattato è funzione di una sola variabile (il tempo, in questo caso). Si vede immediatamente che un’equazione come questa può essere scritta come segue:
Supponiamo ora di avere altre due equazioni differenziali di questo tipo, una per il piruvato e una per i protoni (le altre due funzioni del tempo che sono presenti nell’equazione):
Allora avremmo un sistema di tre equazioni differenziali ordinarie come questo:
I valori iniziali delle funzioni che dobbiamo determinare sono raccolti nell’ultima riga: questi sono i valori che le funzioni incognite assumono all’inizio della simulazione (t = 0). In questo caso, questi valori sono le concentrazioni di lattato, piruvato e protoni nel citosol, a riposo. Le tre funzioni del tempo sono chiamate la soluzione del sistema. Questo tipo di sistema di equazioni è un esempio di problema di Cauchy, e sappiamo dalla teoria matematica che non solo ha una soluzione, ma che questa soluzione è unica. Inoltre, mentre questa soluzione può non essere sempre facilmente trovata con metodi rigorosi, è abbastanza facile risolvere il problema con metodi approssimati, come il metodo di Runge-Kutta o il metodo di Heun. Detto questo, il sistema di equazioni differenziali ordinarie proposto da Lengert e Drossel per il metabolismo energetico è proprio come quello qui sopra, con l’eccezione che comprende 15 equazioni anziché tre. Quindi, la principale difficoltà in questo tipo di simulazione non è l’aspetto computazionale, ma la determinazione dei parametri (come quelli enzimatici) e dei valori iniziali, che devono essere raccolti dalla letteratura medica o devono essere determinati sperimentalmente, se non sono già disponibili. L’altro problema è come progettare le equazioni: esistono spesso diversi modi per costruire un modello matematico di una reazione chimica o di qualsiasi altro processo biologico.
Il modello matematico della ME/CFS
Come adattiamo ai pazienti ME/CFS un modello del metabolismo energetico che è stato impostato con parametri presi da esperimenti condotti su soggetti sani? Questa è un’ottima domanda, e abbiamo visto che Robert Phair ha dovuto usare i dati genetici dei pazienti ME/CFS relativi agli enzimi chiave del metabolismo energetico, al fine di impostare il suo modello. Ma questi dati non erano disponibili quando Lengert e Drossel hanno progettato le loro equazioni. E allora? I due fisici hanno cercato studi sulla fosforilazione ossidativa nei pazienti ME/CFS e hanno scoperto che qusto processo cellulare era stato misurato con diverse impostazioni sperimentali e da diversi gruppi e che il denominatore comune di tuti gli studi era una riduzione di funzione che andava da circa il 35% (Myhill S et al. 2009), (Booth, N et al 2012), (Argov Z. et al. 1997), (Lane RJ. et al. 1998) a circa il 20% (McCully KK. et al. 1996), (McCully KK. et al. 1999). Quindi l’idea degli autori è stata di moltiplicare i parametro enzimatici di ciascuna reazione appartenente alla fosforilazione ossidativa per un numero compreso tra 0,6 (grave ME / CFS) a 1,0 (persona sana). In particolare, i due fisici hanno scelto un valore di 0,7 per la ME/CFS, nei loro esperimenti in silico (cioè esperimenti virtuali condotti nel processore di un computer).
Previsioni del modello matematico
Il modello matematico è stato utilizzato per eseguire prove di esercizio in silico con varie lunghezze e intensità. Quello che Lengert e Drossel hanno trovato è stato che il tempo di recupero nel paziente ME/CFS medio era sempre maggiore se confrontato con quelli di una persona sana. Il tempo di recupero è definito come il tempo necessario affinché una cellula ripristini il suo contenuto di ATP (97% del livello in stato di riposo) dopo lo sforzo. Nella figura 3 si vedono i risultati della simulazione per un esercizio molto breve (30 secondi) e molto intenso. Come potete vedere, nel caso di una cellula sana (a sinistra) il tempo di recupero è di circa 600 minuti (10 ore) mentre una cellula di una persona con ME/CFS (a destra) richiede più di 1500 minuti ( 25 ore) per recuperare.
Un altro risultato interessante della simulazione è un aumento di AMP nei pazienti rispetto al controllo (figura 3, linea arancione). Ciò è dovuto all’uso compensativo delle due vie metaboliche in figura 4: la reazione catalizzata dall’adenilato chinasi, in cui due molecole di ADP sono utilizzate per produrre una molecola di ATP e una molecola di AMP; e la reazione catalizzata dalla deaminasi AMP, che degrada AMP in IMP (che viene quindi convertito in inosina e ipoxantina). Queste due reazioni sono utilizzate dai pazienti ME/CFS più che dal controllo sano, al fine di aumentare la produzione di ATP al di fuori dei mitocondri.
Se diamo un’occhiata più da vicino alle concentrazioni di AMP e IMP nelle 4 ore successive allo sforzo (figura 5), vediamo effettivamente una maggiore produzione di IMP (linea verde) e AMP (linea arancione) nei muscoli scheletrici dei pazienti (destra) rispetto ai controlli (sinistra).
Un’ulteriore via di compensazione utilizzata dai pazienti (secondo questo modello) è la produzione di ATP da ADP da parte dell’enzima creatina chinasi (figura 6). Questo è un altro modo che abbiamo per produrre ATP nel citosol senza l’aiuto dei mitocondri. In questo modello di ME/CFS, vi è un aumento nell’uso di questo percorso, che porta a una diminuzione della concentrazione cellulare di fosfocreatina e un aumento della concentrazione cellulare di creatina (figura 7).