A Mathematical model for the diffusion of Coronavirus 19 among the Italian population

A Mathematical model for the diffusion of Coronavirus 19 among the Italian population

Abstract

In this document, I propose a distribution for the number of infected subjects in Italy during the outbreak of Coronavirus 19. To do that I find a logistic curve for the number of deaths due to this virus, in Italy. I also use a density of probability for the fatality rate and one for the number of days from infection to death. These functions have been built using recently published statistical data on the Chinese outbreak.   

Download the paper (pdf)

Brain Normalization with SPM12

Brain Normalization with SPM12

Introduction

Brain normalization is the rigid rotation and/or deformation of a 3D brain scan so that it can match a template brain. This is a necessary step for the analysis of brain magnetic resonance data (whether it is morphological or functional) as well as of brain PET data. It allows introducing a set of spatial coordinates such that each triplet (x,y,z) identifies the same anatomical region both in the brain we are studying and in the template (Mandal P.K. et al. 2012). So, for instance, once the normalization has been performed on an fMRI of the brain of a patient and on a set of fMRIs from a suited control group, we can compare the BOLD activation of each anatomical region of the patient’s brain with the activation of the corresponding anatomical region of the control group.

Mathematical notes

This part can be skipped, it is not necessary to read these passages for the understanding of the following paragraphs. If we assume that P is a point of the brain before normalization and we call S(P) its position after the normalization, we can consider the vectorial function:

formula 1

which gives the new position of each point of the brain, after normalization. If P_0 is a point of the brain before the normalization, then we can write:

formula 2

and remembering the expression of the differential of a vectorial function, we have

formula 3

With a few passages we can write:

formula 4

From the above formula, we realize that in order to define the configuration of the brain after normalization, we have to define, for each point P, a set of 12 parameters. Of these parameters, 6 describe the rigid movement and can be considered the same for each point. The other 6 (the coefficients of the matrix) are those that describe the change of shape and size and, in general, they are different for each point. The job of SPM is to calculate these parameters.

Brain atlases

There are several templates (also called brain atlases) that have been developed across the years. The very first one was published in 1957 (Talairach J. et al. 1957). The same researcher then participated in building one of the most used brain atlas ever, based on a single female brain, published in 1988 (Talairach J. et Tournoux P. 1988). Another widely used template is the so-called MNI-152. It was built adapting the 3D MRI brain scans of 152 healthy individuals to the Talairach and Tournoux template. The adaptation was achieved using both a rigid roto-translation and a deformation (Maintz J.B. et Viergever M.A. 1988). The second step is required for overcoming the problem of differences in brain shape and dimension that we encounter within the human population.

Limitations

Available brain atlases have some limitations. One of them being the fact that despite diseased brains are the most widely studied, they are also the most difficult to register to a template built from healthy individuals, because of usually marked differences in shape and/or size. This is true for instance for brains of patients with Alzheimer’s disease (Mandal P.K. et al. 2012). Another important limitation is that registration algorithms perform poorly for the brainstem (particularly for pons and medulla) (Napadow V. et al. 2006). This might have represented a problem for the study of diseases where a possible involvement of the brainstem is suspected, like for instance ME/CFS (VanElzakker M. et al. 2019).

SPM12

The SPM software package is one of the most widely used instruments for the analysis of functional brain imaging data (web page). It is freely available for download, but it requires that you have a MatLab copy in your computer. Those who don’t have a MatLab license can request and install a standalone version of SPM12 by following the instructions of this page.

Importing a DICOM file

Once you have installed SPM12 in your computer, the first step in order to register a brain is to convert the format the series of images are written in, to a format that SPM12 can read. MRI images are usually in .dcm format (DICOM) while SPM12 reads .nii files. In order to do that, click DICOM import (figure below, on the left, red ellipse), then click on DICOM files (on the right, red ellipse), then select your .dcm file and click DONE (below, red ellipse). If you then click DISPLAY (blue ellipse, left) you will see your MRI scan in another window (see next paragraph). A video tutorial on these operations is available here.

DICOM import

Setting the origin

To start the normalization process, it is highly recommended to set manually the origin of the coordinates. If this is done properly, the registration will not only take less time but, even more importantly, the chances of a successful normalization will increase. The origin is set at the level of the anterior commissure (figure below). To find this anatomical structure, you can follow this video. Once you have put the cross on the right place in the sagittal, coronal and axial windows, just click SET ORIGIN (red ellipse) and then save your work clicking REORIENT (blue ellipse).

Origin

Normalization estimate

In this step, SPM12 calculates the set of distortions that have to be applied to the source brain to adapt it to the template in MNI space. On the main menu select NORMALIZE (ESTIMATE) (figure, on the left, red). This will open the batch editor where you are asked to load the subject you want to apply normalization to (figure, right, red). You have also a set of estimation options (blue), that we leave as they are.  Then you click the RUN button, the arrow on the top of the batch editor.

Normalization

At this point, your PC will perform a set of calculations that will require a few minutes. At the end of this process, a new .nii file will be saved in the spm12 folder. This is the set of distortions that will allow your subject’s brain to be registered to the template.

Normalization writing

Now click on NORMALIZE (WRITE) on the main menu. The batch editor will then ask you for the deformation field, which is the file generated in the previous step, and for the images to write, which is the scan of your subject (figure below). Select them, then press the RUN button on the batch editor. A new .nii file will be written in the spm12 folder. This is the normalized brain!

Normalization 2

In the next figure, you have the normalized brain on the left and the initial scan of the same subject on the right. As you can see, there is an overall change of shape.

Normalization 3

Anatomical areas

Now that we have normalized our brain in the MNI space, we can easily find anatomical regions within its sections. We can, for instance, load the normalized brain with MRIcron and overlay a template with Brodmann’s areas highlighted in various colours (figure below).

ws886245-0003-00001-000001-01.

I cannot die

I cannot die

“I can’t say if it is titanic patience or endless desperation. What are they waiting for? Have they given up waiting? Which is the present they are immersed in?”

Italo Calvino, Palomar

For most ME/CFS patients (about two thirds), the disease has an oscillating course, with some periods of improvements followed by worsening of symptoms. Some of them can even experience recoveries, only to find themselves trapped again, weeks or months later (Stoothoff J et al. 2017), (Chu L. et al. 2019). Some anecdotes suggest that there might be a correlation with seasons, with improvements in summer, but there are no systematic surveys on that, to my knowledge.

As for me, in the last 20 years of pitiful combat with this monster, I experienced some substantial short-lived improvements, mainly during the core of summer. At the very beginning of the disease, I also recovered for one whole year. It was the year 2001, I was 21 and that year has been the only period of normality in my whole adult life. I spent these 12 months studying desperately and what I am as a person is mainly due to what I learned back then. I had already been very sick for about two years and when I recovered, it was as if I were born again. It was a second chance and I was determined to do all right from day one. I decided what was really important to me and I devoted myself to my goal: learning quantitative methods to use in engineering and – one day – in biology.

When darkness caught me again, I was, among other things, reviewing all the main theorems of calculus (particularly those about differential equations) with my new skills and I remember thinking that I was becoming good at developing my own proofs. I had become good at thinking and so, I reasoned, I could finally start my life! But in a few weeks, my mind faded away, and there was nothing I could do to keep a grip to all my beloved notes and books. They became mute and closed as monolithic gravestones. I remember clearly that along with this severe and abrupt cognitive decline, I developed also orthostatic intolerance, even though I hadn’t a name for it back then. But I couldn’t keep sitting, and I didn’t know why. I was forced to lay as if the gravitational acceleration had suddenly increased. My brain had changed to a lifeless stone, and so did my body.

From that very moment, my only thought has been how could I go back to my books and my calculations. And this still is my first thought, when I wake up in the morning. After almost 20 years.

I have experienced some short improvements in these years, during which I had to learn again how to study, how to do calculations, how to code. I never went back to what I was, though. And my brain is ageing, of course, as anyone else’s brain does. But in these short periods of miraculous come back I experience a rare sense of joy (along with anger and fear). Something that you can experience only if you have been facing death.

I was born and I died dozens of times in the last 20 years, and this gives me the perception that, in fact, I cannot die: I feel as if I were immortal and I had lived for a thousand years while at the same time still being in my twenties, since I have no experience of life.

In fact, I lived only when I crossed these short bridges from one abyss to the following one.

 

Immunosignature analysis of a ME/CFS patient. Part 1: viruses

Immunosignature analysis of a ME/CFS patient. Part 1: viruses

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.  

(a commentary in Dutch is available here)

1. The quest for a pathogen

Scientists have been speculating about an infectious aetiology of ME/CFS for decades, without never 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.

1 ALHHRHVGLRVQYDSG
2 ALHRHRVGPQLQSSGS
3 ALHRRQRVLSPVLGAS
4 ALHRVLSEQDPQLVLS
5 ALHVRVLSQKRPLQLG
6 ALHLHRHVLESQVNSL

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.

Sample
Figure 1. For each match, the matching protein and the organism it belongs to are reported. The protein ID has a link to the NCBI protein database, while the name of the organism has a link to the NCBI taxonomy browser. The host of the microorganism is also indicated, as well as its habitat, with links to further information.

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.

4. Results

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.

ALHHRHVGLRVQYDSG (102_1_F_viruses)
9-LRVQYDS-15
QDP64279.1(29-35)
Prokaryotic dsDNA virus sp.
Archea, Ocean
8-GLRVQYD-14
AYV76690.1(358-364)
Terrestrivirus sp
Amoeba, forest soil
ALHRHRVGPQLQSSGS (102_2_F_viruses)
2-LHRHRVG-8
YP_009619965.1(63-69)
Stenotrophomonas phage vB_SmaS_DLP_5
Stenotrophomonas maltophilia (HP)
ALHRRQRVLSPVLGAS (102_3_F_viruses)
2-LHRRQRV-8
QHN71154.1 (288-294)
Mollivirus kamchatka
Protozoa (R)
8-VLSPVLG-14
QDB71078.1 (24-30)
Serratia phage Moabite
Serratia marcescens (HP)
ALHRVLSEQDPQLVLS (102_4_F_viruses)
7-SEQDPQL-13
BAR30981.1 (151-157)
uncultured Mediterranean phage uvMED
Archea and Bacteria, Med. sea
3-HRVLSEQ-9
AXS67723.1 (494-500)
Cryptophlebia peltastica nucleopolyhedrovirus
invertebrates
2-LHRVLSE-8
YP_009362111.1 (74-80)
Marco virus
Ameiva ameiva
ALHLHRHVLESQVNSL (102_6_F_viruses)
2-LHLHRHV-8
YP_009119106.1 (510-516)
Pandoravirus inopinatum
Acanthamoeba
4-LHRHVLE-10
ASZ74651.1 (61-67)
Mycobacterium phage Phabba
Mycobacterium smegmatis mc²155 (HP)

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.

5. Discussion

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.

phage
Figure 2. Half of all viruses have an almost regular icosahedral shape, but several phages present an irregular icosahedral shape, with a prolate capsid (Luque and Reguera 2013). On the left a wrong representation of a phage. It is wrong because the capsid has 24 faces, instead of 20. On the right, the representation of a regular icosahedron made by Leonardo Da Vinci for De Divina Proportione, a mathematical book by Luca Pacioli.

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).

Mollivirus kamchatka is a recently discovered giant virus whose hosts are presumed to be protozoa that inhabit the soil of subarctic environment (Christo-Fourox E. et al. 2020). Not sure what the meaning might be in this context.

6. Next step

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).

A leap of faith

A leap of faith

During last summer, I’ve pursued a lot of things. I delivered a speech in Turin, after the screening of the documentary Unrest, about the OMF-funded research on the use of the measure of blood impedance as a possible biomarker for ME/CFS (video, blog post, fig. 1, fig. 2).

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Figure 1. Group photo after the screening of Unrest in Turin, Italy, with the organizer of the event (Caterina Zingale, second from the right) and representatives of two Italian ME/CFS associations.
64982079_10217790422048709_8954534129534238720_o.jpg
Figure 2. Question time after the screening of Unrest. On the screen, a drawing of mine.

Then I flew to London to attend the Invest in ME conference, the annual scientific meeting that gathers researchers from all over the world who shared their latest work about ME/CFS. There I met Linda Tannenbaum, the CEO of the Open Medicine Foundation, whom I had the pleasure to encounter for the first time about a year before in Italy, and I introduced myself to Ronald Davis (fig. 3), the world-famous geneticists turned ME-researcher because of his son’s illness. I presented to him some possible conclusions that can be driven from the experimental results of his study on the electrical impedance of the blood of ME/CFS patients, with the use of an electrical model for the blood sample (R, paragraph 6).

61662643_10217615785202897_4802586779179810816_o.jpg
Figure 3. Talking to Ron Davis about a possible explanation for the increase in electrical impedance in the blood of ME/CFS patients in London, during the last Invest in ME conference (blog post).

In London, I was able to visit the National Gallery and while I was passing by all these artistic treasures without being able to really absorb them, to get an enduring impression that I could bring with me forever, I decided to sit down and to copy one of these masterpieces (I can’t draw for most of the time, and when I improve for a few weeks in summer, I usually have to carefully choose where to put my energies). I sat probably beside one of the least important portraits collected in the museum (Portrait of a young man, Andrea del Sarto, figure below) and I started copying it with a pen. When I finished, the museum was closing, so that I missed all the works by Van Gogh, among many other things.

We were at the beginning of June, I was experiencing my summer improvement, a sort of substantial mitigation of my illness that happens every other summer, on average. But because of these travels, I elicited a two-month worsening of symptoms, during which I had to stop again any mental and physical activity: I just lay down and waited. At the beginning of August, I started thinking and functioning again and I almost immediately decided to quit what was my current project (a 600-page handbook of statistics that I commenced in 2017) and I started studying mathematical modelling of enzymatic reactions (figures 4 and 5).

Cattura.JPG
Figure 4. The plot of the reversible Michaelis-Menten equation for ribulose-phosphate 3-epimerase. The intersection of the surface with the plane is the state of equilibrium of the reaction (the rate of production of X5P is the same as the rate of its transformation into Ru5P) (R).
sa.png
Figure 5. The plot of the concentrations of S, P, ES and E for the transformation of L-tryptophan into N-formylkynurenine by IDO-2. This is a semianalytical solution that I found using the approximation of the Lambert function. I also pursued numerical solutions, of course (R).

I knew that these reactions were described by ordinary differential equations and that I could solve them numerically with the methods that I studied just before I got sick, about 18 years ago. I was interested in the metabolic trap theory by Robert Phair, an OMF-funded researcher. So I downloaded a chapter of one of the most known books of biochemistry and a thesis by a Turkish mathematician on metabolic pathways simulation and I started my journey, working on the floor (I have orthostatic intolerance even when I get better in Summer, so I can’t use a desk, figure 6). I ended up learning the rudiments of this kind of analysis, also thanks to a book by Herbert Sauro and to some suggestions by dr. Phair himself! Some of the notes I wrote in August are collected here.

69099435_10218252327836065_3701013412482908160_o.jpg
Figure 6. In August I was studying mathematical modelling of metabolic pathways, sitting on the floor: because of my orthostatic intolerance, I can’t sit for long, especially when I need to think. You can see the book by Sauro opened in the foreground, the thesis by a Turkish mathematician (red cover), and the handbook of Octave (blue/red cover).

At the beginning of September, I was absorbed by the problem of how to study the behaviour of the steady states of tryptophan metabolism in serotoninergic neurons of midbrain as the parameters of the system change. This kind of analysis is called bifurcation theory and I literally fell in love with it… In figure 6 you can also see a drawing: I was drawing a picture I have been thinking about for the last 20 years. It is a long story, suffice it to say that in 1999, just before my mind faded away for 18 months, I started studying the anatomy of a man who carries a heavy weight on his back (see below). That was my first attempt of communicating what was happening to me, of describing my disease.

Only recently I considered to not represent the weight, which is a more appropriate solution since this is a mysterious disease with no known cause, and I made a draft (the one in figure 2) that I then used as a starting point for the drawing below. I finished this new drawing at the beginning of September, in a motel room of San José, in California, just in time for donating it to Ronald Davis (figures below) when I moved to the US to attend the third Community Symposium at Stanford (see here). In California, many surprising things happened: I met again Linda Tannenbaum and Ronald Davis, and yes, I encountered also Robert Phair! But this is another story…

resilience 2

69836282_10218351956686724_1046414613542862848_o

In the following pictures, you can see how the drawing evolved. Notably, the figure in the centre changed his face and some part of his anatomy. The three figures are meant to be a representation of the same figure from three different points of view. It is more like a project for a sculpture, a monument that is much deserved by these patients.

At Stanford, I had the chance to be face to face with one of my preferred sculptures ever: The Thinker, by Rodin, in both its version: the model moulded first, on the top of The Gates of Hell, and the big one (crafted later), now considered the iconic symbol of Philosophy, but likely originally meant to be a metaphor for creative thinking (I say that because the original sculpture included in The Gates of Hell is a representation of the Italian poet Dante Alighieri, depicted in the act of imagining his poem).

At the end of September, my mind started fading away again. I knew that would have happened, even though I had an irrational hope that this year would have been different. At that point, I was in Italy and I asked some friends to help me organize a trip to the southern hemisphere, in order to live another summer. It required more time than I would have hoped. I am going to leave from Italy only tomorrow. My goal: Argentina. I have been able to do something, at a highly reduced speed, in October, though. I have developed a model for solar radiation at sea level, in function of the day of the year, of the latitude, and of the distance from the Sun (I have considered the actual elliptic orbit of our planet). The main problem has been the modelling of absorption and of diffusion of radiant energy from our star by the atmosphere, but I solved it. Part of these notes are here, but I want to self-publish the end product, so I keep the rest to myself. In that period, I was also able to find the exact solution of the improper integral known as the Stefan-Boltzmann law, something I tried to do in the summer of 2008, in vain, in one of my recovery-like periods. In figure 6 you can see one of the results of my model for solar radiation: the monochromatic emissive power at sea level in function of the day of the year, for the city of Buenos Aires.

emissive power.png
Figure 7. The monochromatic emissive power of the sun at noon, at sea level, at a latitude of -32° N, in function of the wavelength and of the day of the year. Note that the vertical axis is expressed in W on microns multiplied by square meters.

My intention was to use that model to choose the perfect place where to move in order to have environmental conditions that closely resemble the ones that we have in Rome from June to September (the period in which my improvements happen). I also wanted to quantitatively study the effect of both infrared radiation and ultraviolet radiation on my biology. There are several interesting observations that can be made, but we will discuss these subjects another time, also because I had to quit this analysis given my cognitive deterioration. The video below is a byproduct of the geometric analysis that I had to pursue in order to build my model for solar radiation at sea level.

Dawn and dusk at a latitude of 42 degrees north, during three years of the silent rolling of the Earth on its silken ellipse. Three years of adventures, suffering, joy and death.

So, by November my mind was completely gone and my physical condition (namely orthostatic intolerance and fatigue) had worsened a lot. This year I have been able to try amphetamines: I had to go from Rome to Switzerland to buy them (they are restricted drugs that can’t be sold in Italy and can’t be shipped to Italy either). One night I felt good enough to take a train to Milan and then to take another transport to the drug store. And back. I managed to do the travel but I pushed my body too far and I had to spend the following month in bed, 22 hours a day, with an even worse mental deterioration. It is like having a brain injury. Amphetamines have been useless in my case, despite two studies on their potential beneficial effect in ME/CFS.

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Right now, I am collecting all the books and the papers that I need with me in Argentina (figure above), in case I will improve enough to study again. But what am I going to work on?

  1. I want to finish my model of solar radiation, with some notes on the effect of infrared radiation, ultraviolet radiation and length of the day on the immune system. There is a mathematical model published recently that links the length of the day to the power of the innate immune system, and I want to write a code that calculates the relative activity of the innate immunity in function of latitude and day of the year. I would like to self- publish it as a booklet.
  2. I want to finish my handbook of statistics.
  3. I need to correct a paper submitted for publication (it has been accepted, but some corrections have been required).
  4. I want to deepen my understanding of the bifurcation theory for metabolic pathways and to continue studying tryptophan metabolism with this new knowledge.
  5. I want to complete my work on autoantibodies in ME/CFS (see this blog post) and to submit it to a journal. I have been working on that for a while, inventing new methods for the quantitive study of autoimmunity by molecular mimicry.

Should I improve again in Argentina, several avenues can be followed in order to understand the reason why summer causes this amelioration in my own case. I have many ideas and I’ll hopefully write about that in the future. Of course, I also want to read all the new research papers I have missed in the last months. I will bring with me my handbook of anatomy for artists because I hope to be able to draw again, and I won’t miss this opportunity to leave some other handcrafted images behind me for posterity, that can’t care less, obviously! I would really like to finish the drawing below because I feel that in this draft I have found a truly elegant (and mechanically correct) solution for the hip joint of a female robot.QR-A_000026

Now I am useless, my mind doesn’t work and I am housebound. I can’t read, I can’t draw, I can’t do calculations, I can’t do coding, I can’t cook… This has been the quality of my life for most of the last 20 years. This is a huge waste: I would have used these years to perform beautiful and useful calculations and to pursue art. I would really make people understand how tragic this disease is in its cognitive symptoms, what we lose because of it. This is, in fact, the reason behind this blog post: I wanted to give an idea of what I can do when I feel better, and of what I would have done if there had been a cure.

I have lost most of my adult life, but I will never accept to waste a day without fighting back.

Ronald Davis at Columbia University

Ronald Davis at Columbia University

All the following studies have been made mainly thanks to private funding. Please, consider a donation to the Open Medicine Foundation, in order to speed up the research. See this page for how to donate to OMF.


OMF Scientific Advisory Board Director Ronald W. Davis, PhD, has just delivered a speech about ME/CFS at the Albert Einstein College of Medicine at Columbia University in New York. In what follows you find several screenshots that I have collected during the lecture, accompanied by a very short description. I imagine that a video will be soon made available but in the meantime let’s take a look at these slides.

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Indoleproprionate is reduced in ME/CFS patients. This molecule is not produced by our own metabolism, it comes from a bacterium of the gut (Clostridium sporogenes) which is low in patients. It has a neuroprotectant effect. Indoleproprionate is currently used in some clinical trials for other diseases and it might be available in the next future as a drug.

Hydroxyproline is high and this is believed to indicate collagen degradation. Ron Davis talked about the case of a ME/CFS patient who turned out to have a problem in the craniocervical junction which was fixed by surgery. Is there a link between high hydroxyproline and abnormalities of the joints (the neck among them) that some patients seem to have?

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The increase in electrical impedance in blood samples (as measured by the so-called Nanoneedle device) only happens when cells from ME/CFS patients are incubated with plasma from patients. When these same cells (white blood cells) are incubated with plasma from healthy donors, the impedance is normal. For an introduction to this experiment, click here. The published work is here.

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The Nanoneedle study has been extended with 20 more patients and 20 more controls.  This device can be used for drug screening, other than for diagnosis.

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The peptide called Copaxone, now used in Multiple Sclerosis, seems to work in reducing the impedance in the nanoneedle device (click on the images to enlarge). Suramin also has some effect (on the right). It doesn’t seem as good as Copaxone though, to me…

SS-31 is an experimental drug for the mitochondrial membrane. It does work when used in the nanoneedle device! (click on the images to enlarge).

Nailbed capillaroscopy could be a new instrument for ME/CFS diagnosis. Inexpensive and already in use in hospitals.

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No new or known pathogen has been found in patients, so far. This project is still in progress. It is updated as new technologies for pathogen hunting become available.

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All the severe patients have at least one defective copy of the IDO2 gene. The same applies to 46 additional ME/CFS patients that have been recently tested for this gene. This is a common genetic problem in the general population, but it is ubiquitous in these patients. And a statistically significant difference is thus present between ME/CFS patients and healthy controls. This discovery has lead to the development of the metabolic trap hypothesis, which has been recently published (here). For an introduction, read this blog post of mine. They are planning to test the metabolic trap hypothesis in vivo using cellular cultures!

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Patients have high mercury (maybe from fish in their diet) and low selenium in hair. Low selenium can reduce the conversion of T4 to T3 in the liver. Low T3 might be a cause of fatigue. High uranium was also detected!

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All these studies have been made mainly thanks to private funding. Please, consider a donation to the Open Medicine Foundation, in order to speed up the research. See this page for how to donate to OMF.


 

 

Historia magistra vitae?

Historia magistra vitae?

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 [1]. 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 [2].

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 [3], [4].

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.

C’è del marcio a Bologna?

C’è del marcio a Bologna?

I disabili possono costituire una fonte di reddito cospicua per chi lavora nell’ambito della assistenza a queste persone. Per le disabilità riconosciute, infatti, il sistema sanitario offre (giustamente) dispositivi costosi e personale con le più varie mansioni. Ma in molti casi appalta questo genere di servizi.

Come funziona un appalto? Si redige un capitolato di gara, che elenca i requisiti che i candidati devono possedere per poter partecipare alla gara. Questo capitolato viene reso pubblico solo al momento del bando. Il vincitore sarà l’ente che, tra i candidati, meglio soddisfa i requisiti del capitolato di gara.

Un anno fa, dopo una indagine di vari mesi, la Guardia di Finanza di Bologna ha iscritto nel registro degli indagati quattro dipendenti Ausl e due rappresentanti della Associazione Italiana Assistenza Spastici (AIAS Bologna) con l’accusa di aver truccato un appalto. Infatti il file del capitolato di gara sarebbe stato corretto più volte – prima ancora del bando – dai rappresentanti di AIAS Bologna, in modo da cucirsi addosso il concorso e assicurarsi la vittoria [1], [2].

Si parla di due milioni e 130 mila euro circa, in tre anni, con possibile rinnovo per altri tre anni. Si tratta della gara per il Centro Regionale Ausili (che include anche il Centro Ausili Tecnologici) e per il Centro Adattamento Ambiente Domestico. La gara è stata sospesa [3], [4].

Dopo ulteriori accertamenti, il procedimento contro uno dei dipendenti Ausl è stato archiviato, ma per il resto l’indagine è ancora in piedi, che io sappia [5].

Io stesso sono il beneficiario dei servizi di una di queste aziende appaltatrici, che assistono le persone con disabilità. E non potrei fare a meno di questi servizi, non sopravviverei.

Proprio per questo mi infastidisce non poco venire a sapere di tali illeciti (presunti, fino a che il procedimento giudiziario non termina il suo corso). E perché sono spiacevoli e pericolosi questi illeciti? Perché in fondo suggeriscono che le disabilità più remunerative sono quelle a cui si presta più attenzione e a cui si offrono più servizi.

Lettera aperta all’Osservatorio Malattie Rare

Non sarebbe necessario scrivere una nota all’articolo pubblicato dall’Osservatorio Malattie Rare (O.ma.r.) sulla malattia di Lyme alcuni giorni fa [1], in cui si liquidano i possibili esiti cronici della patologia in parola come non esistenti o riconducibili ad altre patologie, “non ultime le patologie psichiatriche”. Non sarebbe necessario, ho scritto, perché coloro che si occupano professionalmente della malattia di Lyme, nonché i pazienti, sono consapevoli che in realtà le possibili sequele della infezione acuta da Borrelia burgdorferi sono ben documentate in letteratura e costituiscono un problema di enorme portata su cui si concentra oggi molta ricerca, spesso di alto profilo [2].

E allora perché questa preterizione? Perché un articolo divulgativo pubblicato da O.ma.r. ha notevole risonanza e – se incompleto o impreciso – rischia di alimentare false credenze tra i neofiti. L’articolo in questione è encomiabile nel divulgare nozioni preziose sulla fase acuta della malattia e nel mettere in guardia contro test e trattamenti non provati, ma è del tutto fuorviante nella parte dedicata alle sequele croniche (penultimo paragrafo).

La malattia di Lyme risponde alle attuali cure antibiotiche nel 90% dei casi. Questo significa che un decimo di coloro che ogni anno, in estate, contrae la malattia per il morso di un vettore (principalmente l’Ixodes ricinus in Europa) andrà incontro a una condizione cronica (cioè con durata superiore ai sei mesi) e debilitante, nota in seno alla comunità scientifica con il nome di post-treatment Lyme disease syndrome, PTLDS [3], [4]. Il nome scelto (che si potrebbe tradurre come Sindrome della malattia di Lyme dopo trattamento) sta a indicare che i pazienti sperimenteranno sintomi, nonostante i trattamenti della fase acuta.

La causa della PTLDS è al momento non nota. Alcuni studi supportano l’ipotesi che ci sia una disfunzione immunitaria in questi pazienti. Due studi hanno dimostrato la presenza di anticorpi contro il sistema nervoso centrale nella metà dei pazienti PTLDS [5], [6], solo per citare i più recenti. Per approfondimenti su questo argomento si legga qui e qui. La ricerca in questo campo continua [7].

Altri gruppi hanno dimostrato la persistenza del patogeno – dopo trattamento – sia nel modello animale della malattia di Lyme [8], [9], [10], che negli esseri umani [11], [12]. Presso la Columbia University è stata avviata una raccolta di tessuti provenienti da individui deceduti, che abbiano avuto una ben documentata infezione da Borrelia burgdorferi (link) proprio per indagare ulteriormente questo aspetto.

Numerosi sforzi e investimenti sono stati profusi recentemente nella ricerca di nuovi agenti antimicrobici per questa infezione, nella speranza di scongiurare le sequele croniche, da parte della Università di Stanford [13], [14], della Università Johns Hopkins [15], [16], [17], della Università Northeastern [18].

Nell’articolo di O.ma.r si legge che la sindrome in questione – chiamata impropriamente post-Lyme dall’autore – è caratterizzata da “sintomi soggettivi – e dunque non quantificabili – quali affaticabilità e difficoltà a concentrarsi”. A questo proposito è quasi superfluo ricordare che molti sintomi sono soggettivi, finché l’ingegneria non ci offre uno specifico strumento di misura: si pensi alla risonanza magnetica nella sclerosi multipla o all’elettroencefalogramma nella epilessia. In secondo luogo, questi sintomi sono solo in parte soggettivi, infatti i pazienti PTLDS presentano alterazioni quantificabili nel sistema immunitario [5], [6], nella espressione genica [19], nel metabolismo [20], etc.

Per quanto riguarda il riferimento all’ambito psichiatrico, vale la pena fare delle considerazioni. E’ senz’altro vero che le principali patologie psichiatriche (i disturbi dell’umore da un lato e le psicosi dall’altro) contemplano gli episodi infettivi come fattore di rischio [21], [22], tuttavia la PTLDS semplicemente non si sovrappone alle patologie psichiatriche, né nella presentazione clinica, né nella epidemiologia, per questo è una categoria nosografica a sé stante (vedi qui). Per fare un esempio concreto: negare l’evidenza, come sembra fare questo articolo, è una delle possibili manifestazioni della schizofrenia paranoide [23], ma né questo tipo di sintomi né altri sintomi patognomonici per malattie psichiatriche sono menzionati nella definizione di caso della PTLDS [4].

Paolo Maccallini

Riferimenti

  1. Orzes, E. (2019, Nov. 7). Malattia di Lyme, attenzione alle false credenze. O.ma.r. (link)
  2. Instutute of Medicine (2011, Apr. 20). Critical Needs and Gaps in Understanding Prevention, Amelioration, and Resolution of Lyme and Other Tick-Borne Diseases: The Short-Term and Long-Term Outcomes – Workshop Report. Cap. 7 (link).
  3. Centers for Disease Control and Prevention. Post-Treatment Lyme Disease Syndrome. (link).
  4. Aucott, J., Crowder, L., & Kortte, K. (2013). Development of a foundation for a case definition of post-treatment Lyme disease syndrome. Int J Infect Dis, 17(6), p. e443-e449. (link).
  5. Chandra A, Wormser GP, Klempner MS, et al. Anti-neural antibody reactivity in patients with a history of Lyme borreliosis and persistent symptoms. Brain Behav Immun 2010;24:1018–24 (link).

  6. Jacek E, Fallon BA, Chandra A, Crow MK, Wormser GP, Alaedini A. Increased IFNalpha activity and differential antibody response in patients with a history of Lyme disease and persistent cognitive deficits. J Neuroimmunol 2013;255:85–91 (link).

  7. Maccallini, P; Bonin, S; Trevisan, G. Autoimmunity against a glycolytic enzyme as a possible cause for persistent symptoms in Lyme disease. Med Hypotheses. 2018 Jan. (link).
  8. Hodzic E, Feng S, Holden K, Freet KJ, Barthold SW. Persistence of Borrelia burgdorferi following antibiotic treatment in mice. Antimicrob Agents Chemother. 2008 May; 52(5) (link).

  9. Yrjänäinen H, Hytönen J, Hartiala P, Oksi J, Viljanen MK. Persistence of borrelial DNA in the joints of Borrelia burgdorferi-infected mice after ceftriaxone treatment. APMIS. 2010 Sep 1;118(9) (link).
  10. Embers, M et al. Persistence of Borrelia burgdorferi in Rhesus Macaques following Antibiotic Treatment of Disseminated Infection. PLoS One. 2012; 7(1). (link).

  11. Marques, A. et al. Xenodiagnosis to detect Borrelia burgdorferi infection: a first-in-human study. Clin Infect Dis. 2014 Apr; 58(7):937-45 (link).
  12. Sapi, E. et al.The Long-Term Persistence of Borrelia burgdorferi Antigens and DNA in the Tissues of a Patient with Lyme Disease. Antibiotics 2019, 8(4), 183. (link).
  13. Wagh D, Pothineni VR, Inayathullah M, Liu S, Kim KM, Rajadas J. Borreliacidal activity of Borrelia metal transporter A (BmtA) binding small molecules by manganese transport inhibition. Drug Des Devel Ther. 2015 Feb 11;9:805-16. (link).
  14. Venkata Raveendra Pothineni et al. Identification of new drug candidates against Borrelia burgdorferi using high-throughput screening. Drug Des Devel Ther. 2016; 10: 1307–1322. (link).
  15. Feng J, Wang T, Shi W, Zhang S, Sullivan D, Auwaerter PG, Zhang Y. Identification of novel activity against Borrelia burgdorferi persisters using an FDA approved drug library. Emerg Microbes Infect. 2014 Jul; 3 (7). (link).
  16. Jie Feng, Megan Weitner, Wanliang Shi, Shuo Zhang, David Sullivan, and Ying Zhang. Identification of Additional Anti-Persister Activity against Borrelia burgdorferi from an FDA Drug Library. Antibiotics (Basel). 2015 Sep; 4(3): 397–410. (link).
  17. Feng J, Auwaerter PG, Zhang Y. Drug combinations against Borrelia burgdorferi persisters in vitro: eradication achieved by using daptomycin, cefoperazone and doxycycline. PLoS One. 2015 Mar 25;10(3). (link).
  18. Sharma B, Brown AV, Matluck NE, Hu LT, Lewis K. Borrelia burgdorferi, the Causative Agent of Lyme Disease, Forms Drug-Tolerant Persister Cells. Antimicrob Agents Chemother. 2015 Aug;59(8):4616-24. (link).
  19. Jerome Bouquet et al. Longitudinal Transcriptome Analysis Reveals a Sustained Differential Gene Expression Signature in Patients Treated for Acute Lyme Disease. mBio. 2016 Jan-Feb; 7(1). (link).
  20. Fallon BA et al. Regional cerebral blood flow and metabolic rate in persistent Lyme encephalopathy. Arch Gen Psychiatry. 2009 May;66(5):554-63. (link).
  21. Benros ME et al. Autoimmune diseases and severe infections as risk factors for mood disorders: a nationwide study. JAMA Psychiatry. 2013 Aug;70(8): 812-20. (link).
  22. Benros ME et al. Autoimmune diseases and severe infections as risk factors for schizophrenia: a 30-year population-based register study. Am J Psychiatry. 2011 Dec;168(12). (link).
  23. Rajiv Tandon et al. Definition and description of schizophrenia in the DSM-5. Schizophrenia Research, Volume 150, Issue 1, October 2013, Pages 3-10. (link).