# Six Months

So, it seems that I am improving again. Six months ago I came back from Argentina, where I spent the boreal winter. I felt better there, as I usually do during summer, in Italy. Feeling better means being able to think, to read, to do calculations, to draw. To exist, in one word. And also to move around a bit, which is not truly relevant for me, though.

I came back to Italy at the end of March (blog post), sure that I would have had other months of improvement ahead of me, given that we were at the beginning of Spring. But it hasn’t been the case, I got worse: For six months I haven’t thought, and I have been living horizontally, in silence. There were days in which it seemed that I was starting to improve (like when I recorded this video), but then it didn’t last. I can’t remember these six months, in my subjective time they sum up to a week or less.

Not sure why it happened: perhaps the 48 hours of the chaotic journey back to Italy damaged me so badly that it took half a year for me to regain the status quo ante, or maybe the strange flu I got in March, while in Argentina, made the disease worse. In the life of an ordinary person, this would be a rather exceptional episode, for me it is the rule: the improvements are the rare exception. I have lived like that since I was 20.

And now, because I usually get worse at the end of September, I know that I am about to start my descend to Hell again. And this time I can’t move to the austral hemisphere, because of the pandemic. So what am I supposed to do in the few days of life I have left? I’ll do what I have always wanted to do: applied maths and drawing, with only very short term goals. Something that I can finish.

I share these private vicissitudes only because I think that it is important to let the world know about this struggle. It seems unlikely that I can discover the reason why this curse has stricken my life, but I will continue studying this phenomenon: most of what I study, when I can, is about new tools to apply to my own biology.

# My first time with LaTeX

Each mathematical formula I have used in my blog till now was an image: I wrote them in a Word document using the equation editor by Microsoft (that I like very much), then I captured the screen and saved it as an image and then I uploaded them in my blog.

In the past, I tried to find a way to write them as text, without succeeding. But in fact, it is possible, using the LaTeX syntax and a few HTML commands.

These are the first “true” mathematical formulae present in this blog. I will use this page to test the LaTeX syntax for mathematical expressions (a handbook is available here).

$\int_{A_1}\int_{A_2}\frac{\partial \Psi(x,y)}{\partial x}dxdy$

$i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$

A symbol within the paragraph: $\pi$. A inequality within the paragraph: $x_i>0$. This is an example of an expression with a pedix that has a pedix: $f_{X_1}$.

# The time machine

I am aware that these are just messages floating in the silence, stored somewhere in the planet as binary numbers. I am writing to myself, mainly, from my remote hiding place.

I have travelled through ages, without really being part of them. All alone with my problem. As a patient with a rare disease that doesn’t even have a proper description, I do not belong to humankind.

But humans have paradoxical behaviours, they care more about a man who lived five thousand years ago in the north of Italy, trapped in the ice of our highest mountains, than of clochards that live right now in pain and loneliness in their community. So it might be that generations from now, someone will find these notes, an archaeologist who will try to build my story, from fragments of what I left behind: drawings and calculations. Mathematics is a universal language, after all, and to some extent, even art is universal; not always but often, good art is forever.

If I fail my mission, history will never record my existence. But it might be that at some point in the future someone will find these notes frozen in the ice of a planet long forgotten by humans themselves, as we now have forgotten Africa, the place we all come from.

# Why I study my own disease

A lot of patients have asked me why I use my little energies to study my disease, instead of just waiting for science to conquer it.

There are many reasons, the first one being that I am desperate because of the cognitive disability that is worse than death. I am not concerned about the physical limitations, at all, even though I have been mostly housebound for the last 20 years. Another reason is that I like computational biology, and I started studying engineering before getting sick with the idea of switching to bioengineering after graduating. So, this is my job.

The other point is that even though I fit the criteria for ME/CFS, I have a rare disease, granted that ME/CFS is not a rare disease: it has a prevalence of 0.4% according to some studies, so it is relatively common. Then why am I a rare patient? Let’s do some calculations: since the median age at onset is 36.6 years with a standard deviation of 12.3 years, the proportion of males is 19% and the proportion of those who are housebound for most of their disease is 25% (R), the probability for a ME/CFS patient of having my same characteristics is (assuming that these are all independent random variables) given by p=0.0075. So, less than 1 out of 100 ME/CFS patients has my type of illness. If we consider also that pain or aching in muscles is present in 59% of patients and it is mostly absent in my case, the above-mentioned probability is even lower: p=0.0031. Which means that only 3 ME/CFS patients out of 1’000 have my illness.

Taken all these data together, the prevalence of my disease in the general population becomes 1/100’000, which means that I have a rare disease, according to the European definition (where a disease is defined rare if it has a prevalence ≤1/2’000) [R]. In the US a disease is defined rare only if it has a prevalence ≤1/200’000, though [R].

And besides that, it is pretty obvious that I am a unique case. I have never found a patient like me, so far. It can also be noted that in Italy, given a population of 60 million inhabitants, those who have my condition are only 600. This might be the reason why I haven’t met them, yet.

This means that I am probably the only one who is studying my disease, on the planet! This is why I’m doing what I’m doing.

Above, my personal book of immunology, built page by page, paper by paper. I have three other books about this discipline. One of them was a gift from a neurologist that perhaps thought that gift was the only thing she could do to save me. Another one is a very sophisticated text on cutting edge immunology. But this one is the best one because I have selected and read each one of its pages. It is by no means a complete book, it is mainly focused on B cells and B cell autoimmunity, but it has been very useful.

I have built several other books like this, on computational methods in immunology, on metabolism, on neurosciences, on microbiology, and on some diseases: Lyme, ME/CFS, mast cell activation, POTS…

I have learned a great deal, even though outside academia. But I had no choice, I have been too sick and too slow to study at university: I had only a few weeks in which I could study, and then months or years in which I had to wait. This has been my routine. Moreover, given the lack of energy and time, I had to study only what was truly important for my health. Because my goal was to cure myself and save me from a lifetime of cognitive disability.

# Testing hypotheses

Introduction

My ME/CFS improves during summer, in the period of the year that goes from May/June to the end of September. I don’t know why. I have several hypotheses. One possible reason for the improvement in summer is an interaction between the light from the Sun and some parts of my physiology, the immune system for instance. We know that ME/CFS tends to have an oscillating course in most of the patients (Chu L. et al. 2019), but the presence of a seasonal pattern in this patient population has not been investigated so far, to my knowledge. And yet, if you ask directly to patients, many of them say that they feel better in summer. Unfortunately, we don’t have scientific data on that, this is an area worth investigating with some carefully done survey.

Seasonal variation of the immune system

The immune system has a high degree of variation for several reasons (Brodin P et Davis MM 2017). In particular, there are studies about the seasonal fluctuations in the expression of some crucial genes of the immune response (Dopico XC et al. 2014).

How does this regulation happen? Different mechanisms are possible, some of them might be related to changes in the light we receive from the Sun as the Earth rotates around it. We know that the length of the day has an effect on innate immunity: the more the hours of light, the lower the power of the innate immune system (Pierre K. et al. 2016). We also know that ultraviolet radiation, particularly UVB, is an agonist for the aryl hydrocarbon receptor (AhR) (Navid F. et al. 2013). This receptor seems to reduce the expression of the major histocompatibility complex II (MHC II) in dendritic cells (DCs), thus reducing their antigen-presenting activity (Rothhammer V. et Quintana F.J. 2019). UVB might be able to reach dendritic cells when they are circulating near the skin, during summer, thus inhibiting their antigen-presenting activity. Infrared radiation, on the other hand, seems to have an effect on energy metabolism: in Fall we lose a significant amount of infrared radiation in a wavelength range (0.7-1.0 nm) that is known to have an effect on mitochondrial activity (Nguyen L.M. et al. 2013) and it might perhaps have an indirect effect on immunity too.

As further proof of seasonal fluctuation in immunity, some immunological diseases have this kind of seasonality: Rheumatoid arthritis (Nagamine R. et al. 2014) and Rheumatic fever (Coelho Mota C.C. et al. 2010) are two examples. Moreover, the prevalence of Multiple Sclerosis is directly proportional to the latitude (Simpson S. et al. 2011). We also know that there is seasonal fluctuation in serum autoantibodies (Luong T.H. et al. 2001).

Of course, sunlight might be just one of the variables into play. The other aspect I am considering is the seasonal distribution of some common pathogens. Streptococcus, Enteroviruses and Fungi of the genus Penicillium are known to have a seasonal distribution with a peak in Fall and/or Winter (Ana S.G. et al. 2006), (Salort-Pons M et al. 2018), (Coelho Mota C.C. et al. 2010). Common influenza has this pattern too. Rheumatic fever, a disease due to an abnormal immune response to Streptococcus, has its flares in Fall because Streptococcus is more common in that period of the year (Coelho Mota C.C. et al. 2010). Even the composition of the gut microbiota has a seasonal pattern (Koliada A. et al. 2020). I am currently investigating my immunosignature, measured with an array of 150.000 random peptides, to see if I can find some relevant pathogen in my case. You can find this study here.

(A few months after I wrote these notes a pivotal study has been published on these same topics, avalilable here).

An experiment

I moved from Rome (Italy) to Rosario (Argentina) at the beginning of January. I was very sick and I steadily improved after about 40 days. I became a less severe ME/CFS patients and I could work several hours a day and care for myself, granted that I did not exceed with aerobic exercise. At the end of March, I started deteriorating as it usually happens at the end of September, when I am in Rome. In order to study this phenomenon, I have built a complete model of solar radiation at sea level, which considers the inclination of sunrays in function of the latitude and of the day of the year. It takes into account the effect of the atmosphere (both diffusion and absorption) and the eccentricity of the orbit (Maccallini P. 2019). If you look at the figure below (a byproduct of my mathematical model) you can see that when I started deteriorating in Rosario, the power of sunrays at noon in that city was still as high as it is in Rome during the summer solstice (this is due to the fact that the Earth is closer to the Sun in this period and to the fact that Rosario is closer to the Equator than Rome is).

So I have to discard the original idea that the power within the infrared range, or the ultraviolet radiation, or the visible one is responsible for my improvement in summer. If I still have to consider that sunlight has something to do with my improvement, I must conclude that it is the length of the day the relevant parameter: I may need more than 12 hours of light to feel better. Why? Because the longer the day, the lower the strength of the innate immunity. This is now my working hypothesis and I will start from the following mathematical model to pursue this research: (Pierre K. et al. 2016).

I will also use full-spectrum lamps early in the morning and in the evening to reproduce a 15 hours day, so to dampen down my innate immune system in a safe, drug-free way. I have to reproduce a day of 15 hours and see what happens. In the figure below the hours of the day at dawn and at dusk and the length of the day for Rome, for each day of the year (this is also a plot from my model).

What follows is the script I have coded in order to plot the first figure of this post. More details on this model of solar radiation are here: (Maccallini P. 2019). As a further note, I would like to acknowledge that I started pursuing this avenue in the summer of 2009: I was building the mathematical model of solar radiation (see figure below, made in 2009) but as the summer finished, I turned into a statue and I had to stop working on it. When I improved, about a year later I started working on the systematic analysis of the mechanical equilibrium of planar structures (it is a chapter of this book). I am proud of that analysis, but it has not been very useful for my health…

% file name = sun emissive power sea level Rosario vs Roma
% sun emissive power per unit area, per unit wavelength at sea level
clear all
% three parameters of the orbit
A = 6.69*( 10^(-9) ); % 1/km
B = 1.12*( 10^(-10) ); % 1/km
delta = pi*313/730;
% the two parameters of Plunk's law
C_1 = 3.7415*( 10^(-16) ); % W*m^2
C_2 = 1.4388*( 10^(-2) ); % mK
% Stefan-Boltzmann parameter ( W/( (m^2)*(K^4) ) )
SB = 5.670*( 10^(-8) );
% radius of the photosphere (m)
R_S = 696*(10^6); % m
% temperature of the photosphere (K)
T_S = 5875;
% conversion of units of measurments
N = 20; % dots for the equator
R = 3.8; % radius of the orbit
ro_E = 1.3; % radius of the earth
lambda_Rosario = -32*pi/180; % latitude of Rosario (radiants)
lambda_Roma = 41*pi/180; % latitude of Rome (radiants)
delta = 23.45*pi/180; % tilt angle
% the array of theta
theta(1) = 0; % winter solstice (21/22 December)
i_ws = 1;
day = 2*pi/365;
days = [1:1:366];
for i = 2:366
theta(i) = theta(i-1) + day;
if ( abs( theta(i) - (pi/2) ) <= day )
i_se = i; % spring equinox (20 March)
endif
if ( abs( theta(i) - pi ) <= day )
i_ss = i; % summer solstice (20/21 June)
endif
if ( abs( theta(i) - (3*pi/2) ) <= day )
i_ae = i; % autumn equinox (22/23 September)
endif
endfor
% the array of the radius (m)
for i=1:1:366
o_omega (i) = (10^3)/[ A + ( B*sin(theta(i) + delta ) ) ]; % m
endfor
% the array of the wavelength in micron
N = 471;
L(1) = 0.3;
L(N) = 5.0;
delta_L = ( L(N) - L(1) )/(N-1);
for j = 2:N-1
L (j) = L(j-1) + delta_L;
endfor
% the array of beta*L
% the array of L in metres
L_m = L*( 10^(-6) );
% angle psi
psi(1) = 0;
minute = pi/(12*60);
for i = 2:(24*60)+1
psi(i) = psi(i-1) + minute;
endfor
% -----------------------------------------------------------------------------
% Rosario
lambda = lambda_Rosario
% angle between n and r at noon in Rosario
for i= [i_ws, i_ae, i_ss, i_se]
for j=1:(24*60) + 1
% scalar product between n and r
scalar_p(j) = [cos(lambda)*sin(psi(j))*cos(delta) + sin(lambda)*sin(delta)]*( -cos(theta(i)) )+ [(-1)*cos(lambda)*cos(psi(j))]*( -sin(theta(i)) );
endfor
% value of psi at noon
for j=1:(24*60) + 1
if ( ( scalar_p(j) ) == ( max( scalar_p ) ) )
j_noon = j;
psi_noon (i) = psi(j);
endif
endfor
% angle between n and r at noon
cos_gamma (i) = scalar_p(j_noon);
endfor
% the array of the emissive power (W/(m^2)*micron) in Rosario
for i = i_se:i_se
for j=1:N
num = C_1*( (R_S)^2 );
den = ( (L_m(j)^5)*( (e^(C_2/( L_m(j)*T_S ))) - 1)*( (o_omega(i))^2 ) )*10^6;
power(j,i) = ( num/den )*( e^(-S(j)/cos_gamma (i)) );
endfor
% plotting
plot (L (1:N), power(1:N,i), '-r', "linewidth", 2)
xlabel('wavelenght ({\mu})');
ylabel('W/m^{2}{\mu}');
axis ([0.3,5,0,1500])
grid on
endfor
hold on
% -----------------------------------------------------------------------------
% Rome
lambda = lambda_Roma
% angle between n and r at noon in Rosario
for i= [i_ws, i_ae, i_ss, i_se]
for j=1:(24*60) + 1
% scalar product between n and r
scalar_p(j) = [cos(lambda)*sin(psi(j))*cos(delta) + sin(lambda)*sin(delta)]*( -cos(theta(i)) )+ [(-1)*cos(lambda)*cos(psi(j))]*( -sin(theta(i)) );
endfor
% value of psi at noon
for j=1:(24*60) + 1
if ( ( scalar_p(j) ) == ( max( scalar_p ) ) )
j_noon = j;
psi_noon (i) = psi(j);
endif
endfor
% angle between n and r at noon
cos_gamma (i) = scalar_p(j_noon);
endfor
% the array of the emissive power (W/(m^2)*micron) in Rosario
for i = [i_ae, i_ss]
for j=1:N
num = C_1*( (R_S)^2 );
den = ( (L_m(j)^5)*( (e^(C_2/( L_m(j)*T_S ))) - 1)*( (o_omega(i))^2 ) )*10^6;
power(j,i) = ( num/den )*( e^(-S(j)/cos_gamma (i)) );
endfor
endfor
hold on
plot (L (1:N), power(1:N,i_ae), '-k', "linewidth", 2)
plot (L (1:N), power(1:N,i_ss), '--k', "linewidth", 2)
legend ('spring equinox in Rosario', 'autumn equinox in Rome', 'summer solstice in Rome', "location",'NORTHEAST')
hold on
plot ([0.4,0.4], [0,1500], '--k', "linewidth", 1)
plot ([0.7,0.7], [0,1500], '--k', "linewidth", 1)

# Back home

Continuation of this post.

Forty-four hours of travelling, in total, from Rosario to Rome, by pullman, by plane, and by train. With 40 kilos of books and papers.

I had a flight for Rome that was programmed to take off from Ezeiza, the International airport of Buenos Aires, on April 13th, but I decided to take the one organized by the Italian government for March 23th, a special flight set up to bring back home Italian citizens abroad, before a complete shut down of international flights from Argentina to our country. There were no flights from Rosario, my city, to Buenos Aires, though, but I managed to find a company that organizes transportations by pullman from one city to the other, in Argentina: Tienda Leon.

So, on March 22nd, I moved to Ezeiza where I waited several hours before sitting on my chair, on a brand new Boeing 787 bearing the colours of the Italian company Neos.

While at the airport, I met most of the Italians that were going to get the same flight, all wearing their masks. Some of them with some very fancy models, that made them look like a Star Wars character. I was there, well aware that I was going far beyond the limit set by my disease. I had to lay down continuously and I could see how frail I was in comparison with the other passengers waiting for the flight. No one knew how sick I was, I told nobody. No one knew that I have been living in my bedroom for most of the last 20 years. And that this was the very first long travel abroad for me.

I have just received the notification that my flight for April 13th has been cancelled, so my choice to come back as soon as possible has been a wise one. I took that decision also because of the advice from the diplomatic offices of the Italian Consulate in Rosario.

A friend has crafted the picture above, not knowing how much Indiana Jones has meant for me when I was a teenager. But, even though an appealing adventure, the tragedy behind it is real, it is not a movie. Once in Milan, I could start seeing the effects of the pandemic in the eyes of the staff of the airport of Malpensa: the fear and the concern. Then I moved from Milan to Fiumicino, where I found a train for Rome, my city. A city that I left two and a half months ago full of life and noise, now empty as in a dream.

# From Argentina to Italy, during a pandemic

It has been a great ride, my almost-three-month period here in Rosario, next to the huge slowly flowing river of Paranà. This is a city full of life, embraced by the warmest summer I have ever seen. Populated by wonderful citizens.

I have been living in an apartment where the sun awakes me very early in the morning, through a wide window next to my bed. I could see the roofs of the centre of the city as I opened my eyes, including the top of the Monumento National a la Bandera, a gigantic building that celebrates this great nation. For the second half of the day, I had the light from the opposite window and I could follow its changes, while I was working, as the hours passed by; I saw every day the same magic ritual: as the photons from our star went through thicker layers of the atmosphere, they changed their frequency, turning redder and redder, culminating in a warm explosion, just before the night.

And in the meanwhile, news from Italy was scarier and scarier and the hypothesis that the new coronavirus could reach this continent was more obvious as the weeks passed by. Now we have the virus here, and president Alberto Fernandez has declared the state of quarantine from March 20th.

At that point, the connection between Argentina and other countries (including Italy) has become uncertain; my flight planned for March 28th has been cancelled and I have decided to get one of the special flights organized by the Italian government to bring back its citizens from Argentina, before a complete shut down of international travels. So I had about 48 hours to find a means of transport from Rosario to the airport in Buenos Aires, where the flight will take off tomorrow, at 1:00 AM.

But there was no way I could find a flight from Rosario to Buenos Aires in such a short time, also because of the shut down of Argentina, and no trains were available. Fortunately enough I have found a Pullman, and I am going to leave this apartment in a few hours.

My come back to Italy is becoming more and more adventurous also because I will land in Milan, one of the places most hit by the infection in the whole planet. There I have to reach Rome. I have been able to find a plane from Milan to Rome, so it will be possible to be at home on the evening of March 23rd. I have to avoid to get the virus though, during this travel. I will be exposed to it for sure, so I am taking any possible measure to ensure my safeness.

This travel to Argentina has been a success. My health has improved, even though now I am deteriorating again, as was expected, as the light of the summer of the southern hemisphere becomes weaker. But I have been able to use my new energies to write and submit a paper on the cingulate cortex in ME/CFS, I have gone further with my studies on the analysis of the immunosignature (measured using random peptides) in my own serum (R), I have started the study of a mathematical model for the diffusion of Coronavirus 19 among the Italian population (R). I have learnt a great deal about computational neuroanatomy (R) and neurosciences in general. I have finished a complete model for solar radiation at sea level (R) and I might have found one of the environmental parameters that determine my improvement during summer. And yes, I have also been able to draw a portrait.

The adventure in the realm of science and art has been great, now I have to live the adventure of coming back home going through a world that is facing one of the greatest health challenges of the last century.

# 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.

Go to the article

# 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:

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:

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

With a few passages we can write:

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.

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).

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.

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!

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.

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).

.