**1. Introduction**

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 The other one has been presented by Alan Moreau during the NIH conference on ME/CFS, and it is unpublished (R).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.

**2. Impedance**

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. Impedance** **of 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 Z_cl and of its imaginary component to R_cl and C_cl can be got from figure 4. The absolute value of Z_cl 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 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 C_cl which is due to the dielectric properties of cell membranes. A change in composition in these membranes could lead to a reduction in C_cl 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 R_su, 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 C_cl. 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.

**11. Mathematical note****s **

The calculation of the impedance Z_cl of the sample (figure 3) is as follows:

Then you have to add the resistance R_su to the real part and you obtain Z_tot. In order to calculate the dielectric constant of the lipid membrane just follow these passages:

In order to choose the range of variation for C_cl and R_cl 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

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:

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 clear all % 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; end % 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; end % we register the array of the real part and of the imaginary part of impedance and its module for i=1:n_c for j=1:n_r 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) ); endfor endfor % we plot the real part of the impedance figure(1) mesh(r(1:n_r), c(1:n_c), Z_r(1:n_c,1:n_r)); grid on ylabel('capacitance (pico Farad)'); xlabel('resistance (Mega Ohm)'); zlabel('Ohm'); legend('Real part of Impedance',"location","NORTHEAST"); % we plot the imaginary part of the impedance figure(2) mesh(r(1:n_r), c(1:n_c), Z_i(1:n_c,1:n_r)); grid on ylabel('capacitance (pico Farad)'); xlabel('resistance (Mega Ohm)'); zlabel('Ohm'); legend('Imaginary part of Impedance',"location","NORTHEAST"); figure(3) mesh(r(1:n_r), c(1:n_c), Z_m(1:n_c,1:n_r)); grid on ylabel('capacitance (pico Farad)'); xlabel('resistance (Mega Ohm)'); zlabel('Ohm'); legend('Module of Impedance',"location","NORTHEAST");