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A direct current of 1.28V is applied between six electrodes placed symmetrically on the forehead, hands, and feet of the study subject. Each electrode is alternatively cathode and anode (bipolar mode), which permits the recording of 22 segments from the human body (measurement sequence according to the figure 1). The intensity is transmitted with a numeric form for each segment to an informative program.

The intensity value is converting to conductivity by application of the Law of Ohm U = RI then C = 1/R, incorporated in a diagram. The graph of 22 segments is called an Electro Interstitial Gram (E.I.G) (Figure 2).

Normal range of ESG conductivity
The normal ranges of conductivity C of the EIG graph (Figure 3) were estimated by the formula of the TWB and a coefficient ? related to the age, height, weight, and the gender of the subject. Formula of the calculation of TWB (total body water) v =c Ht 2/R = > R= c v/ Ht2 = > C= c Ht2/v The estimated coefficient had been determinate with the statistical analysis raw data of healthy control groups of the pre-studies and clinical investigations.

The techniques used are the electrical Bio Impedance Analysis (BIA) and the Bio Impedance Spectrometry (BIS) . The BIA is used in many applications like the estimated of the body composition and water balance ⁽⁵⁾, ⁽¹⁴⁾ but also in cardiology ^{(3) (13)} and imaging ⁽¹⁹⁾. The BIS is used for estimated the body composition and water balance ⁽⁵⁾, ⁽¹⁴⁾, but also for estimated the neurotransmitters ^{(23) (24)} .The specificity of the examination is the utilization of a voltage of 1.28 V in DC (direct current) that cannot cross the cellular membranes and capillaries (High resistance in KOhms and reactance 0 Figure 4) and therefore can only reach the interstitial fluid (Interstitial tissue) , whose intensity, resistance, and conductivity can then be measured. These facts were confirmed by the research of Kanai and Meijer ⁽¹¹⁾, ⁽¹⁸⁾, i.e., that the cellular membrane and capillaries behave as one capacity because of dielectric properties, so a direct current cannot penetrate its membranes and circulate solely in the interstitial fluid. The tissues constitute an electrolytic environment; conduction of electric current is assured by the ionic porters under the effect of a tension applied between two electrodes. ⁽¹⁴⁾ The conductivity is also related to the volume (water content) of the space traversed ⁽¹⁴⁾ (Interstitial Fluid)

The electric current is sending from anode to cathode and therefore the sodium (higher extracellular concentration in positive charges) represents the main ionic porters. Figure 5 and 6 are showing the correlation of the traversed compartment intensity and the Na+ concentration. ⁽⁵⁾.. The figure 7 is showing the correlation between the volume (water content) and the traversed compartment conductivity. ⁽¹⁴⁾.

The normal range of interstitial fluid sodium concentration is from 121.6 to 129 mmol/L and it should be corresponding in Intensity (Cottrell equation) from 12.4 to 20 ¬µA (the normal range can range in function of the age/gender/age/weight/age of the subject according to the coefficient c)

Estimated of Tissue Oxygen delivery

1. Estimated of oxygen delivery related to the inter-capillary distance The figure 8 is showing the effect of inter capillary distance variations (interstitial fluid volume) in relation with the tissue oxygen delivery. In case of increased of interstitial volume, the oxygen delivery is reduced.

2. Bio impedance monitoring and Oxygen ⁽³¹⁾ Low frequencies Bio impedance measurement and lack of oxygen The electrical impedance of a living tissue can be continuously measured in order to determine its patho-physiological evolution. Some pathology like ischemia, infarct or necrosis implies cellular alterations that are reflected as impedance changes. As it was described in the introduction, the bio impedance monitoring has been proposed for myocardium ischemia detection, for graft viability assessment and for graft rejection monitoring. In most of the cases, the event is detected or monitored because an alteration of the extra-intracellular volumes occurs. The following figure illustrates how ischemia is monitored by bio impedance measurements. During the normoxic condition, a significant amount of low frequency current is able to flow trough the extracellular spaces. When ischemia and the following lack of oxygen (hypoxia) is caused by any means, the cells are not able to generate enough energy to feed the ion pumps and extracellular water penetrates into the cell. As a consequence, the cells grow and invade the extracellular space. This causes a reduction of the low frequency current that yields an impedance modulus increase at this low frequency. Thus, the bio impedance measurement at low frequencies is an indicator of the tissue ischemia.

This simplistic description of the ischemia-impedance relationship could be not correct for cells containing gap junctions. In those cases (e.g. myocardium) the observed impedance increase at low frequencies is mostly attributed to the closure of the gap junctions (Gersing, 1998) (Groot, 2001). As an example, the following graph shows the evolution of the impedance modulus at 1 kHz for six impedance probes inserted in a beating pig heart subjected to regional ischemia (see the method in Groot, 2001). Three of them are within a normoxic area and the other three are within the area influenced by the ischemia.

The necrosis process that follows a long ischemia period can also be detected because the loss of membrane integrity allows continuity between the extra and intra-cellular media and, consequently, the impedance magnitude at low frequencies decreases (Haemmerich et al., 2002). Single-frequency measurements are relatively easy performed and provide the necessary information to follow the ischemia processes. Therefore, some researchers have promoted them as the basis for a clinical parameter to monitor the tissue condition. However, multiple frequency bio impedance measurements (bio impedance spectrometry) and the subsequent characterization (Cole-Cole model) provide additional information and improve the reproducibility of the results (Raicu et al., 2000).

By Using the Spectrometry technique and in particular the Chronoamperometry ⁽¹⁾, ⁽²⁾, The EIS system makes the calculation and estimated the interstitial fluid ionograms and interstitial fluid H+ concentration ^{(21) (22)} (Figure 11) according to the ionic flux (Diffusion coefficient of the ions) ^{(12) (16)}

Result of BIS: Applications of the measurement of the estimated interstitial fluid Na+ concentration:

The interstitial fluid Na+ concentration gives access to the estimated activity of: Na+/K+ ATPase (Fig.12)

Effect of the interstitial fluid pH in human body ^{(27), (28) (29), (30)}

The interstitial fluid or tissue pH has action on the enzyme activities and therefore in the function of the liver and the pancreas ^{(28) (29), (30)}

The interstitial fluid or tissue pH has action also in the brain functions. ⁽²⁷⁾,

Hydrostatic and Osmotic pressure: The Starling equilibrium

No direct methods for sampling interstitial fluid are currently available. The composition of interstitial fluid, which constitutes the environment of the cells and is regulated by the cells activity and ionic distribution, has previously been measured by the suction blister or liquid paraffin techniques or by implantation of a perforated capsule or wick. The results have varied, depending on the sampling technique and animal species investigated. In one study, the ionic distribution between vascular and interstitial compartments agreed with the Donnan equilibrium ^{(25) (26)} ; in others, the concentrations of sodium and potassium were higher in interstitial fluid than in plasma ^{(25) (26)} . However, the publications ^{(25) (26)} could establish the following elements:

What is a modeling? The modeling is not the same imagery conventionally used in medicine. The approach is more like that of a physicistÄôs approach. We reduce the diversity and complexity of the bodily functions by an appropriate choice of assumptions and measurements. We are only keeping the physical properties of the bodily system which relate to the posed problem. In short, we approach reality through a model. Abstraction is the conceptual base of a model: a real object, a phenomenon is analyzed in order to save only the essential characteristics, those that have an influence on that which we wish to study. We must break up complex problems into simpler problems. This method was expressed by Rene Descartes (France) in his Discourse on the Method: ÄúÄ¶divide each of the difficulties for me to examine into tiny fragments and that will be necessary to solve them allÄ¶Äù The medical modeling is a control tool and helpful in therapeutic decisions. Modeling is not intended to reproduce reality exactly; only a model identical to the system could be regarded as an exact representation of reality. Simulation provides comprehension, it makes it possible to formulate theories and to test them and sometimes it leads to the understanding of that which is incomprehensible without it, by functioning according to a logic centred on the computer.

A first localization of organs by direct problems came out through application of the mathematical calculation of Venn diagrams and application of the Maxwell equation for the value of intensity of the different zone of the human body modeling

The modeling of the EIS system is made according to a chromatology from blue to red related to the conductivity of the zone.