One of the main objectives of modulated electro-hyperthermia (mEHT) [1] is its selective heating [2] , which is supposed to be by energy-absorption of the transmembrane protein clusters (rafts) [3] . However, the measurement of the effect in nano range is highly complicated. The development of information technology allows simulating the radio-frequency (RF) induced electromagnetic (EM) field and its absorbed energy in model structures.

The main components of the cell membrane are sphingolipid, cholesterol, steroid, carbohydrate and transmembrane proteins. The rafts are structured parts of the membrane, a cluster of transmembrane proteins, and contain high proportion of saturated lipids and cholesterols as well [4] . The cholesterol and protein content increase the stability of the membrane. Furthermore, proteins are responsible for the structure and signal transduction, functioning like receptors on the surface of the membrane. The rafts are just the 2% of the membrane components but give the 50% of the membrane mass due to their size, [5] . The main part of the proteins is clustered in raft domains. They form the 25% - 60% of the raft depending on the location of dynamic proteins, [6] . These ordered domains have high lateral mobility in the membrane [7] , which allows their easy shifting by the applied electric field, situating in the most optimal absorption position.

The size of the membrane rafts depends on the ratio of protein and lipid content, which differs in their location and could change by time. The geometry of the planar rafts in the recent literature is 25 - 700 nm, 100 - 200 nm and 10 - 100 nm average diameter, [8] [9] [10] . Of course, the thickness of these domains is higher (due to the high protein content) than the non-structured part of the membrane which is only about 5 nm [11] . Furthermore, the cholesterol which wedged in the proteins widens perpendicular the transmembrane region of the domain.

The dielectric constant and the conductivity determine the electric properties of the membrane and the rafts. The raft and its micro-environment have a considerable diversity, which complicates its average characterization. The dielectric constant (relative permittivity, ε_r) of the intra- and extracellular space is approx. ε_r ≈ 73 [5] , showing large displacement field: D ≈ ε_r∙E. The membrane layer has a low dielectric constant, (ε_r ≈ 2). However, the membranes are heterogenous. The layers of phospholipid heads and tails have different dielectric constants in the shell model, [12] [13] [14] [15] [16] .

The raft domain contains a high portion of protein; therefore, this region has undoubtedly higher permittivity than its membrane neighborhood. The average dielectric constant of the raft domain takes into consideration the proteins in the cluster. The protein permittivity has multiple variants in the literature. There is measurement showing an extreme high ε_protein ≈ 6300 value in the integral protein next to the low ε_lipid ≈ 2 value in the lipid region, and the transmembrane region of the protein also has low permittivity because the ability of polarization is blocked in this area [17] . In other membrane measurement ε_m = 12.5 (with 1.6 standard deviations) [18] . This high value is probably a local peak in the measured average dielectric value of protein including membrane.

The transmembrane protein clusters have even more heterogeneity and complex interactions, and so their simulation and measurements are more complicated. The hydrophobic region of the proteins shows low dielectric constant 2 < ε_protein < 5; however, the outer regions with bounded water increase up to more than ε_protein > 100 in some regions, and proves the extreme values in some cases [17] . The water bound to the protein further increases the average dielectric constant, like it is shown by the Kirkwood-Fröhlich approximation in 21 types of proteins in water solution, [19] . Simulations [20] show that the protein dielectric constant was ε_protein @ 6 - 7 in the inner protein region and ε_protein @ 20 - 30 on its wet surface. Generally, although the cholesterol and lipid contents of the raft domain cause decreasing in the relative permittivity of the inner raft area (2 < ε_raft < 5), but the high density of protein chain ends lead to an outstanding raft region with high relative permittivity (40 < ε_{raft protein} < 80), [21] . We assume the dielectric constant of the complex membrane rafts as ε_raft ≈ 40.

The electric conductivity also shows the difference between the raft and non-raft part of the membrane. The average conductivity of the cell membrane is 3 × 10⁻⁷ S/m, [5] . In the membrane having high proportions of transmembrane proteins nearly ten times higher conductivity was measured, [22] . Models of the added protein domains with different concentration into the lipid layer showed between one and three orders of magnitude higher conductivity in the presence of protein fractions than the lipid membrane alone [23] . We conclude that the high protein portion of raft domain causes at least ten times higher electric conductivity, which well identifies the rafts by the forced RF-current. In the case of multilayer model, the conductivity of the outer part of rafts is estimated nearly 3 × 10⁻³ S/m, [24] .

The absorbed energy heats the mass of the raft. The mass determines their developed temperature. The membrane mass is made up of 52% protein, 40% lipid, and 8% carbohydrate, [25] . The main part of membrane proteins is located in membrane rafts. The mass density of the non-raft membrane region is examined in several projects, [26] [27] [28] . The mass density of the inner parts of the protein chains is lower than their surfaces, but of the mass density of the outer part of the complex raft is higher than the value of the electrolyte. The average mass density of electrolyte is 1000 kg/m³, while of the lipid is approx. 900 kg/m³, [28] [29] [30] . The presence of sphingomyelins and cholesterols (which are typical in the raft) increases of the membrane mass density, which is enhanced further by the presence of transmembrane proteins, [31] [32] [33] [34] . Taking these facts into consideration the mass density of membrane rafts is estimated pretty high, up to 1150 kg/m³.

Our objective is to calculate the specific energy distribution in the above described well heterogeneous membrane structures, with particular emphasis of the energy-absorption of their rafts. The summary of the values of parameters, which are used in this article to examine the electric loss distribution in the membrane raft domains is presented in Table 1.

The CST EM Studio from Computer Simulation Technology software (Darmstadt, Germany) [35] was used to simulate the electromagnetic (EM) field effect on the 3D cellular models. The calculation is based on the Finite Integration Technique (FIT) [36] which enables to solve the Maxwell equations under certain conditions applying a mesh for numerical calculation. Considering the created structure and material properties of the model and the defined excitation conditions the software calculates the direction and the magnitude of EM field vectors for each mesh unit. Due to the extremely high mesh number, the simulation resolution does not allow precise solution; therefore, in our cellular models, a homogenous membrane layer was generated.