Objective The simulated CSF and brain were set up.The aim of this project is to use them to study characteristics of real human brain in laboratory condition.Methods Edible gelatine was used to simulate the brain.A concentration of 6 g/100 ml gelatine had physical characteristics similar to real brain.A series of different salt jelly concentrations were tested.Results The frequency and temperature characteristics of simulated CSF conductivity were measured at room temperature （27℃）,body temperature （37℃） and above the body temperature （45℃）.Conclusions Kinds of direct comparisons of the results of mathematical calculations with experimental results is done using tangential and radial dipoles which insert into the simulated SCF and simulated brain,to check on the validity of the parameters of simulated brain. 　　

【关键词】  SCF;simulated brain;dipole

　　Correspondent to ZHOU Zhi-zun,Department of Medical Imaging,Mudanjiang Medical Institute,Mudanjiang,Heilongjiang 157011,China

    　E-mail:zhou007@hotmail.com

　　 INTRODUCTION

    Electric sources in the cortex can be modeled as equivalent dipoles,and both mathematical modeling and experimental measurements of the fields produced by dipoles in saline are used to show wether the relevant patterns would be produced by dipoles located approximately 1～2 mm apart in the cortex.In order to solve many magnetic and electric potential patterns of human head,the CSF （cerebrospinal fluid） and brain are constructed and simulated in this paper.A human head is constructed of different tissues,with different conductivities.Conductivity of scalp and brain is same,0.33 s/m.The values of conductivity used in most head models are based on the values published by Geddes and Baker （1967）.Conductivity of the skull is very small,only 0.0042 s/m.Skull conductivity is only one eighth that of the brain.Cerebrospinal fluid conductivity is 1.4 s/m,and the conductivity of cartilage is 0.4 s/m.

    METHODS

    In our project,edible gelatine was used to simulate the brain.A concentration of 6 g/100 ml gelatine had physical characteristics similar to real brain when it was totally set.A series of different salt jelly concentrations were tested and it was found that the necessary concentration of NaCl was 0.075 g/100 ml in 6% gelatine for a conductivity of 0.33 s/m.Physiological saline is 0.9 g/100 ml and its conductivity was measured at 1.4 s/m （the same as that of cerebrospinal fluid）.

    Figure 1 shows the circuit used to do the conductivity measurements.The chamber was made of plastic and each end was consisted of a stainless steel electrode,held in place by a screw-on cap so that no fluid could leak out of the chamber.The internal diameter of the cylinder was 25 mm and the length 100 mm.

    Figure 1  Circuit for measuring the conductivity of the testing material

    A 5 V,100 Hz sinusoid was applied across the electrodes and were measured using a digital voltmeter.Alternating current was used for this measurement because direct current caused polarization of the electrodes,and gave a continuously changing voltage reading.Conductivity  was calculated using the formulae:R=ρl   A，σ=lI   AΔV,σ=LAR   100VCA=2.038VR   VC    First,body of the brain was constructed by edible Gelatine from 1 g/100 ml to 10 g/100 ml.If the amount of gelatine in the hot water was too small the gelatine will take long time to set （normally two hours）.After series testing we find that physical characteristic of the 6 g/100 ml concentration jelly was nearly same as real human brain.The conductivity of 6 g/100 mlpure gelatine was 0.198 s/m.So we can use it by adding certain amount of salt to reach the conductivity value of 0.3 s/m.It costs more time to testing the series different salt jelly concentrations.And finally we find that the salt concentration of 0.33 s/m brain conductivity is 0.075 g/100 ml in 6% jelly.It was very important to follow the procedures which we summarized in this experiment.

    The series certain concentration of salt jelly was made and tested.The concentration of NaCl used to simulate brain was 0.075 g/100 ml in 6 g/100 ml gelatine and its conductivity was 0.3 s/m at temperature and 100 Hz.

    Table 1  Final Experimental Measurement Figures of NaCl Concentration for Brain,Scalp,and Conductivity of Cerebrospinal Fluid

        RESULTS AND CONCLUSION

    The frequency and temperature characteristics of simulated CSF conductivity were measured at room temperature （27℃）,body temperature （37℃） and above the body temperature （45℃）.The frequency from 5 Hz to 500 Hz was investigated.

　　　Figure 2  Frequency and temperature characteristic of simulated CSF conductivity

    Figure 3  Temperature characteristic of simulated brain conductivity

    Figure 2 shows that with temperature increases,the conductivity of the simulated CSF  increass.That means the temperature will play a role in the human head simulation.The ideal temperature for the experimental measurement would be body temperature.

    The conductivity varies when the frequency changes from 5 Hz to 500 Hz.From 0 Hz to 100 Hz the conductivity changes sharply （the variation was 0.2 s/m）.From 100 Hz to 500 Hz,the conductivity tends to saturate even though the conductivity still slightly increases.So the ideal range of frequency is from 100 Hz to 500 Hz.In this range the conductivity is almost constant during the experiment.The frequency over 500 Hz was not considered because the biomedical signal in the human brain is below 100 H.In the low frequency range relevant to human EEG the conductivity varies with frequency.

    Above method was used for room temperature below 20℃.If the room temperature was much higher the salt gelatine would be not set.We try to make different concentration of jelly and find that for different concentration of jelly the conductivity was different.By a series testing,the concentration of jelly for conductivity 0.33 s/m was 10 g/100 ml water for 100 Hz at body temperature.The graph （Figure 3） was the temperature characteristic of this jelly conductivity.

    Figure 3 shows that with temperature increases,the conductivity increass.The ideal temperature for the experimental measurement would be body temperature because the human brain was very sensitive to the variation of the temperature.If the temperature in the human brain increases （above the body temperature） the conductivity of the human brain will also increase.

    Measurements were made with only one dipole.A series of different measurements was made as the dipole was shifted with respect to the electrode array.The results of various pairs of individual measurements are presented on the same graph,for comparison.The test can be seen in Figure 4.

    Tangential dipole potential distributions were measured with the dipole at a depth of 0.5 cm.In this experiment a 40 Hz,300 mV peak to peak sinusoidal signal was applied to the tangential dipole.A glass container with an array of sintered Ag/AgCl pellet electrodes was used for recording.The reference electrode was at the edge of the container.The distance from centre to centre between the electrodes in the recording array was 10 mm and from edge to edge was 5 mm.The distance from the dipole to the array was set 5 mm.For this experiment the concentration of NaCl in the water was 0.9 g/100 ml.Polarity was taken into account by measuring the voltage at a particular time after the start of data acquisition.

    One tangential dipole,0.5 cm away from the electrode array,was moved along the array and the results from various dipole positions were compared.The purpose was to see how close two dipoles can be before they cannot be distinguished.

    Figure 4  Dipole,array and reference locations on surface of the saline solution

        Figure 5A  Tangential dipole resolutions testing in simulated CSF.In this situation,when this tangential dipole was moved 8 mm,its potential distributions from this testing array can be totally separated  Figure 5B  Radial dipole resolutions testing in simulated CSF

        Figure 6  Potential distribution comparisons.Solid line is mathematical calculation and dotted line represents experimental data.Distance from dipole to array was set to 5 mm and all other conditions were same  Figure 7  Potential distribution comparisons.For mathematical model,the distance from dipole to array was set 4.2 mm and all other conditions were same

    Everything was same as above except using a radial dipole to replace a tangential dipole.

    In this situation,when this radial dipole was moved 11 mm,its potential distributions from this testing array could be totally separated,observed in Figure 5A and 5B.Comparison of mathematical calculations with physical recordings.In this section,a direct comparison of the results of mathematical calculations with experimental results is done,to check on the validity of the calculations.This result was shown in Figure 6.

    From Figure 7 we can see that experimental data parallel to mathematical model.The experimental data were bigger than calculation because the distance from dipole to array was not exact 5 mm,probably less than 5 mm.If we change this distance from 5 mm to 4.2 mm the potential distributions of experimental data were feeded to mathematical model.This case distance of two dipoles was 1 mm.

    Kinds of direct comparisons of the results of mathematical calculations with experimental results were done using tangential and radial dipoles to insert into the simulated SCF and simulated brain.The experimental results show that the parameters of simulated brain were valid and true.The simulated CSF and brain were very useful to study characteristics of real human brain in laboratory condition.

    FUNDING:This paper was supported by Heilongjiang provincial government education department foundation of overseas scholar（ No.1 151hq026）

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（Editor Jaque）