the investigations leading to the present invention will now be described in more detail . tetrapolar impedance measurements were made as shown in fig1 by applying a sinusoidally varying current of constant 1 ma peak to peak amplitude between the left upper arm 1 and left calf 2 of a human subject and measuring the potential resulting between the right upper arm 3 and right calf 4 . the measurements obtained should principally relate to the impedance of the trunk 5 . the electrodes used were ag / agcl types ( conmed 140 - 2545 trademark !) and the electrode impedances measured were typically & lt ; 500 ohms at 9 . 6 khz . the current waveform was successively doubled in frequency from 9 . 6 khz to 614 . 4 khz and each step lasted for 3 . 33 ms . this allowed a complete set of measurements at 7 frequencies with a 3 . 33 ms gap between sets to be made in 26 . 7 ms , thereby giving 37 . 5 data sets per second . the potentials recorded were first amplified and then de - modulated using a high frequency multiplier to extract the in - phase component of the signal , in other words , the real part of the complex impedance . ac coupling used within the amplifier allowed the signal to settle to better than 0 . 1 % within the 3 . 3 ms periods . the resulting signal was then low pass filtered ( 4 pole with 3 db at 25 hz ) before being digitized at 50 or 200 samples per second to 12 bit resolution and passed to a computer . the a - d interface was a das - 8pga8 ( keithley ) and the computer a research machines 386 / 20 . data was collected using commercial software ( asyst , easyestlx , keithley ). the system was calibrated using resistances up to 20 ohms and parallel resistor - capacitor combinations ( 300 ohms and 10 nf ) to represent the electrodes . the measurement accuracy was within 3 % over the 7 frequencies . twelve normal subjects with no known respiratory or cardiac abnormalities were used for the measurements ( average age 37 years ; range 23 years to 51 years ; 9 male and 3 females ). although not shown in fig1 the subjects were seated on an insulating surface during the measurements and placed their hands on a wooden bench . care was taken to see that the knees did not touch during the measurements as this would present an uncontrolled path for current flow . two recordings , or measurement sets , were made from each subject , the first recording was 10 seconds duration and the second recording was 40 seconds . during the first recording the subject was asked to inspire total lung capacity and to hold his or her breath for the 10 second recording . during the second recording , each subject again held his or her breath for 10 seconds but was then told to expire and breath normally for an additional 30 seconds . each recording was collected as 2048 data points . the first recording was used to measure the real part of the absolute impedance at the seven frequencies and also the amplitude of the cardiac related changes . the second was used to record the amplitude of the impedance change on expiration following the breath hold . because of the high frame rate of 37 . 5 s - 1 the measurements at the 7 frequencies were in effect made simultaneously . the measurements of the amplitudes of the cardiac and respiratory related components were made by printing the waveforms and then manually measuring the peak to peak amplitude of the signals . in every case , the waveforms were digitally low pass filtered at 10 hz in order to reduce noise . it was found that no attenuation of the cardiac related changes occurred as a result of the filtering . a trace of the impedance measured at 9 . 6 khz from one of the 40 second recordings is shown in fig2 a . the cardiac related changes are clearly visible during the first 12 seconds when the breath is held . on expiration the impedance falls and the changes during tidal breathing can be seen . the cardiac changes show a rapid decrease in impedance during systole and then a slower increase during diastole . the ecg was recorded in one subject and confirmed that the rapid decrease in impedance did correspond to the start of cardiac systole . fig2 b shows the measurements made at 307 khz in the same recording as that shown in fig2 a . it can be clearly seen that the relative amplitude of the cardiac and respiratory related changes are different at the respective frequencies , the cardiac related changes being smaller in the recording made at 307 khz . the group mean values of impedances measured at the 7 frequencies and the amplitudes of the respiratory and cardiac related changes are given in tables 1 and 2 presented below . the mean impedance and the cardiac related changes were measured during the 10 second breath hold at total lung capacity . the respiratory component was measured from the second recording as the change from total lung capacity to normal tidal breathing . in all cases , it is the real part of the impedance which is shown so that impedances are given as ohms in the case of the respiratory changes and milli - ohms in the case of the cardiac related changes . the recording illustrated in fig2 a and 2b show mean impedances at total lung capacity of about 21 . 2 ohms at 9 . 6 khz and 14 . 2 ohms at 307 khz . these figures compare with the group means of 24 . 56 ohms at 9 . 6 khz and 17 . 81 ohms at 307 khz . standard deviations are given for all the measurements . these standard deviations are quite large because they depend upon the shape and size of the subject as well as on the internal resistivities . in table 2 normalized results are presented such that 100 % represents the measurement at 9 . 6 khz . the standard deviations given here are significantly less than in table 1 because they show only the change in impedance with frequency in each individual . ______________________________________ impedance respiratory cardiac componentfrequency ( ω ) component ( ω ) ( ω × 10 . sup .- 3 )( khz ) z δz . sub . r δz . sub . c______________________________________9 . 6 24 . 56 ± 4 . 09 1 . 68 ± 0 . 43 98 . 4 ± 33 . 019 . 2 23 . 93 ± 4 . 10 1 . 66 ± 0 . 43 89 . 1 ± 32 . 538 . 4 22 . 64 ± 4 . 08 1 . 62 ± 0 . 42 79 . 4 ± 32 . 776 . 8 21 . 04 ± 3 . 96 1 . 55 ± 0 . 41 63 . 5 ± 26 . 2153 . 6 19 . 35 ± 3 . 78 1 . 47 ± 0 . 39 54 . 1 ± 22 . 5307 . 2 17 . 81 ± 3 . 50 1 . 37 ± 0 . 36 40 . 4 ± 17 . 9614 . 4 15 . 70 ± 2 . 80 1 . 10 ± 0 . 30 28 . 2 ± 12 . 4______________________________________ table 1 , presented immediately above , shows mean data for the 12 subjects . the respiratory component ( δz r ) is the respiratory related impedance change , i . e . the impedance change between total lung capacity ( breath held ) and normal tidal breathing . the cardiac component ( δz c ) is the cardiac related impedance change measured from the peak to peak amplitude of the fluctuating impedance signal at total lung capacity . ______________________________________ impedance respiratory cardiac componentfrequency ( ω ) component ( ω ) ( ω × 10 . sup .- 3 )( khz ) z δz . sub . r δz . sub . c______________________________________9 . 6 100 100 10019 . 2 97 . 4 ± 1 . 1 98 . 9 ± 1 . 2 89 . 9 ± 6 . 238 . 4 92 . 0 ± 1 . 4 96 . 5 ± 2 . 3 78 . 7 ± 8 . 976 . 8 85 . 4 ± 2 . 0 92 . 1 ± 3 . 4 63 . 1 ± 9 . 1153 . 6 78 . 4 ± 2 . 5 87 . 5 ± 3 . 8 53 . 7 ± 8 . 6307 . 2 72 . 2 ± 2 . 4 80 . 1 ± 5 . 2 40 . 7 ± 10 . 5614 . 4 64 . 0 ± 2 . 1 65 . 4 ± 3 . 4 28 . 2 ± 6 . 5______________________________________ table 2 , presented immediately above , shows mean data for the 12 subjects . the values have been normalized to the measurements made at 9 . 6 khz before taking the mean for the group . in all twelve cases , the amplitude of the cardiac related impedance changes ( δz c ) decreased more rapidly with increasing frequency than did the respiratory related impedance change ( δz r ). the cardiac change fell from 100 % to 28 . 2 % ( range 18 . 6 - 39 . 4 %). the respiratory change fell from 100 % to 65 . 4 % ( range 59 . 8 - 71 . 1 %). a decrease of impedance with frequency has typically been found in biological tissue , but the difference in the case of the cardiac and respiratory components was unexpected . subsequent studies by the inventors have confirmed these findings , and tests carried out with the subject following different breathing patterns and using various different configurations of electrodes have also produced results consistent with those described above . because the relaxation frequency for blood has been quoted as typically 1 - 3 mhz it was expected that the cardiac related changes would not fall significantly in amplitude at frequencies up to 600 khz . some modelling was carried out in order to investigate this observation of a relatively rapid fall in the amplitude of the cardiac related changes . many studies have used a simple r c combination as shown in fig3 to model tissue impedance . in this case r can be loosely related to extracellular conduction and s to intracellular conduction across the membrane capacitances represented by c . however , a close fit cannot be obtained to in vivo data because there is a dispersion of time constants in tissue ; in other words , there is a range of time constants present in tissue . some studies have used susceptance vs . conductance plots ( h . kanai , m . haeno and k . sakamoto , electrical measurement of fluid distribution in legs and arms , medical progress through technology , 12 , 159 - 170 , 1987 ) based upon the work of cole and cole ( k . s . cole and r . h . cole , dispersion and absorption in dielectrics , journal of chemical physics , 9 , 341 - 351 , 1941 ) to obtain the loci of tissue equivalent circuits . these require measurements to be made over many frequencies and require both real and imaginary components to be available . in the study described above , measurements at only seven frequencies were made and only the real part was recorded . it is possible to record the out - of - phase component , but it is thought that cable capacitances and body capacitance to ground make in vivo recording of the out - of - phase component unreliable . because of this and the fact that measurements were only made at seven frequencies , the results have been modelled as follows . a general impedance which establishes a circle in the complex impedance plane can be written : where r . sub .∞ is the very high frequency impedance , r o the low frequency impedance , f the frequency , f r the relaxation frequency for the tissue and α is the constant which characterizes the cole - cole distribution function . extracting the real part of equation ( 1 ) gives : ## equ1 ## to be consistent with the notation of fig3 r ═ r o and r . sub .∞ ═ rs /( r ═ s ). this has been used to perform a least square fit to the data of table 1 . parameters r , s , f r and α were thus obtained for the total impedance , the respiratory component and the cardiac component . the results of this modelling are illustrated in fig4 which shows both the measured values of the different impedance components and the equivalent values from the model . the curves are measured absolute impedance 20 , measured cardiac component 21 , measured respiratory component 22 , modelled absolute impedance 23 , modelled cardiac component 24 and modelled respiratory component 25 , all shown as percentages of that measurement at 9 . 6 khz . the modelling shows that the measured data can be modelled very well to equation ( 2 ). the following parameters were obtained . ______________________________________total impedance : r = 26 . 13ω s = 23 . 38ω f . sub . r = 158 khz α = 0 . 39respiratory related component : r = 1 . 68ω s = 1 . 44ω f . sub . r = 421 . 5 khz α = 0 . 21cardiac related component : r = 118 . 7ω s = 7 . 26ω f . sub . r = 86 . 8 khz α = 0 . 43______________________________________ it can be argued that it is more logical to see the cardiac and respiratory related components as a perturbation of the base impedance . if the modelling is done in this way , then we can find the equivalent changes in r and s which explain the observations . the results of this are as follows . ______________________________________respiratory related component : change in r is 1 . 45ω change in s is 3 . 83ωcardiac related component : change in r is 0 . 104ω change in s is 0 . 136ω______________________________________ as can be seen from the results above the measurements of trunk impedance fall with a frequency which can be modelled very well using a cole - cole equation . the fall in impedance in an individual is very consistent . however , the differences in absolute impedances between individuals are quite large and probably largely reflect differences in body shape and size . if a simplified model were assumed for the trunk then it would be possible to express the impedance in terms of tissue volume . however , such a simplified model would require so many assumptions that its utility would be questionable . the results show a significant difference in the way in which the cardiac and respiratory related impedance changes vary with frequency . if a multi - frequency electrical impedance tomographic ( eit ) system is used to calculate the impedance spectrum for each pixel , then it is possible to identify cardiac and respiratory signals on the basis of their different frequency behavior . single frequency eit imaging has demonstrated images of impedance changes from both the heart and lungs . however , the spatial resolution is poor and in many cases it is not possible to differentiate tissues . the in vivo images published have used a 2 - d solution to fit a 3 - d problem and the spatial resolution is at best 10 % of the imaged diameter . however , based on the present invention , by making multi - frequency measurements , it is possible to identify tissues on the basis of the impedance spectrum and the spectrum of the changes in impedance . it was expected that the tissue impedance would fall with frequency and that the changes during lung ventilation would fall in a similar manner . however , if the cardiac related changes arise from changes in blood distribution , then perhaps only small changes with frequency would be expected . blood has no alpha dispersion but a beta dispersion is observed . a relaxation frequency ( i . e ., the 3 db frequency corresponding to the mean tissue time constant ), for blood of 3 mhz has been suggested ( kanai ), and other studies have found values about 1 - 2 mhz . if these values are correct , then over the frequency range of the measurements of the tests described above ( 9 . 6 to 614 khz ), relatively small changes should be seen . the modelling of the cardiac related changes showed a relaxation frequency of 86 . 8 khz , which is not consistent with kanai &# 39 ; s figures for blood . one possible explanation of the observations of the tests described above is that the origin of the cardiac related impedance changes could be the pulsatile blood volume changes in the upper part of the pulmonary tree . these could be shunted by the non - pulsatile lung tissue that has a decreasing impedance at high frequencies , and thus , decreases the relative magnitude of the cardiac related impedance changes . it has been shown that cardiac related impedance changes can be recorded from the area of the lungs , and that these might arise from changes in blood volume in the lungs . most of these changes are likely to occur in the larger vessels where the pressure waveform is pulsatile , and hence , changes in vessel cross - section occur . two reasons can be found to identify the lungs as the major possible origin of the cardiac related changes . first , the impedance falls during systole whereas one would expect the impedance of the heart to rise , and second , for a large undispersed volume of blood , such as is found in the heart and major vessels , one might expect to see the high relaxation frequency found from measurements on whole blood . it is , however , not possible to make a straightforward comparison between the frequency dispersion of blood and that of the whole trunk . further investigations have been carried out into the frequency response of the impedance changes associated with different regions of a tomographic image of a cross section of a human trunk . fig5 graphically shows the results of these investigations , the horizontal axis representing frequency and the vertical axis representing the ratio , expressed as a percentage , of the change in resistivity between inspiration and expiration referenced to resistivity on expiration , ( z insp - z exp )/ z exp . the subject was told to breath in fully and hold his breath , and then to expire fully and again hold his breath . the four curves 30 , 31 , 32 and 33 show the frequency response of different areas of clinical interest , and respectively represent the right lung response , the left lung response , the spinal column response , and the response of the central region of the image , which is thought to represent the cardiovascular system . the curves of fig5 clearly show how , by examining the frequency response of the dynamic impedance changes , selective determination of different parts of the tomographic image is possible . the gradients of the curves , especially in the 0 - 100 khz frequency range , show a clear distinction for different anatomical regions of interest . as expected , the response associated with the spinal column is virtually a flat line , as the spinal column exhibits minimal change in state over the respiratory cycle . any change in this value is probably due to some contamination by lung data in the selected region . fig6 shows a set of eit images illustrating the use of the above - mentioned effect . the eight images were produced using a standard eit technique , the impedance measurements being made effectively simultaneously at eight different electrical signal frequencies , from 9 . 6 khz to 1228 . 8 khz , successive images representing a doubling of the frequency . the pixel values in the images represent the values of ( z insp - z exp )/ zexp over the respiratory cycle , i . e ., the resistivity change referenced to resistivity at expiration . the images are normalized to the maximum change in the image set . the progressive changes in the images as the frequency is increased illustrate the use of the technique of the invention , such changes being in no way predicted prior to the invention . the values used to produce the curves at fig5 are taken from these images by selectively localizing regions of interest on an image and determining resistivity values for those regions . more particularly , for each lung region , the image data were examined to find the peak change in resistivity associated with that lung over the respiratory cycle at 9 . 6 khz . a region was then determined including pixels displaying a change in resistivity over the cycle of 50 % and above of this peak change . this region was assumed to represent the area of that lung . the values used for the curves of fig5 represent mean values over the relevant region . a similar approach was used to fix a central region of the image , and therefore , to produce curve 33 in fig5 . for the spinal region , this was fixed by eye from dual frequency static imaging , and again the values used to construct curve 32 in fig5 represent mean values over that region . the invention has been described and illustrated with reference to a cardiac and respiratory related impedance response . however , it is to be understood that it may also be applied to investigate different parts of the human or animal body where a change in internal state occurs . for example , the technique may find application in investigating the movement of food or fluid through a subject &# 39 ; s oesophagus or the movements of a subject &# 39 ; s gastric contents . the movement of the contents or peristaltic effects will provide the change in internal state . the technique might also find application outside medical or veterinary areas .
a method of investigation of a body including applying interrogatory electrical signals at different frequencies to the body . first signals are obtained representing first electrical impedance measurements at the different frequencies . second signals are obtained representing subsequent second electrical impedance measurements at the different frequencies after a change in the internal state of the body . characteristics of part of the body are selectively determined in response to the first and second signals at the different frequencies . the invention has application in electrical impedance tomography techniques where the different frequency behavior of different parts of the body associated with temporal changes can be used to improve organ resolution and tissue differentiation .