Magnetic induction phase shift captures changes of CBV
For MIPS detection, the tissue to be tested is placed between the excitation coil and the detection coil, as show in Fig. 1(a) An alternating current in the excitation coil generates a sinusoidal alternating primary magnetic field (B). This primary magnetic field generates an induction current in the measured tissue and then generates an induced magnetic field (ΔB). Both the primary magnetic field and the induced magnetic field received by the detected coil are converted into induced voltage. The vector relation at point P between the induced magnetic field and the primary magnetic field is shown in Fig. 1(b). According to Griffiths et al.29,30, if a sinusoidal signal with an angular frequency of ω is used for excitation, the magnetic vector potential:
(1)
Here, σ represents the conductivity of the measured tissue, µ0 and ε0 represent the vacuum permeability and the vacuum permittivity respectively, εr represents the relative permittivity of the measured tissue, and Q represents geometric constants, which relating to the location, structure and size of the measured tissue.
For biological tissues, the ΔB produced by the measured tissue is much smaller than B, so Δ can be approximated as imaginary part of ΔB/B; that is, the induced magnetic field received by the detection coil lags behind the primary magnetic field by a phase shift Δ.When the frequency of excitation voltage is set, the MIPS is influenced by the conductivity σ of the measured tissue:
Since the conductivity of brain tissue, blood and cerebrospinal fluid are different, the bulk conductivity σ of the brain altered by the changes of the relative volume of those types tissues reflects the MIPS value.
Preprocessing of original signals (ABP, ICP, MIPS) for CRx and PRx
ABP, ICP and MIPS were simultaneously monitored for CVAR function evaluation from the experiment rabbits. Figure 2 shows the time waves of the original signals on different scales. Compared with the ICP and MIPS of the control rabbits, the ICP (Fig. 2(e)) and MIPS (Fig. 2(f)) of the ischemic rabbits (5-minute scale) slowly oscillated with inverting regularity, which were different from the frequencies of respiration and heartbeat. Respiration components were found in ABP, ICP and MIPS, and heart beat components were found in ABP and ICP (1-second scale). It can be seen that respiration has an influence on all signals, especially on MIPS which is completely submerged by respiration (5-second scale). As we cannot directly analyze the relationship between the SSO of the three signals, raw signals require to be preprocessed to remove high frequency interference, such as respiration and heart beat components, and extract SSO of ABP, ICP and MIPS. In order to analyze the relationship between SSO of MIPS or ICP and SSO of ABP for detecting CVAR, SSO signal was extracted from the collected signal. The ABP and ICP signals with a sampling rate of 20Hz and the MIPS signals with a sampling rate of 6Hz were down sampled to 1 Hz. Significant baseline drift can be seen from thec down sampled signal spectrum in Fig. 3(e). After, the baseline drift removed by wavelet decomposition and reconstruction, SSO components were extracted by a low pass filter set cutoff frequency at 0.1Hz and passed through a high pass filter set cutoff frequency at 0.001Hz. The processing results are shown in Fig. 3(a)-(d). According spectrum of extracted SSO components (Fig. 3(f)), frequency band of the SSO signal were divided into ultra-low frequency (0.001-0.005Hz), low-frequency (0.005-0.05Hz), and mid-frequency (0.05-0.1Hz). The SSO waveform in ultra-low frequency and low-frequency band of ABP, ICP and MIPS were compared in Fig. 3(g)
The result of SSO in ABP, ICP and MIPS in IS rabbit
When cerebral ischemia is caused by reduced intracranial blood supply in rabbits, CVAR function changes the slow wave oscillations of ICP and MIPS in order to maintain constant blood flow. SSO was extracted from ABP, ICP and MIPS signals simultaneously collected from ischemic rabbits. The period of ultra-low frequency SSO increases in ischemia rabbits (control group: 508.29s; ischemia group: 569.37s), as shown in Fig. 4(a). Ischemia rabbits had more frequency components in low frequency SSO than control rabbits, as shown in Fig. 4(b). The phase difference between ultra-low frequency SSO in ABP, ICP and MIPS signals changed after ischemia, as shown in Fig. 4(c). This phase difference is related to CVAR function and can be evaluated by calculating the correlation between excitation SSO in ABP and response SSO in ICP/MIPS.
The result of CVAR indexes calculated with SSO in ABP, ICP and MIPS
In order to estimate the CVAR function, we calculated the autoregulation index - ICP pressure reactivity index, PRx. Both ABP and ICP signals are averaged over a 3 second period to get the mean ABP(MAP) and the mean ICP (MICP) value to eliminate the influence of artifacts and ventilation. Then, the Pearson correlation31 between MAP and MICP is calculated using a 2-minute time window as formula (1). This calculation process is repeated with a moving window every 3 seconds.
PRx = r[MAP(t);MICP(t)] (1)
Conductivity reactivity index-CRx is calculated between MAP and the mean MIPS in the same way:
CRx = r[MAP(t);MMIPC(t)] (2)
Finally, the time trend of the PRx and CRx index is shown in Fig. 5(a)-(d). The PRx index of the control group oscillated below zero, indicating normal CVAR function, and PRx index of rabbits in ischemic group oscillated above zero for more time, indicating impaired CVAR function (Fig. 5(a)). Basically, the CRx value oscillates inversely with respect to the PRx index(Figure(c)(d)). The spectrum analysis diagrams for CRx and PRx in the two groups of rabbits are shown in Fig. 5(e)(f). The low frequency component of two indexes in ischemic rabbits was more than that in control rabbits.
The comparison of PRx and CRx between the cerebral ischemic group and control group
Statistical analysis of PRx and CRx was performed to compare CVAR in the cerebral ischemia group and the control group. There were significant differences in the CRx values (t = 2.385, SE = 0.064, p = 0.030 < 0.05, 95% CI [0.181 to 0.285]) and PRx values (t=-6.118, SE = 0.048, p = 0.000 < 0.05, 95% CI [-0.394 to -0.191]) between the two groups. The mean values of CRx and PRx from two groups were calculated and shown in Fig. 6. The average PRx was − 0.126(SD = 0.124)in the control group which means the ICP is not directly driven by ABP and hence the CVAR is intact, and the average PRx was 0.167(SD = 0.086) in the cerebral ischemia group which indicates impaired CVAR due to a passive relationship between ABP and ICP. On the other hand, the mean CRx decreased from − 0.002(SD = 0.164) to -0.153(SD = 0.117).
The relationship between PRx and CRx for the CVAR evaluation
The correlation analysis shows the CRx index and PRx index were significantly negatively correlated, with a correlation coefficient r=-0.633(95% CI [-0.840 to -0.265], p = 0.003 < 0.05). The linear regression analysis with the mean values CRx and PRx of the 20 sample cases was shown in Fig. 7(a). The relationship between two exponential measurements is obtained by linear regression: CRx=-0.551PRx − 0.066 (R2 = 0.401). Figure 7(b) shows the Bland-Altman diagram for the two indexes, which shows the mean value of the difference between PRx and CRx was 0.098, (p = 0.172 > 0.05, 95% CI [-0.046 to 0.243]). The difference in the measured values with the two indexes was not statistically significant, which indicated a good consistency of the two indexes, and the consistency of the two indexes was 0.620.
Finally, we studied the sensitivity and specificity of the two indexes to identify the cerebral ischemic rabbits from the control group. The area under the ROC curve of the mean value of PRx was 0.990(p < 0.001). The sensitivity and specificity for cerebral ischemia identification were 90% and 10% respectively in PRx. The area under the ROC curve of the mean value of CRx was 0.780(p = 0.034). The sensitivity and specificity for cerebral ischemia identification were 80% and 30% respectively in CRx, as shown in Fig. 7(c).