Synopsis

The BOLD signals related to brain activation is often nonlinear with change in TE. In contrast to extravascular component, the nonlinearity is attributable to intravascular component due to chemical exchange between plasma and deoxy-Hb. Recently, activity-evoked pH change on the brain has been demonstrated. Since the chemical exchange is often pH-dependent, the time for the chemical exchange would change. Thus, the two-compartment model that incorporates the change would be more accurate for estimation of parameters than the model with fixed exchange time. In this study, we measured the nonlinearity by multi-echo GRE-EPI and estimated parameters of the proposed model.

Introduction

Method

(Two-compartment model) The IV component is supposed to originate from venous blood, and the EV component predominantly originates from tissues.

$$S(t)=(V+\Delta{V})\cdot\exp(-R_{2,IV}^{*}\cdot{t})+(1-V-\Delta{V})\cdot\lambda\cdot\exp(-(R_{2,EV,0}^{*}+\Delta{R_{2,EV}^{*}})\cdot{t})$$

, where the parameters were defined in Table 1. $$$R_{2,IV}^{*}$$$ is modulated by the chemical exchange model^1,2,7,8.

$$R_{2,IV}^{*}(t)=R_{2,IV,0}^{*}+R_{2,IV,Hb}^{*}\cdot\left[1-\left(Y+\Delta{Y}\right)\right]^2\cdot\left(1+\frac{\Delta\tau_{ex}}{\tau_{ex}}\right)\cdot\left\{1-\frac{2(\tau_{ex}+\Delta\tau_{ex})}{t}\cdot\tanh\left[\frac{t}{2(\tau_{ex}+\Delta\tau_{ex})}\right]\right\}$$

The signal percent change for activation is calculated at some TE.

$$\%S(t)=\frac{S(t)-S_0(t)}{S_0(t)}\times100(\%)$$

$$${S_0}$$$ was a signal when stimulus-dependent parameters were zero. The two-compartment model was used with time-varying $$$\Delta\tau_{ex}$$$ (TV-model) or $$$\Delta\tau_{ex}=0$$$ (zero-model).

(Parameter estimation) Combinations of parameters in Table 2 were used for the estimation with the following resultant limitations to reject unrealistic results.

$$\begin{cases}{-0.1<\%S_{IV}\space{and}\space\%S_{EV}<\%S}&{when}\space\%S\geq0\\{\%S<\%S_{IV}\space{and}\space\%S_{EV}<0.1}&{when}\space\%S<0\end{cases}$$

A set of parameters was chosen by minimizing the error.

$$Error\space(s^{-1})=\frac{1}{N\cdot100(\%)}\cdot\sum_{t\in{TE}}\mid\%S_{m,t}-\%S_{e,t}\mid/t$$

, where and denote measured and simulated signal changes at echo time t, respectively. N is the number of TEs. Also, the corrected Akaike information criterion (AICc) was evaluated to validate a goodness of fit with the complexity of the model.⁹

(Experiment) In 3T Skyra-fit system (Siemens, Germany) with a standard 20-channel head coil, the six-echo-time EPI was performed with the TEs of 11,26,41,56,71 and 86 ms, TR of 2s, FA of 90°, in-plane resolution of 3.44 mm, slice thickness of 3.4 mm, an acceleration factor of 2 along PE, and fifteen slices parallel to the calcarine sulcus. Visual stimulation of 8-Hz flickering checkerboard was given with 8 blocks of 16/36s on/off. Nine volunteers (three females) participated with the consent. The multi-echo images were reconstructed by home-made MATLAB codes (MathWorks, USA) and motion-corrected by SPM12 (London, England) with the first echo images. Through Brain Voyager (Brain Innovation B.V., the Netherlands), the event-related responses were evaluated with high-pass-filtering and ROI-selecting. The ROI was defined as a cluster of voxels that satisfied the statistical condition of t-value>3.0 (p<0.001) for all TEs.

Result

In Fig. 1, the nonlinearity of TE-dependent BOLD signals for TE intervals of 11 to 41 ms was compared with the results from a linear model.

In Fig. 2a, the minimum fitting error for TV-model was significantly lower than for zero-model or for linear model (0.025±0.003s^-1, 0.035±0.004s^-1 and 0.059±0.010s^-1, respectively). The values of $$$\tau_{ex}$$$ were chosen to 4 ms in TV-model and 2 ms in zero-model. The average blood volumes (V) were 5.7%±0.5% in TV-model and 6.4%±0.8% in zero-model, which were within a typical range of 2%–8%. AICc values were -66.6±8.3 in TV-model, -59.5±9.0 in zero-model and -56.0±19.9 in linear model. There was a significant difference of -6.6±3.8 (p<0.001, paired Student's t-test) between TV- and zero-models. TV-model was considered to improve the goodness of fit (Fig. 2b).

As the echo time increased from 26 to 86 ms, the ratios of IV signal to the actual BOLD signal decreased from 0.44 to 0.24 in TV-model and from 0.61 to 0.44 in zero-model (calculated by Fig. 2c and 2d). The result from TV-model was consistent with the result of the previous study showing that the IV fraction decreased from 0.40 to 0.22 in TE of 32.7 to 70.7 ms.¹⁰

The stimulus-sensitive parameters were estimated (Fig. 3a–d). In Fig. 3b and d, the average values in the post-stimulus undershoot were almost zero for $$$\Delta\tau_{ex}$$$ (0.04±0.19 ms, p=0.54, one-sample t-test) and non-zero for $$$\Delta{Y}$$$ (-1.62%±0.66%, p<0.001, one-sample t-test). These implied that the source of $$$\Delta\tau_{ex}$$$ might be different from that of $$$\Delta{Y}$$$.

Discussion

Conclusion

Acknowledgements

References

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