J Korean Neurosurg Soc.  2023 Jul;66(4):382-392. 10.3340/jkns.2022.0180.

Numerical Model for Cerebrovascular Hemodynamics with Indocyanine Green Fluorescence Videoangiography

• Cheon H
• Son YJ
• Park SB
• Shim PS
• Son JH
• Yang HJ

• KMID: 2543529
• DOI: http://doi.org/10.3340/jkns.2022.0180

Abstract

Objective
: The use of indocyanine green videoangiography (ICG-VA) to assess blood flow in the brain during cerebrovascular surgery has been increasing. Clinical studies on ICG-VA have predominantly focused on qualitative analysis. However, quantitative analysis numerical modelling for time profiling enables a more accurate evaluation of blood flow kinetics. In this study, we established a multiple exponential modified Gaussian (multi-EMG) model for quantitative ICG-VA to understand accurately the status of cerebral hemodynamics.
Methods
: We obtained clinical data of cerebral blood flow acquired the quantitative analysis ICG-VA during cerebrovascular surgery. Varied asymmetric peak functions were compared to find the most matching function form with clinical data by using a nonlinear regression algorithm. To verify the result of the nonlinear regression, the mode function was applied to various types of data.
Results
: The proposed multi-EMG model is well fitted to the clinical data. Because the primary parameters—growth and decay rates, and peak centres and heights—of the model are characteristics of model function, they provide accurate reference values for assessing cerebral hemodynamics in various conditions. In addition, the primary parameters can be estimated on the curves with partially missed data. The accuracy of the model estimation was verified by a repeated curve fitting method using manipulation of missing data.
Conclusion
: The multi-EMG model can possibly serve as a universal model for cerebral hemodynamics in a comparison with other asymmetric peak functions. According to the results, the model can be helpful for clinical research assessment of cerebrovascular hemodynamics in a clinical setting.

Keyword

Cerebrovascular circulation; Vascular surgical procedures; Indocyanine green; Fluorescence angiography; Hemodynamic monitoring; Computer-assisted numerical analysis

Figure

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  Fig. 1. Shapes of the intravenous bolus signal. Intravenous bolus injection may cause a pulse shape in the signal (A). However, the real measured cerebral hemodynamic curve may be changed to the asymmetry Gaussian function (B) because a rapid injection would increase the indocyanine green (ICG) concentration in a short period. Nevertheless, the ICG diffusion at the plasma level would be relatively slow. In other words, duration of the elimination phase is longer than that of the absorption phase in the peak function form.

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  Fig. 2. Fitting results on the peak and whole areas of the indocyanine green videoangiography (ICG-VA) data curve. A : Standard shape of the quantitative ICG-VA clinical data. The number of peaks changed; however, the curve was mainly composed of peaks and a long tail. B : Comparison of the fitting curves with peak functions at the peak area. Exponential modified Gaussian (EMG; black line) fitted better than other peak functions (extra lines) on the shape of the peak. C : To include the tail part, the linear bi-summation of the peak functions was needed. Bi-EMG presented the best fitting curve on the whole data area.

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  Fig. 3. Fitting curves (grey line) for the measurement data (open circle) of various forms using the multi- exponential modified Gaussian (EMG) model. A-H : Various shapes of the cerebral hemodynamic curves for vascular blood flow are observed. The curves are fitted by the multi-EMG function. The number of EMG functions required for effective fitting is one more than the number of peaks. The measured data are applied with a low-degree Savitzky-golay filter to remove the fluctuation of data and ease the derivation. Each center of peaks defined by the point of the first derivative values is equal to zero at the local peaks. The center of peaks of the fitting curves (grey numbers) are substantially accorded with the ones (black numbers) of their measured data.

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  Fig. 4. Prediction of center of peaks on data (open circles) with missing parts. A-D : Some data points can be missed from saturation owing to the measuring equipment limitation. The fitting model (grey line; multi-EMG model) provides the estimated values of the parameter, center of peaks (grey numbers), and data. EMG : exponential modified Gaussian.

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  Fig. 5. Dominance of a single EMG function on each peak area. A : Fitting curve (grey line) of the multi-EMG for the clinical data and each component EMG (black line and grey dashed line). B : The same curve in the logarithmic scale. The black dashed lines show the exponential line in the logarithmic scale. The growth and decay parts of the peak predominantly match the first EMG. Therefore, the single EMG, which is the first EMG in this case, is dominant at the peak area. The peak properties can be obtained by analysing the first EMG. EMG : exponential modified Gaussian.

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  Fig. 6. Evaluation of multi-EMG model reconstruction. A and B : To check the model validity, the top of the main peak in the measured data was removed from 0% to 40% based on the peak height. C and D : Reconstructed data curve by the multi-EMG model. E : Comparison with the relative error of the estimated four primary parameters : center of peaks, peak height, steepness of growth (w), and decay constant (1t0). The smaller is the area of missing data, the more accurate is the prediction of the reconstructed parameters in all parameters. COP : center of peak, EMG : exponential modified Gaussian.

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