Practical steps for applying a new dynamic model to near-infrared spectroscopy measurements of hemodynamic oscillations and transient changes: implications for cerebrovascular and functional brain studies

Abstract

Rationale and objectives: Perturbations in cerebral blood volume (CBV), blood flow (CBF), and metabolic rate of oxygen (CMRO2) lead to associated changes in tissue concentrations of oxy- and deoxy-hemoglobin (ΔO and ΔD), which can be measured by near-infrared spectroscopy (NIRS). A novel hemodynamic model has been introduced to relate physiological perturbations and measured quantities. We seek to use this model to determine functional traces of cbv(t) and cbf(t) - cmro2(t) from time-varying NIRS data, and cerebrovascular physiological parameters from oscillatory NIRS data (lowercase letters denote the relative changes in CBV, CBF, and CMRO2 with respect to baseline). Such a practical implementation of a quantitative hemodynamic model is an important step toward the clinical translation of NIRS.

Materials and methods: In the time domain, we have simulated O(t) and D(t) traces induced by cerebral activation. In the frequency domain, we have performed a new analysis of frequency-resolved measurements of cerebral hemodynamic oscillations during a paced breathing paradigm.

Results: We have demonstrated that cbv(t) and cbf(t) - cmro2(t) can be reliably obtained from O(t) and D(t) using the model, and that the functional NIRS signals are delayed with respect to cbf(t) - cmro2(t) as a result of the blood transit time in the microvasculature. In the frequency domain, we have identified physiological parameters (e.g., blood transit time, cutoff frequency of autoregulation) that can be measured by frequency-resolved measurements of hemodynamic oscillations.

Conclusions: The ability to perform noninvasive measurements of cerebrovascular parameters has far-reaching clinical implications. Functional brain studies rely on measurements of CBV, CBF, and CMRO2, whereas the diagnosis and assessment of neurovascular disorders, traumatic brain injury, and stroke would benefit from measurements of local cerebral hemodynamics and autoregulation.

Keywords: Hemodynamic model; cerebral autoregulation; cerebral blood flow; metabolic rate of oxygen; near-infrared spectroscopy.

Figure 1

Workflow of determining (cbv(t)) and cbf(t)−cmro₂ (t) with the new hemodynamic model. (a) Normalized total oxy- and deoxy-hemoglobin (ΔO(t) and ΔD(t)) are the input quantities, measured with functional near-infrared spectroscopy, for the model. By assuming specific values for the physiological model parameters, the optical measurements can be converted into cbv (t) and cbf (t) − cmro 2(t) traces (b). The traces in (b) were obtained by using Eqs. (9) and (10). cbf, relative changes in cerebral blood flow with respect to baseline; CBV, cerebral blood volume; cbv, relative changes in CBV with respect to baseline; crmo₂, relative changes in metabolic rate of oxygen with respect to baseline; FFT, fast Fourier transform; S^(a), arterial saturation; t^(c), capillary blood transit time; Ƒ^(c), Fåhraeus factor in capillaries; blood transit time in capillaries; t, time; t^(v), venous blood transit time.

Figure 2

Sensitivity of cbf(t)−cmro₂(t) on the model parameters and comparison to the steady-state predictions, with cmro₂ indicating metabolic rate of oxygen. (a) The dependence on the capillary blood transit time (t^(c)), (b) the venous blood transit time (t^(v)), (c) the relative capillary blood volume, and (d) on the arterial to venous blood volume ratio. Dynamic model results (solid light gray lines); steady-state results (dashed dark black lines). Insets show the peak time of cbf(t)−cmro₂(t) (on the x axis) calculated with the dynamic model with respect to the peak time of O(t) (broken line at 0) as a function of the parameters considered in each panel. See Figure 1 for additional definitions.

Figure 3

Experimental results of frequency-resolved measurements of cerebral hemodynamic oscillations during a paced breathing protocol in human subjects. (a) Phase difference between phasors O and T, arg(O) − arg(T); (b) amplitude ratio |O|/|T|; (c) phase difference between D and O, arg(D) − arg(O); and (d) amplitude ratio |D|/|O|. The symbols and error bars were obtained by averaging the data over the 11 subjects and taking the standard errors. A set of spectra corresponding to a range of χ² values corresponding to model results that fall within the data error bars is shown (shaded areas).