Parametric transfer function analysis and modeling of blood flow autoregulation in the optic nerve head

Abstract

The aim of the study was to establish a parametric transfer function to describe the relationship between ocular perfusion pressure (OPP) and blood flow (BF) in the optic nerve head (ONH). A third-order parametric theoretical model was proposed to describe the ONH OPP-BF relationship within the lower OPP range of the autoregulation curve (< 80 mmHg) based on experimentally induced BF response to a rapid intraocular pressure (IOP) increase in 6 rhesus monkeys. The theoretical and actual data fitted well and suggest that this parametric third-order transfer function can effectively describe both the linear and nonlinear feature in dynamic and static autoregulation in the ONH within the OPP range studied. It shows that the BF autoregulation fully functions when the OPP was > 40 mmHg and becomes incomplete when the OPP was < 40 mmHg. This model may be used to help investigating the features of autoregulation in the ONH under different experimental conditions.

Keywords: Optic nerve head; autoregulation; intraocular pressure; transfer function.

Figure 1

A schematic view of the relationship between OPP and BF. The middle segment of the curve represents the autoregulation range, within which the autoregulation remains effective. When OPP fluctuations exceed this range, i.e. higher than the upper or lower than the lower limit, BF will passively increase or decrease.

Figure 2

Simplified transfer function representation of the relationship between BF and OPP. Where the OPP is considered as an input, determined by both BP and IOP, and utilizing the black box system, the BF or the output is processed and exported.

Figure 3

A typical recording of OPP (calculated based on the BP and IOP) and BF response. A: IOP was acutely increased from 10 mmHg to 40 mmHg, starting at the 10th second and induced an OPP decrease from 76 to 46 mmHg; B: BF decreases correspondingly during the initial OPP decrease for approximately 10-15 seconds (dAR phase) and then gradually returns towards a stabilized level (sAR).

Figure 4

The simulated BF response (red dotted) fits with the in vivo BF response (solid black). In this typical example, the IOP was increased from 10 mmHg to 40 mmHg. As shown in the 60 seconds recording (solid black curve), BF response induced by this IOP increase underwent dAR and sAR phases. The simulated BF response by the parametric transfer function was fitted well with the experimental derived BF response.

Figure 5

The sAR measured at a range of OPP. Each data point (averaged from three repeated measures) represents the sAR at a given level of OPP. The data is best fit with a polynomial function. Since the highest OPP in these anesthetized animals can only be reached to a certain level below 70 mmHg, the curve represents only a portion of the autoregulation curve within the lower OPP range.

Figure 6

Estimations of K_p, T_p, T_w and ζ from experimental data. Each parameter is a nonlinear function of OPP to gain (A), the time constants T_p (B) and T_w (C), and a damping ratio ζ (D).

Figure 7

Comparison of predicted transient BF responses with the measured BF responses during OPP lowing. The OPP was reduced manometrically by IOP₁₀₃₀ (A), IOP₁₀₄₀ (B) and IOP₁₀₅₀ (C), respectively (top panels). The BF responses at each corresponding OPP decrease are shown in bottom panels. The broken red lines are the BF responses simulated by the parametric transfer function. The solid blue lines are mean BF responses obtained experimentally from the 6 animals (solid lines = mean, dotted lines = SD).