Functional signal- and paradigm-dependent linear relationships between synaptic activity and hemodynamic responses in rat somatosensory cortex

Abstract

Linear relationships between synaptic activity and hemodynamic responses are critically dependent on functional signal etiology and paradigm. To investigate these relationships, we simultaneously measured local field potentials (FPs) and optical intrinsic signals in rat somatosensory cortex while delivering a small number of electrical pulses to the hindpaw with varied stimulus intensity, number, and interstimulus interval. We used 570 and 610 nm optical signals to estimate cerebral blood volume (CBV) and oxygenation, respectively. The spatiotemporal evolution patterns and trial-by-trial correlation analyses revealed that CBV-related optical signals have higher fidelity to summed evoked FPs (SigmaFPs) than oxygenation-derived signals. CBV-related signals even correlated with minute SigmaFP fluctuations within trials of the same stimulus condition. Furthermore, hemodynamic signals (CBV and late oxygenation signals) increased linearly with SigmaFP while varying stimulus number, but they exhibited a threshold and steeper gradient while varying stimulus intensity, suggesting insufficiency of the homogeneity property of linear systems and the importance of spatiotemporal coherence of neuronal population activity in hemodynamic response formation. These stimulus paradigm-dependent linear and nonlinear relationships demonstrate that simple subtraction-based analyses of hemodynamic signals produced by complex stimulus paradigms may not reflect a difference in SigmaFPs between paradigms. Functional signal- and paradigm-dependent linearity have potentially profound implications for the interpretation of perfusion-based functional signals.

Figure 1.

ROI determination and spatiotemporal dynamics of 570 and 610 nm optical intrinsic signals. ROIs were determined from a response to a 0.8 mA, five pulse, 200 msec ISI stimulus (the standard stimulation). A–D, Optical responses are displayed at three time periods using two grayscale coding schemes to differentially enhance capillary bed activity (A, C) or pial vessel activity (B, D). The 0.5-, 1-, 1.5-, and 2-mm-diameter circular ROIs (A, C) were determined to record the maximum response values in Δratio images at two time epochs (570 nm early and peak phases, 0.5–1.5 and 2–3 sec; 610 nm early negative and late positive peakphases, 0.5–1.5 and 3.5–4.5 sec). E,G, 570 and 610 nm raw images, corresponding to the area (EFG) circumscribed by dotted lines at the top of B. F, A composite image made from the middle of B (green channel) and the bottom of D (red channel) emphasizing activated arterioles (green) and veins (red). The 570 nm early-phase (circles) and peak-phase (dashed circles) ROI outlines are superimposed on E, early-phase 570 nm (circles) and 610 nm (dotted circles) ROIs are superimposed on F, and 610 nm early phase (dotted circles) and late positive-peak phase (circles) are superimposed on G. In the 610 nm late early negative phase (D, middle), vascular signals come from both draining veins (filled arrowheads) and dilated arterioles (open arrowheads). Orientation: top, sagittal; right, rostral. Scale bar, 1 mm. Elec, Microelectrode. Note that arterial signals in the later phase remained strongly activated, whereas diffuse signals originating from the capillary bed decreased near the level of the early phase (B, top, bottom; see Discussion).

Figure 2.

Time courses of optical intrinsic signals at 570 and 610 nm averaged across nine rats. Error bars indicate SEMs. A, Dependence of optical signal magnitude on ROI size inresponse to the standard stimulation (0.8 mA, 5 pulses, 200 msec ISI). B–D, Dependence of optical signal magnitude on variable stimulus intensity (protocol 1) measured in the 0.5 mm ROI (B), on variable stimulus number (protocol 2; C), and on variable ISI (protocol 3; D).

Figure 3.

Comparisons between spatiotemporal profiles of 570 and 610 nm signals revealed by contour maps and cross sections (same subject as in Fig. 1). A, B, E–H, Optical signal responses to the standard stimulation. A and B depict 570 nm peak-phase (2.25–2.75 sec) and early-phase (1–1.5 sec) profiles, respectively. Vascular signals started from pial arterioles near the center of the response (B) and then extended to neighboring arterioles (including arterioles traced to different sources) or proximal, upstream territories of the arterioles (A). E and F show the 610 nm responses during peak (1–1.5 sec) and post-peak (1.5–2 sec) epochs of the early negative phase. G and H show the 610 nm response during peak (4.5–5 sec) and pre-peak (2.5–3 sec) epochs of the late positive phase. C, D, 570 nm peak-phase (1.75–2.25 sec) responses to two-pulse stimulation with different color-coded scales. Black dashed circles represent 2 and 0.5 mm ROI outlines. Dotted cross hairs represent center lines of horizontal and vertical cross sections. Although venous signals showed biphasic patterns [violet dashed line (filled arrowhead) inE,G; vertical cross-sections] like the capillary bed, the arteriolar signals displayed a direction opposite to the capillary bed in the late phase [red dashed line (open arrowhead) in G; vertical cross section], indicating that 610 nm vascular signals changed heterogeneously. Scale bar, 1 mm.

Figure 4.

Evoked field potentials and areal extent of 570 and 610 nm signals represented by absolute threshold maps and ANOVA p value maps. The leftmost column (A) shows local FP evoked by variable stimulus intensity, number, and ISI in three different subjects. Each row in absolute threshold maps (B) and ANOVA p value maps (C) depicts optical signals elicited by the neuronal population activity shown in A. Color-coded scales at the bottom were selected to visualize the wide range of absolute Δratio values and log p values. Absolute Δratio value scales of 570 and 610 nm late-phase optical responses are 10 and 5 times as large as those of 610 nm early-phase responses, respectively. Negative log p value scales of 570 and 610 nm late-phase responses are 5 and 2.5 times as large as those of 610 nm early-phase responses, respectively. Calibration: (in A) 200 msec, 1 mV. Scale bar: C, 2 mm.

Figure 5.

Correlation analyses between ΣFP and optical signal magnitude and areal extent based on averaged data from nine subjects. In each panel, the equation and r² value apply to the solid black regression line. A, The relationship between raw ΣFP and peak signal Δratio data depends on ROI size. Error bars indicate SEM. The legend in each panel represents four different ROI sizes. B, The relationship between normalized ΣFP and peak Δratio data is independent of ROI size. In B, left, Int. refers to protocol 1, N refers to protocol 2, and ISI refers to protocol 3. Error bars indicate SD of the means. C, D, Threshold dependence of the relationship between normalized ΣFP and the square root of the peak response area quantified by three representative thresholds of absolute Δratio values (C) and ANOVA p values (D). The key in each panel shows the three representative thresholds. Error bars indicate SEM.

Figure 6.

Correlation analyses between normalized ΣFP and optical signal magnitude based on individual trial data from nine subjects. A–D, Scatter plots of normalized ΣFP versus 570 nm, 610 nm early-negative, and 610 nm late-positive peak signal responses. A, Protocol 1, variable stimulus intensity. B, Protocol 2, variable stimulus number, including the data from 0.8 mA, five pulse, 200 msec ISI stimulation (protocol 1) and 0.8 mA, two pulse, 200 msec ISI stimulation (protocol 3). C, Protocol 3, variable ISI. D, Total trial data correlations (n = 1305).

Figure 7.

Trial-by-trial analyses of 570 and 610 nm early and late signals. A–C, Scatter plots of normalized ΣFP and 570 nm peak (A), 610 nm early-peak (B), and 610 nm late-peak (C) signals for protocol 1 in a representative case. D, Time series of ΣFPs, 570 and 610 nm early-peak, and 610 nm late-peak signals for 15 trials of the standard stimulation (the same subject as in A–C). E, Distribution of determination coefficients (r²) in 27 trial sets of protocol 1 across nine rats shows the difference between the fidelity of 570 and 610 nm signals to intrinsic ΣFP fluctuations within trials of the same stimulus condition. F, G, The relationships between 610 nm early and late peak responses in protocols 1 (F) and 2(G). Although the average data evidenced positive linear correlations (F, G, inset), individual trial data showed no overall correlation and negative correlations within trials of the same stimulus paradigm (F, G).

Figure 8.

Stimulus paradigm dependence of linear relationships between ΣFP and hemodynamic responses. A, Scatter plots of normalized ΣFP versus 570 nm signal responses in the stimulus paradigms of protocols 1 and 2. These relationships are approximated by straight lines and geometric curves and are compared between protocols. The slopes of regression lines were significantly different between protocols 1 and 2 (p < 10^–27; Student's t test). The power for the best-fitting geometric curves in protocols 1 and 2 approximated 2.4 and 1, respectively. B, A simple model of the relationships between ΣFP and hemodynamic responses in the stimulus paradigm with sufficient ISI for recovery of individual FP responses. The relationships are modeled by the following two equations: the linear equation (Y = k₁X, k₁ is a function of stimulus intensity) for the paradigm of variable stimulus number, and the geometric curve equation [Y = k₂X^b, k₂ is a function of stimulus number (N), where b = 2.427 and k₂ = 0.091 × 5^1.427 × N^–1.427 to fit the data sets as shown in A] for the paradigm of variable stimulus intensity. P_N is a point on the geometric curve of stimulus number N that falls on the same value of the ΣFP axis.