2.1.

Animals

All animal experimental procedures were reviewed and approved by the Massachusetts General Hospital Subcommittee on Research Animal Care. We used CD1-Elite mice (Charles River Laboratories, $n=10$, male, 3 to 4 months old, $\sim 35\mathrm{g}$) in this study. All surgical procedures, including the sealed cranial window preparation and the cannulation of femoral artery, were conducted under 1.5% to 2% isoflurane anesthesia in $\text{air}/{\mathrm{O}}_2$ mixture. In experiments, mice ($n=10$) were separated into two groups: group 1 ($n_1=6$) and group 2 ($n_2=4$). Acquisition was conducted under $\alpha$-chloralose administered intravenously.¹⁰ Body temperature was maintained at $\sim 37°\mathrm{C}$ throughout all experiments. In experiments, the mean systemic arterial blood pressure and arterial partial pressure of ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ averaged over $n=10$ mice were $\sim 93$, 96, and 35 mmHg, respectively; the pH of systemic arterial blood was $\sim 7.36$.

2.2.

Spectral-Domain Optical Coherence Tomography

Capillary RBC-passage B-scans were conducted using an optimized commercial spectral-domain OCT (SD-OCT) system (Thorlabs Inc.).⁷ The light source has a central wavelength of 1310 nm with a 170-nm bandwidth yielding an axial resolution of $3.5\mu \mathrm{m}$ in brain tissue. The transverse resolution was $3.5\mu \mathrm{m}$ when using the $10\times$ objective ($\mathrm{NA}=0.26$). This SD-OCT system has a maximum acquisition rate of $\mathrm{47,000}\mathrm{A}\text{-}\text{lines}/\mathrm{s}$.

2.3.

Determination of the Red Blood Cell Flux

The details of the RBC-passage technique have been described elsewhere.⁷ Figures 1(a) and 1(b) help explain the acquisition protocol of the RBC-passage B-scan. Figure 1(a) displays a picture of a typical cranial window over mouse cortex. As shown by the red lines in Fig. 1(a), three lines were typically selected in the cranial window in each mouse for conducting the OCT RBC-passage B-scans. Each RBC-passage B-scan consisted of 30 or 60 A-lines and spanned a distance of 50 or $100\mu \mathrm{m}$ in the $X\text{-}Z$ cross-sectional plane, which yields $\mathrm{\Delta }t=\sim 0.75$ or $\sim 1.5\mathrm{ms}$, respectively. Each line was consecutively scanned for 2 min. Because the OCT speckle fluctuation in rodent cortex is mainly due to the motion of RBCs,¹⁵ capillaries [bright pixels in Fig. 1(b)] could be identified and manually selected based on the B-scan variance images. For each selected capillary, the pixel intensities at the same coordinate of the consecutive B-scans were extracted to reveal the RBC-passage time course. Here, we used a custom-developed MATLAB graphic user interface to make sure the selected points were in capillaries by selecting points that had the largest intensity fluctuations. Next, the RBC-passage time courses were denoised by a temporal 1-D Gaussian filter with standard deviation $\sigma =1.5\mathrm{ms}$ to reduce false-positive noise peaks when counting the RBC passages. The $\sigma$ relates to the FWHM as $\mathrm{FWHM}=2\sqrt{2\ln 2}\sigma$, so, $\sigma =1.5\mathrm{ms}$ would yield a FWHM of $\sim 3.5\mathrm{ms}$. The RBC-flux of $200\mathrm{RBCs}/\mathrm{s}$ corresponds to an RBC passing every 5 ms in average. Thus, using a Gaussian filter with $\mathrm{FWHM}=3.5\mathrm{ms}$, we expect to diminish the noise but not mask the RBC passages when RBCs pass every 5 ms. Such a high flux of $200\mathrm{RBCs}/\mathrm{s}$ was observed, which was driven by high RBC linear density instead of high speed.¹⁴ The RBC-passage time courses were then normalized with the range from 0 to 1 (i.e., the minimum value was subtracted from the time course then the time course was normalized by the maximum value). A MATLAB function “findpeaks” was used to count the RBC-passage peaks by employing a threshold set at the half-maximum intensity (i.e., the threshold was 0.5 after the time courses were normalized by the maximum value) of each RBC-passage time course. The number of RBC-passage peaks was averaged over the 2-min scan for each capillary to obtain a mean flux.

Fig. 1

(a) The picture displays a typical cranial window showing the vasculature of the cortical surface. The red lines indicate where repeated B-scans were performed to obtain the RBC-passage time courses. (b) Interlaced B-scan images illustrate the repetitive RBC-passage B-scan. (c)–(f) Representative RBC-passage time courses (0.5 s) of four different capillaries are presented.

The performance of the RBC-passage peak counting procedure was evaluated by simulations. Briefly, speckle noise (filtered from experimental data) was added to synthetized RBC passages (described in Sec. 2.4). Peak counting was performed on those RBC passages with and without filtering ($\sigma =1.5\mathrm{ms}$). Without filtering, the ratio of the estimated flux to true flux was $\sim 179\%$ due to false detections associated with noise. With filtering, the ratio decreased to $\sim 101\%$.

2.4.

Numerical Modeling of Red Blood Cell Flux

We modeled the intensity change due to RBC passage in a virtual capillary by a Gaussian function: $f(t^{\prime })=\exp [-\frac{{(t^{\prime }-t_o)}^2}{2{\sigma }^2}]$, where $t^{\prime }$ represents a time point in an RBC-passage time course; $t_0$ is the center time point of a single RBC passage. According to the previous study,⁷ the RBC-speed (${\mathrm{V}}_{\mathrm{RBC}}$) relates to the RBC-diameter (${\phi }_{\mathrm{RBC}}$) and the Gaussian FWHM by $V_{\mathrm{RBC}}=\frac{{\phi }_{\mathrm{RBC}}}{2\sqrt{2\ln 2}\sigma }$. Here, we set ${\phi }_{\mathrm{RBC}}$ in our simulations to $6.5\mu \mathrm{m}$.⁷ As reported,¹⁴ the flux ($f_{\mathrm{RBC}}$) relates to $V_{\mathrm{RBC}}$ and the distance between neighboring RBCs ($d_{\mathrm{RBC}}$) as $f_{\mathrm{RBC}}=V_{\mathrm{RBC}}/d_{\mathrm{RBC}}$. Then we numerically investigated the RBC-passage time courses for a range of $V_{\mathrm{RBC}}$ and $d_{\mathrm{RBC}}$. Specifically, 40 $V_{\mathrm{RBC}}$ were evenly selected between 0.1 and $3.5\mathrm{mm}/\mathrm{s}$, which covers the range of capillary $V_{\mathrm{RBC}}$ reported in the literature.^{11–14,16–26} The mean value of $⟨d_{\mathrm{RBC}}⟩$ was reported to be $14\pm 2\mu \mathrm{m}$.¹⁴ In simulation, 20 different $⟨d_{\mathrm{RBC}}⟩$ were evenly chosen between 12 and $26\mu \mathrm{m}$. For each RBC-passage time course, $V_{\mathrm{RBC}}$ is fixed for all the RBCs in that time course; and the specific $d_{\mathrm{RBC}}$ between neighboring RBCs was uniformly distributed around a certain mean $⟨d_{\mathrm{RBC}}⟩$. So, combinations of 40 $V_{\mathrm{RBC}}$ and 20 $⟨d_{\mathrm{RBC}}⟩$ result in $40\times 20=800$ RBC-passage time courses. Every RBC-passage time course was generated for 2 min of simulation time with $\mathrm{\Delta }t=0.75\mathrm{ms}$. Each of the 800 RBC-passage time courses was regenerated 100 times with different random RBC distributions for averaging. In order to investigate the impact of $\mathrm{\Delta }t$, each of the $800\times 100=\mathrm{80,000}$ RBC-passage time courses with $\mathrm{\Delta }t=0.75\mathrm{ms}$ was downsampled to $\mathrm{\Delta }t=1.5$, 3, and 4.5 ms. With these four different $\mathrm{\Delta }t$’s, a total of $4\times \mathrm{80,000}=\mathrm{320,000}$ RBC-passage time courses were obtained; each of them yielded a mean flux $⟨f_{\mathrm{RBC}}⟩$. The $⟨f_{\mathrm{RBC}}⟩$ from the individual RBC-passage time courses was binned for comparing results with different $\mathrm{\Delta }t$’s.

3.1.

Effect of B-Scan Temporal Resolution: Numerical Modeling

We first investigate the impact of $\mathrm{\Delta }t$ on the estimation of flux by numerical modeling. Figures 2(a)–2(c) show three synthetized RBC-passage time courses (0.2-s trace). In these three time courses, the mean $d_{\mathrm{RBC}}$ was fixed at $14\mu \mathrm{m}$; but the individual $d_{\mathrm{RBC}}$ between neighboring RBCs were randomly varied around $14\mu \mathrm{m}$. In Figs. 2(a)–2(c), the $V_{\mathrm{RBC}}$ is 2, 1, and $0.8\mathrm{mm}/\mathrm{s}$, and the resultant flux is 100, 50, and $40\mathrm{RBCs}/\mathrm{s}$, respectively. The RBC-passage time courses with $\mathrm{\Delta }t=0.75\mathrm{ms}$ are in red; and the $\mathrm{\Delta }t=4.5\mathrm{ms}$ in blue. This illustration indicates that $\mathrm{\Delta }t=4.5\mathrm{ms}$ might be appropriate for accurate estimation of flux when the $V_{\mathrm{RBC}}<0.8\mathrm{mm}/\mathrm{s}$ but underestimates flux when $V_{\mathrm{RBC}}>1\mathrm{mm}/\mathrm{s}$.

Fig. 2

(a)–(c) Illustration of aliasing with simulated RBC-passage time courses with $V_{\mathrm{RBC}}=2$, 1 and $0.8\mathrm{mm}/\mathrm{s}$, respectively. The “true” time courses ($\mathrm{\Delta }t=0.75\mathrm{ms}$) are in red, while the downsampled ones ($\mathrm{\Delta }t=4.5\mathrm{ms}$) are in blue. (d) Comparison between simulated fluxes with $\mathrm{\Delta }t=0.75\mathrm{ms}$, and the simulated fluxes with all $\mathrm{\Delta }t$’s (0.75, 1.5, 3, and 4.5 ms). (e) Comparison between experimental fluxes with $\mathrm{\Delta }t=0.75\mathrm{ms}$, and the experimental fluxes with all $\mathrm{\Delta }t$’s (0.75, 1.5, 3, and 4.5 ms). (f)–(h) Histograms of experimental fluxes with $\mathrm{\Delta }t=1.5$, 3, and 4.5 ms.

To quantify this ceiling effect with simulations, we synthetized RBC-passage time courses with different combinations of $V_{\mathrm{RBC}}$ and $d_{\mathrm{RBC}}$ (see details in Sec. 2.4). The comparison between the simulated fluxes with $\mathrm{\Delta }t=0.75\mathrm{ms}$ and the fluxes with $\mathrm{\Delta }t=0.75$, 1.5, 3, and 4.5 ms is presented in Fig. 2(d). Here, the $x$-axis is the simulated flux with $\mathrm{\Delta }t=0.75\mathrm{ms}$; the $y$-axis is the simulated fluxes with $\mathrm{\Delta }t=0.75$, 1.5, 3, and 4.5 ms. The green line shows flux with $\mathrm{\Delta }t=0.75\mathrm{ms}$, which serves as a reference for comparison. Ideally, the estimated flux should match the true flux. We expect that as $\mathrm{\Delta }t$ becomes longer that the estimated flux will underestimate the true value, particularly at large flux values. Comparing with the fluxes with $\mathrm{\Delta }t=0.75\mathrm{ms}$, Fig. 2(d) shows that with $\mathrm{\Delta }t=1.5$, 3, and 4.5 ms, the fluxes are underestimated by 9%, 57%, and 74%, respectively, at the true flux of $150\mathrm{RBCs}/\mathrm{s}$. At the true flux of $130\mathrm{RBCs}/\mathrm{s}$, $\mathrm{\Delta }t=1.5$, 3, and 4.5 cause an underestimation of $\sim 6\%$, $\sim 50\%$, and $\sim 70\%$, respectively.

3.2.

Effect of B-Scan Temporal Resolution: Experimental Data

In experiments, the RBC-passage B-scans were performed in mice of group 1 ($n_1=6$) with $\mathrm{\Delta }t=1.5\mathrm{ms}$, and group 2 ($n_2=4$) with $\mathrm{\Delta }t=0.75\mathrm{ms}$. In both groups, the measurements were obtained at cortical depths up to $\sim 700\mu \mathrm{m}$ but mainly around $\sim 500\mu \mathrm{m}$. The original RBC-passage time courses of group 1 that were acquired with $\mathrm{\Delta }t=1.5\mathrm{ms}$ were downsampled to get two additional datasets with $\mathrm{\Delta }t=3$ and 4.5 ms. Similarly, the original RBC-passage time courses of group 2 that were acquired with $\mathrm{\Delta }t=0.75\mathrm{ms}$ were downsampled to get three additional datasets with $\mathrm{\Delta }t=1.5$, 3, and 4.5 ms. We then calculated the mean flux for each RBC-passage time course with different $\mathrm{\Delta }t$’s to investigate the impact of $\mathrm{\Delta }t$. Figure 2(e) shows fluxes measured in group 2. In Fig. 2(e), the $X$-axis presents the experimental fluxes with $\mathrm{\Delta }t=0.75\mathrm{ms}$, which served as the “truth” in the experimental scenario; and the $Y$-axis is the fluxes with $\mathrm{\Delta }t=0.75$, 1.5, 3, and 4.5 ms. Comparing with the fluxes with $\mathrm{\Delta }t=0.75\mathrm{ms}$, Fig. 2(e) showed that fluxes with $\mathrm{\Delta }t=1.5\mathrm{ms}$ are accurately estimated with an underestimation of $\sim 5\%$ at $130\mathrm{RBCs}/\mathrm{s}$, which is the maximum flux measured in our experiments. In contrast, with $\mathrm{\Delta }t=3$ and 4.5 ms, the fluxes are underestimated by 19% and 42%, respectively, at the flux of $130\mathrm{RBCs}/\mathrm{s}$.

The histograms in Figs. 2(f)–2(h) present the distribution of flux measured in 313 capillaries over $n=10$ mice. As shown, when $\mathrm{\Delta }t$ becomes longer, the distribution of flux becomes more compressed and left-shifted to lower fluxes, as would be expected due to aliasing introducing a ceiling effect. The mean flux is 57, 47, and $38\mathrm{RBCs}/\mathrm{s}$, with $\mathrm{\Delta }t=1.5$, 3, and 4.5 ms, respectively, showing a reduction of the mean flux with longer $\mathrm{\Delta }t$’s.