Here, we first describe the OCT system and animal preparation, along with methods of somatosensory stimulation and response localization. We then present simple models to explain OCT dynamic and static signals in terms of attenuation and backscattering. Finally, we describe two complementary protocols for investigation of steady state and transient compartment-resolved hemodynamics with OCT angiography.
2.1 OCT system description
A 1310 nm spectral/Fourier domain OCT microscope was constructed for in vivo imaging of the rat cerebral cortex. The light source consisted of two superluminescent diodes combined using a 50/50 fiber coupler to yield a bandwidth of 150 nm. The axial (depth) resolution was 4.8 µm in air (3.6 um in tissue). A spectrometer with a 1024 pixel InGaAs line scan camera operated at 47 kHz. Imaging was performed with a 10x objective, yielding a transverse resolution of 3.6 microns, or a 5x objective, yielding a transverse resolution of 7.2 microns.
2.2 Animal preparation
The animal procedures were approved by the Subcommittee on Research Animal Care at the Massachusetts General Hospital, where these experiments were performed. Male Sprague-Dawley rats (N = 5; 250-300 gms) were used in this study. The rats were initially anesthetized with 2-2.5% v/v isoflurane with a gas mixture of 80% air and 20% oxygen. Tracheostomy for mechanical ventilation and cannulation of the femoral artery for blood pressure monitoring and femoral vein for anesthetic administration were performed. Following catheterization, the animal was mounted on a stereotactic frame and a craniotomy was performed. Briefly, the scalp was retracted and a metal plate was attached to the exposed skull using bone screws. Using a dental burr, a ~5 × 5 mm2 skull region over the left forepaw region was thinned to translucency and then removed along with the dura. The exposed cortex was filled with 1.5% agarose (Sigma, MO USA), mixed in aCSF (pH 7.4; KCl 5mM, NaCl 125 mM, Glucose 10mM, CaCl2 3mM, and MgCl2 1mM, Sigma Aldrich, MO USA), and covered with a glass coverslip. Dental acrylic was used to seal the cranial window to the skull. To relieve excess intra-cerebral pressure, a ventriculostomy of the IVth ventricle was performed.
Following the surgical procedures, the anesthesia was changed to alpha-chloralose (loading dose – 40 mg/kg; maintaining dose – 50 mg/kg/hr). Throughout the surgical and imaging procedures, the blood pressure was monitored (SYS-BP1, WPI Inc., USA) via a transducer (BLPR2, WPI Inc., USA) connected to the arterial cannula and the animal’s core temperature was maintained at 37 degrees Celsius using a heating blanket (Harvard Apparatus USA). Periodic measurement of blood gases ensured that the values of pO2, pCO2 and pH were within physiological limits (pO2 = 100 – 130 mmHg, pCO2 = 32-40 mmHg, and pH = 7.35 – 7.45).
Two hypodermic needles were inserted into the plantar surface of the rat forepaw. The needles were connected by alligator clips to a stimulus isolator that delivered 300 μs pulses at motor threshold (~1-1.5 mA) when receiving computer controlled triggers. Electrical pulses were delivered at 3 Hz.
2.4 Response localization
Localization of the center of the neuronal response was performed before sealing the cranial window using a ball electrode [19
]. The center of the neuronal response was determined by maximizing the measured electrical signal over a 3 x 3 grid spanning the cranial window. Two-dimensional optical intrinsic signal imaging (OISI) of the exposed cortex was then performed through the window by illuminating the cortex with a spectrally filtered Hg:Xe light source (570 ± 5 nm). Two-dimensional images were acquired with a CCD camera during 25 second blocks with 2 second stimuli at 3 Hz. (Infinity 2-1M, Lumenera, CA). The CCD camera was connected by a USB cable to a computer, which saved the images. The images were later analyzed as a time series to determine the average response to a stimulus. While the map based on the peak fractional reflectance change was heavily weighted towards pial arteries where volume changes were the largest ( and ), the map based on the response temporal width yielded a more well-defined activation region ( and ) that agreed with the ball electrode data. The improved localization provided by the response temporal width is due to the fact that a faster return to baseline is typically observed in the periphery as compared to the center of activation [19
]. OCT imaging was always performed at the center of the OISI response, where the response width was maximal ( and ).
Fig. 1 OCT angiography location was chosen based on optical intrinsic signal imaging (OISI). (A) Peak fractional reflectance change (R/R) map for OISI imaging at 570 nm, for a two second stimulus. The map is heavily weighed to the pial arteries, where (more ...)
2.5 Model of static and dynamic scattering
Previously, it was proposed that a complex OCT image can be considered as a superposition of fields from multiple scatterers [15
]. Neglecting noise, the complex OCT signal can be described as the superposition of a static signal component and a dynamic signal component [21
] within a single voxel. The temporal properties of the signal from a given voxel are characterized by the autocorrelation function. Moreover, one may distinguish between flow decorrelation time scales (<20 milliseconds) and hemodynamic changes time scales (>100 milliseconds), by analysis of time courses with a sliding window. We use the variables τ and T to designate the fast and slow time scales, respectively. Each term in the autocorrelation function can be associated with a specific component of the complex OCT signal. The autocorrelation can be represented as shown below:
The static signal power (Is
) and dynamic signal power (Id
) are defined by evaluating the corresponding terms in the autocorrelation at a time lag τ = 0.
2.6 Model of signal attenuation and correction procedure
Here, we outline and justify methods for quantifying changes in dynamic red blood cell (dRBC) content. Briefly, our method involves removal of static signal, estimation of dynamic signal power, and finally, normalization of dynamic signal power to the static signal power from nearby non-vascular tissue to determine relative changes in dynamic backscattering.
First, we present models of static and dynamic scattering to further describe the signals described above. We assume a simple single scattering model with an attenuation coefficient that includes the effects of scattering and absorption.
The scattering coefficient µs
can be taken to comprise both scattering from static brain tissue and moving blood cells, whereas the absorption coefficient µa
is mainly due to water at 1300 nm. (A more accurate version of Eq. (4)
can be obtained by replacing µs
], where a(g) accounts for detection of multiply forward scattered light). Secondly, we assume that the detected OCT signal can be divided into a static signal, Is
), and a dynamic signal, Id
). If only single scattered light is detected, the static and dynamic signals are distinguished by whether the single backscattering event occurs from a stationary or moving particle. A simple single scattering model therefore describes the depth dependence of the static signal:
The dynamic signal can be described similarly:
In the above expressions, hconfocal
are functions of path length z that account for the confocal gate and spectrometer sensitivity roll-off, respectively. The static and dynamic backscattering are given by Bs
2.6.1 Dynamic backscattering and dynamic RBC content
Two important changes occur in Eq. (5)
and Eq. (6)
during activation. Firstly, the dynamic backscattering (Bd
) increases, due to an increase in red blood cell density and velocity. Secondly, the attenuation coefficient (µt
) increases due to increased attenuation from scattering. As µt
z appears in the exponent of Eq. (5)
and Eq. (6)
, an increase in µt
has a greater influence on signal levels at greater depths. The static backscattering (Bs
) is assumed not to change. Approximately constant static backscattering was confirmed by performing measurements of signal intensity in avascular regions near the cortical surface. We note here that fast-optical signals, while they would constitute changes in static scattering, are at least two orders of magnitude smaller than the observed slow hemodynamic scattering changes [24
], and therefore are not considered here. The assumption that static backscattering remains constant over time may not be valid under pathological conditions such as cortical spreading depression or severe ischemia.
The attenuation coefficient µt
is known to increase due to increased scattering during functional activation [25
], resulting in reduced signals from greater tissue depths. The most likely mechanism for the rise in µt
is an increase in red blood cell number during activation. Red blood cell orientation changes, astrocyte swelling, and tissue compression resulting from increased blood volume are other possible mechanisms. Critically, both static and dynamic signals were assumed to experience the same attenuation coefficient. If static backscattering does not change, the static signal conveniently serves as a “reference.” Thus, it is possible to normalize the dynamic signal to the static signal acquired at the same time and depth to remove the confounding effects of attenuation coefficient changes, as shown below.
The normalized signal Inorm
in Eq. (7)
gives the ratio of dynamic to static backscattering. In practice Is
is averaged over a local region, devoid of vessels, to reduce speckle noise. The relative normalized signal,
, can then be defined as follows:
Combining Eq. (7)
with Eq. (8)
, we obtain the following:
Hence, under the aforementioned assumptions, the quantity in Eq. (9)
is a depth-specific measure of hemodynamics. While there are other scattering components in blood, RBCs are the most numerous intravascular scatterers; hence dynamic backscattering changes are an indicator of changes in dRBC content that accompany activation. The critical assumptions in arriving at this interpretation are that 1) static backscattering does not change and that 2) both static and dynamic signals experience the same attenuation with depth due to scattering.
shows the dynamic signal image (Id
, log scale), with relative changes in a region of interest (white rectangle) plotted. The dynamic signal, averaged over the region of interest, increases during activation. However, the quantitative interpretation of this increase is confounded by the above-mentioned increase in µt
. shows the OCT intensity image (Is
, log scale), along with the mask used to exclude dynamic signal in black. The static signal during activation is reduced (), due to an increase in µt
). Therefore, dynamic signal was normalized to static signal to correct for the change in µt
), and relative changes were plotted in . When the normalized time courses are plotted, laminar differences in response magnitude are evident, apparently showing that the largest dynamic backscattering changes occur between 500 and 700 microns cortical depth (). The mean
for a 4 second 3 Hz stimulus, averaged over the 20 period after stimulus onset, was 0.014+/− 0.003 mm−1
(N = 4).
Fig. 2 A correction procedure was applied to determine depth-specific dynamic backscattering changes. (A) The OCT angiogram, representing the dynamic signal Id, with relative changes in a region of interest (white rectangle) plotted during stimulation (average (more ...)
2.7 Angiography protocols
Two imaging protocols were used: i) continuous stimulation at 3 Hz with steady-state three-dimensional scanning at baseline and during activation () and ii) asynchronous block stimulus and repeated three-dimensional scanning (). For both protocols, a 3.6 micron transverse resolution was used, the focus was placed 100-200 microns below the cortical surface, and data was analyzed up to a cortical depth of 400 microns.
Fig. 3 OCT angiography scanning protocols. (A) Three-dimensional scanning protocol used to determine compartment-resolved steady-state changes during a long stimulus (>10 s). (B) Four-dimensional asynchronous scanning protocol used to determine time-courses (more ...) 2.7.1 3-D angiography
shows a three-dimensional scanning protocol for volumetric angiography that samples the same transverse location twice per volume. OCT angiograms were acquired by repeating a volumetric scanning protocol that sampled each spatial location twice [26
]. A total of 1024 images at 512 y locations were acquired in 12 s to generate a single volumetric angiogram of 1.25 mm x 1.25 mm. At 512 axial scans per image, each location was sampled at 11 ms intervals. A first volume was acquired, then stimulation was performed for 10 seconds without data acquisition, and simulation continued uninterrupted during acquisition of the second volume.
2.7.2 4-D angiography
shows a four-dimensional scanning protocol with asynchronous, or staggered, stimulation and data acquisition, used to investigate time courses of compartment-resolved changes. The central goal of this protocol was to simultaneously achieve a large field-of-view and high temporal resolution. At 256 axial scans per image, each location was sampled at 7 ms intervals. A total of 512 images at 256 y locations were acquired in 3.6 seconds to generate a single volumetric angiogram of 0.63 mm x 0.63 mm. A 2 second stimulus with an inter-stimulus interval of 23 seconds (block period of 25 seconds) was used. 10 blocks were presented per run. Three computers were involved in these experiments; 1) a stimulus computer generating stimulus trains at a period of trep
= 25 seconds controlling an amplifier and linear stimulator, an OCT computer that acquired camera line triggers and generated frame triggers and galvanometer signals for acquisition control, and a third computer that acquired both the stimulus triggers and the frame triggers. For the purposes of this discussion, we assume that the time between consecutive B-scans
t = t2n
is small. Angiograms were generated by taking the absolute value of the complex difference between consecutive frames:
In the above expression, t is given by (t2n
)/2. If the time interval
t = t2n
between consecutive frames is much greater than the decorrelation time, the angiogram amplitude is insensitive to velocity changes. However, if the time interval is on the order of the decorrelation time, the amplitude will be affected by both velocity changes and changes in RBC content. The complex subtraction of Eq. (10)
can be explained as a digital filtering procedure, shown in , which removes static scattering, or “clutter” [15
Fig. 4 Separation of static and dynamic signal can be interpreted as a high-pass filtering procedure. A change in the dynamic spectrum width (related to velocity) or area (related to red blood cell number or orientation) may affect the measured dynamic signal (more ...)
By asynchronously running a block stimulus paradigm such that the least common multiple of the inter-stimulus interval trep
and the volumetric repetition time tvol
was greater than the time for one run (set of trials), a given spatial location was sampled at a different time with respect to the stimulus, for each repeated volume. The frame triggers and the stimulus triggers were recorded, thus the y location of the angiogram as well as the temporal location with respect to the stimulus could be determined. Therefore it was possible to determine the exact location of each angiogram pixel in space and in time relative to the last stimulus. A four-dimensional volume of functional activation, Id
(x,y,z,T) could thus be constructed as shown below:
In the above expression, vy
is the velocity of y scanning. The acquisition for repeated volumes begins at t0,vol
, while the first stimulus begins at t0,stim
. Due to the asynchronous scanning protocol, each location is not sampled at uniform time intervals with respect to the stimulus. Thus it was necessary to interpolate and resample this data at evenly spaced times before displaying movies. The interpolation procedure is valid if dynamics are repeatable on successive stimulus trials. Similar scanning protocols are used frequently in fMRI experiments where multiple slices are acquired asynchronously with respect to the stimulus.