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22-01-2019 14-Jul-2016 13-Apr-2017

Final Report: STIR: Multi-Modal Brain Interface System for the Study of Neurovascular Coupling

The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an official Department of the Army position, policy or decision, unless so designated by other documentation.

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19b. TELEPHONE NUMBERRamin Pashaie

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University of Wisconsin - MilwaukeeP.O. Box 340

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Proposal Number: 68750LSII

Address: P.O. Box 340, Milwaukee, WI 532010340 Country: USADUNS Number: 627906399 EIN: 391805963

Date Received: 22-Jan-2019Final Report for Period Beginning 14-Jul-2016 and Ending 13-Apr-2017

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Submitted By: Ramin PashaiePhone: (414) 229-2273

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Agreement Number: W911NF-16-1-0407

Organization: University of Wisconsin - Milwaukee

Title: STIR: Multi-Modal Brain Interface System for the Study of Neurovascular Coupling

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Major Goals: Major goal of the project was the development of a multi-modal brain interface platform capable of selectively modulating the activity of neurons and imaging induced activities in neurons and the corresponding changes in the vascular network all with light.

Accomplishments: We finished the process of developing the system. We included spectral domain optical coherence tomography to trace vascular dynamics. We included patterned optogenetic brain stimulation to selectively modulate any neural population of interest with any arbitrary spatial-temporal pattern. We also included simultaneous ECoG recording to keep the track of electrophysiology signals. Fluorescence microscopy was also included but not in the form of multi-photon imaging. We did not have enough funding for the fs laser. We submitted a proposal to DURIP but unfortunately it was not funded. Nonetheless, what we made was truly powerful and we started the experiments immediately and good manuscripts were published.

Training Opportunities: At least two PhD students were supported by this grant partially. I used this grant and my NSF Career award to support them and they both functioned very well. One PhD student graduated before and his thesis is available. The second graduate student finished his second major paper and he finished his proposal defense successfully. He will graduate in about 2 years from now and the new ARMY grant will help us to support him. We have also tried to submit papers in which we discuss our design strategy and techniques.

Results Dissemination: Nothing to Report

Honors and Awards: We have received 2 new federal grants from NSF and ARO to continue this research.The PI received the Excellence in Research award from the University of Wisconsin system

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Technology Transfer: Nothing to Report

Report Date: 13-Jul-2017

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Phone Number: 4142292273Principal: Y

Name: Ramin Pashaie Email: [email protected]

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Person Months Worked: 9.00 Funding Support: Project Contribution: International Collaboration: International Travel: National Academy Member: N



Participant: Ramin Pashaie

Other Collaborators:

Participant Type: Graduate Student (research assistant)Participant: Farid Atry


Participant Type: Graduate Student (research assistant)Participant: Rex Chen


ARTICLES:

Publication Identifier: First Page #: Volume: 15

Date Submitted: 1/17/19 12:00AM

Authors: Farid Atry, Rex Chin-Hao Chen, Jane Pisaniello, Sarah Brodnick, Aaron J Suminski, Joseph Novello, Jared Ness, Justin C Williams, Ramin Pashaie

Distribution Statement: 1-Approved for public release; distribution is unlimited.Acknowledged Federal Support: Y

Publication Type: Journal ArticleJournal: Journal of Neural Engineering

Publication Location: Article Title: Optogenetic interrogation of neurovascular coupling in the cerebral cortex of transgenic mice

Keywords: Optogenetics, Coherence Tomography, Neurovascular CouplingAbstract: Objective. We introduce an engineering approach to study spatiotemporal correlations between vasodynamics and the nearby neural activity in open-loop and closed-loop paradigms. Approach. We integrated optogenetic technology with optical coherence tomography to apply spatiotemporal patterns of optical neurostimulation to the cortex of transgenic optogenetic mice and measure blood flow-rate, velocity, and diameter changes of selected middle cerebral artery branches. Main results. The spatiotemporal characteristics of blood flow-rate, velocity, and vessel diameter responses to localized neurostimulation light pulses were measured. It was observed that the location of stimulation relative to the surrounding vascular topology had notable effects on temporal patterns of vasodynamic responses. This effect was studied by creating velocity, flow-rate, and diameter sensitivity maps for selected arteries.

Publication Identifier Type: ISBNIssue: 5

Date Published: 9/5/18 5:00AM

Peer Reviewed: Y Publication Status: 1-Published


Publication Identifier: First Page #: Volume:

Date Submitted: 1/17/19 12:00AM

Authors: Farid Atry, Israel Jacob De La Rosa, Kevin R. Rarick, Ramin Pashaie

Distribution Statement: 1-Approved for public release; distribution is unlimited.Acknowledged Federal Support: Y

Publication Type: Journal ArticleJournal: International Journal of Optics

Publication Location: Article Title: Design and Implementation Guidelines for a Modular Spectral-Domain Optical Coherence Tomography Scanner

Keywords: Spectral-Domain Optical Coherence Tomography, AngiographyAbstract: In the past decades, spectral-domain optical coherence tomography (SD-OCT) has transformed into a widely popular imaging technology which is used in many research and clinical applications. Despite such fast growth in the field, the technology has not been readily accessible to many research laboratories either due to the cost or inflexibility of the commercially available systems or due to the lack of essential knowledge in the field of optics to develop custom-made scanners that suit specific applications. This paper aims to provide a detailed discussion on the design and development process of a typical SD-OCT scanner. The effects of multiple design parameters, for the main optical and optomechanical components, on the overall performance of the imaging system are analyzed and discussions are provided to serve as a guideline for the development of a custom SD-OCT system.

Publication Identifier Type: ISBNIssue:

Date Published: 2/2/18 6:00AM

Peer Reviewed: Y Publication Status: 1-Published

CONFERENCE PAPERS:

Date Received: Date Published: 14-Apr-2018Conference Date: 14-Apr-2018

Authors: Ramin PashaieAcknowledged Federal Support: Y

Date Received: 17-Jan-2019 Date Published: 27-Jan-2018Conference Date: 27-Jan-2018

Authors: Rex Chen,Farid Atry, Ramin PashaieAcknowledged Federal Support: Y

Publication Type: Conference Paper or PresentationConference Name: Society for Brain Mapping and Therapeutics

Conference Location: Los Angeles, CA, USAPaper Title: Functional Neuroimaging via Optical Coherence Tomography Angiography

Publication Type: Conference Paper or PresentationConference Name: SPIE Photonic West

Conference Location: San Francisco, CA, USAPaper Title: Modeling of cerebral blood flow in reaction to neural stimulation

Publication Status: 1-Published

Publication Status: 1-Published

DISSERTATIONS:

Date Received: 17-Jan-2019

Authors: Farid AtryAcknowledged Federal Support: Y

Publication Type: Thesis or DissertationInstitution: University of Wisconsin-Milwaukee

Title: Optogenetic Interrogation and Manipulation of Vascular Blood Flow in CortexCompletion Date: 12/1/17 6:08PM

Journal of Neural Engineering

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Optogenetic interrogation of neurovascular coupling in the cerebralcortex of transgenic miceTo cite this article: Farid Atry et al 2018 J. Neural Eng. 15 056033

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Optogenetic interrogation of neurovascular coupling in the cerebral cortex of transgenic mice

Farid Atry1,4,5, Rex Chin-Hao Chen1,5, Jane Pisaniello2, Sarah Brodnick2, Aaron J Suminski2,3, Joseph Novello2, Jared Ness2, Justin C Williams2,3 and Ramin Pashaie1

1 Department of Electrical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, United States of America2 Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, United States of America3 Department of Neurological Surgery, University of Wisconsin-Madison, Madison, WI, United States of America

E-mail: [email protected]

Received 12 February 2018, revised 13 July 2018Accepted for publication 2 August 2018Published 5 September 2018

AbstractObjective. We introduce an engineering approach to study spatiotemporal correlations between vasodynamics and the nearby neural activity in open-loop and closed-loop paradigms. Approach. We integrated optogenetic technology with optical coherence tomography to apply spatiotemporal patterns of optical neurostimulation to the cortex of transgenic optogenetic mice and measure blood flow-rate, velocity, and diameter changes of selected middle cerebral artery branches. Main results. The spatiotemporal characteristics of blood flow-rate, velocity, and vessel diameter responses to localized neurostimulation light pulses were measured. It was observed that the location of stimulation relative to the surrounding vascular topology had notable effects on temporal patterns of vasodynamic responses. This effect was studied by creating velocity, flow-rate, and diameter sensitivity maps for selected arteries. Generally, neural stimulation in the vicinity of downstream capillaries of an artery evoked a fast transient increase in the blood flow-rate, velocity, and vessel diameter which was followed by a long-lasting secondary peak-response. The temporal span of the flow-rate response was quasi-linearly proportional to the length of stimulation. When neural stimulation was delivered to the area in the vicinity of one daughter branch of an artery, in other branches, we observed some drop in blood velocity and/or flow-rate and concurring increase of the vessel diameter. To examine the reliability of the coupling between neural activity and regional blood flow, a closed-loop feedback controller was implemented which is capable of maintaining blood flow-rate at any desired level for relatively longer periods by continuously adjusting the width of stimulation pulses. Significance. The proposed approach opens new lines of research with potential applications in understanding the role of different cell types in the cerebrovascular regulatory mechanisms and the study of the adaptive process of angiogenesis in the cerebral cortex. The observation of incoherent responses of vessel diameter, blood flow-rate, and velocity suggests that such detailed information is necessary to obtain an accurate interpretation of the data acquired via hemodynamic based functional imaging techniques.

F Atry et al

Optogenetic interrogation of neurovascular coupling in the cerebral cortex of transgenic mice

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4 Present address: Department of Biomedical Engineering, University of Wisconsin-Madison, Madison, WI, United States of America5 Authors contributed equally.

2018

1741-2552/18/056033+18$33.00

https://doi.org/10.1088/1741-2552/aad840J. Neural Eng. 15 (2018) 056033 (18pp)

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Keywords: optogenetics, optical coherence tomography, neurovascular coupling, hemodynamic response, closed loop control, cerebral blood flow, receptive field

S Supplementary material for this article is available online

(Some figures may appear in colour only in the online journal)

1. Introduction

The ubiquitously distributed vascular network of the brain is primarily responsible for the delivery of vital metabolic and respiratory substances to the cells and the removal of del-eterious metabolic by-products to keep the tissue alive and functional. The regulatory process that controls the flow of blood in the vascular network is mainly influenced by the level of activity in local networks of neurons which are the most energy demanding cells in the brain [1, 2]. Consequently, the dynamics of the vascular network and neural circuitry of the brain are intimately tied. Understanding the mechanisms that mediate this coupling provides insight into the brain’s infor-mation processing pathways and pathophysiology of neuro-logical diseases in which neurovascular coupling is perturbed.

Neurovascular coupling has been studied at the cellular level by investigating the role of intermediary cells and the signaling mechanisms that relate changes in the level of neural activity to the local fluctuations of hemodynamic sig-nals [3–5]. In recent years, optogenetics, as a reliable means for direct modulation of activity in cell-populations of interest in a versatile yet minimally invasive manner [6, 7], has been employed to investigate hemodynamic response in the brain (e.g. [8–11]). Uhlirova et al [12] used optogenetics to demon-strate the role of inhibitory neurons in arteriolar dilation and constriction. Moreover, they observed a decrease in dilation onset and time-to-peak as the arteriolar depth increases. In our previous work, we quantified multiple attributes of vas-cular response to wide-field optogenetic stimulation, and the timing and magnitude of vasodynamic reactions were meas-ured ([13] and supplementary note 1 (available at stacks.iop.org/JNE/15/056033/mmedia)). In Channelrhodopsin (ChR2) positive animals, we observed 20%, 35%, and 100% increases in diameter, blood velocity, and blood flow-rate following photostimulation pulses, respectively. The corresponding changes were smaller than 10% in wild-type animals which rules out the significance of thermal effect [14–16] on the vas-cular responses.

Nonetheless, the vascular response to optogenetic stimula-tion of neuronal populations has not been extensively inves-tigated from the system engineering point of view. In the current study, we employ the new advances in photostimula-tion and imaging techniques to propose a versatile approach to discern different temporal and spatial characteristics of cerebral microvascular dynamics following confined optical neurostimulation in genetically modified animals. We study the effect of length and amplitude of stimulation on the tem-poral pattern of changes in the blood flow-rate, blood velocity, and diameter of the pial vessels. To investigate the spatial

features of vasodynamics, we introduce sensitivity map of a surface artery which assesses the influence of stimulation location on the shape and amplitude of the vessel response. The spatiotemporal properties of the response are further analyzed by applying multiple simultaneous stimulations to different locations and comparing the results with single-site neurostimulation.

Once the dynamics of surface cortical arteries were charac-terized, this information was used to design and implement a blood flow controller which uses locally and temporally engi-neered optogenetic stimulation pulses to maintain the flow-rate of blood at various user-defined levels in selected arteries. The implementation of closed-loop blood flow controller requires a fast and reversible manipulation of the arterial blood flow. While different mechanisms can be used to induce such per-turbations, we employ optogenetics to modulate the activity of a spatially confined neuronal population mostly consisting of pyramidal cells as an indirect mechanism to adjust the flow-rate in the desired arteries. In this mech anism, the photostimulation is continuously adjusted according to the vascular flow-rate continuously measured by a spectral-domain optical coherence tomography scanner. We demonstrate that the proposed method is capable of maintaining the blood flow-rate of selected arteries at user-defined level over a relatively long duration. A closed-loop controller can be used to better understand the dynamics of the system [17] or to valid ate mathematical models of the system dynamics [18] which may not be possible via deliv-ering a short predefined stimulation. While optogenetic-based feedback control systems have been used to adjust the cellular activity (e.g. [17, 19, 20, 21]), no similar approach has been proposed to control the arterial flow-rate in cortex.

2. Methods: all-optical interrogation of vascular response

For our experiments, we developed a spectral-domain optical coherence tomography (OCT) scanner [22–24] and extra comp onents were integrated to simultaneously perform flu-orescence imaging and patterned optogenetic stimulation (figure 1(a)) ([13, 25, 26]).

2.1. Optical setup

The implemented spectral-domain OCT scanner uses a low coherence light source (central wavelength 1300 nm, band-width >170 nm, total power 10 mW, Thorlabs, NJ, USA) and a 10x OCT objective lens (LSM02, Thorlabs, NJ, USA) to achieve axial and lateral resolutions of ∼4.4 μm and ∼5.1 μm, respectively [26]. A scan/tube lens mechanism is designed

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and used to open up the space before the back focal plane of the objective [25]. This space is used to install a dichroic beamsplitter (D1, FF875, Semrock) before the OCT objective lens to combine the OCT light and visible beam pathways [26]. The visible path is devoted to the delivery of optoge-netic stimulation light pulses and/or fluorescence excitation beam. The same path is also used to capture fluorescence or bright field images. For this purpose, another dichroic beam-splitter is installed in the visible path (FF440_520, Semrock) which passes the excitation/stimulation blue light toward the objective lens and reflects the emitted green light toward a charge-coupled device (CCD) camera (EXi Aqua, QImaging, BC, Canada) (figure 1(a)). The camera is used to visualize the location of stimulation or to capture images of pial ves-sels in the cortex. When necessary, this imaging path can be used for various fluorescence imaging techniques (such as cal-cium imaging, NADH recording). The spatial distribution of photostimulation in this setup is independently controlled by a pair of galvanometric mirrors which are dedicated to steer the beam of a fiber-coupled visible laser (λ = 450 nm, I ∼ 20 mW, LP450-SF15, Thorlabs, NJ, USA) at the focal plane of

the objective. The spot size of the laser on the tissue was tuned by adjusting the position of a collimating lens in front of the laser fiber to achieve illumination disks of diameters changing from 266 μm to 800 μm. For multi-site stimulation, we used time intervals between consecutive stimulating pulses to re-position the galvanometer and steer the beam to a new loca-tion. The CCD camera in the optical path of the fluorescence microscope was used either for fluorescence or bright field imaging to visualize pial vessels during experiments, mark the main vessel cross-sections for OCT recordings, and guide the laser beam for optogenetic stimulation (figure 1(b)).

The platform of OCT scanner and optogenetic stimulation setup is operated by a custom software developed in LabVIEW environment, which enables us to capture either three-dimen-sional volumetric images or periodic two-dimensional cross-sectional images from a set of user-defined location(s). In the three-dimensional setting, typically three-dimensional angiograms [27–30] or velocimetric images [31, 32] are cap-tured from any predefined region of interest (figures 1(c) and (d)), while the two-dimensional setting is used to periodi-cally monitor cross-sections of a set of target vessels (figure

Figure 1. Simultaneous optogenetic stimulation and optical coherence angiography and velocimetry: (a) Schematic of the optical setup which integrates spectral-domain OCT, fluorescence imaging, and optogenetic stimulation. L: lens, ML: movable lens, SL: scan lens, TL: tube lens, OL: objective lens, FP: focal plane, GM: galvanometric mirror, FC: fiber coupler, SLD: superluminescent diodes, D: dichroic mirror, CCD: charge-coupled device, RM: reference mirror. (b) A typical fluorescence image captured from the cortical tissue of a Thy1-YFP+ transgenic mouse. (c) The maximum intensity projection of a 3D OCT angiogram obtained from a region of interest marked in the fluorescent image of panel (b). OCT angiograms are used to measure vessel diameters. (d) The maximum intensity projection of 3D Doppler-OCT measurement. The color represents the blood flow toward (green) or away (red) from the objective lens. The color reflects the flow direction with respect to the OCT objective not the actual flow direction in the vessel. (e) Snapshots of the Doppler velocity profile of a sample artery captured within a single heart cycle. By locating a bounding box which encapsulates the vessel cross-section and adding the value of all pixels inside the set, we obtain an axial blood flow-rate index for the vessel at each time point. (f) Examples of vessel diameter (top), blood velocity (middle), and blood flow-rate (bottom) measurements from a typical cortical artery performed via OCT imaging. Diameter measurement time-traces are noisy since the lateral resolution of OCT angiography (∼5 μm) is comparable to the percentage of the observed changes in vessel diameters. Heart pulsation directly affects all OCT angiography and Doppler measurements. The heart pulsation contamination was eliminated by the use of a moving average (MA) filter (black curve) or an extended Kalman filter (red curve). (g) Block-diagram of the closed-loop controller. The system uses OCT to measure the difference between the user defined target for blood flow-rate and the actual value measured in the vessel(s) of interest. The difference is fed to a PID compensator to adjust the pulse width of photostimulation.

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1(e)). During two-dimensional scanning, synchronous actions between OCT and stimulation laser is obtained by using four clocks with three different frequencies on two data acquisi-tion (DAQ) devices (USB-6363 and USB-6210, National Instrument, USA). For OCT imaging, a master clock is gen-erated on the first DAQ (USB-6363) at a frequency between 140 Hz and 200 Hz. This master clock triggers the start of one OCT cross section recording and synchronizes two slave clocks which control the line CCD and OCT galvanometers individually. Therefore, the frequency of the master clock determines the OCT B-scan rate where the practical frame rate of each vessel cross-section is this frequency divided by the number of vessels. On the stimulation setup, a second master clock operates at 15 kHz, and synchronizes the second pair of galvanometers and the blue laser pulses.

The two-dimensional OCT scanning protocol is used to monitor and calculate changes in three different attributes of vasodynamic responses to optogenetic stimulation. First, cross-sectional angiograms are obtained to measure temporal changes in diameters of vessels. In the second step, Doppler images are reconstructed to extract quantitative measures of blood flow-rate and blood velocity responses.

2.2. Blood flow-rate and velocity responses

We use phase resolved Doppler OCT [31] to obtain cross-sectional velocity profiles of the desired vessels. Structural heterogeneities in the tissue can cause artifacts in phase infor-mation and introduce a bias to the Doppler OCT velocimetry data. This distortion can be avoided by using a bidirectional scanning mechanism and averaging the velocity profiles of forward and return paths. The structural noise in the forward and return paths of the galvanometric mirrors are additive inverse of each other. To reduce the structural and measure-ment noise, we apply a moving average of size 3 × 7 × 2 (zxt) to bidirectionally scan cross-sectional velocity profiles prior to any further processing.

By locating a bounding box, which encapsulates the vessel cross-section (figure 1(e)), and summing the velocity values for all pixels inside the bounding box, we obtain the axial flow-rate index of the vessel at each point in time. The relation between the actual flow-rate and the measured flow-rate index is influenced by the OCT voxel size, the overlap between voxels, the angle between the direction of the vessel and the OCT beam etc. When there is no change in the configuration of the system or the physical orientation of the vessel during the experiment, the relative fluctuations in the OCT flow-rate index reflects relative changes in the actual flow-rate in the vessel [13].

In this work, we define blood flow-rate response (BFR) as a percent change in the blood flow-rate index with respect to a baseline flow-rate index which is obtained prior to any optogenetic stimulation. Since we report the BFR as a relative value, it is insensitive to scanning parameters and the physical orientation of the vessel. To detect the stimulation evoked flow-rate response, the Doppler OCT measurement was

performed for a period of at least 40 s. The OCT recording starts prior to an stimulation onset. We call this period the baseline period which was changing between 4 s to 30 s in different experiments. The baseline flow-rate index was cal-culated by averaging the flow-rate signal during the baseline period. Then, the blood flow-rate response was calculated by:

BFR(t) = 100 F(t)−FBFB

, where F(t) is the flow-rate index at

time t and FB is the baseline value. This signal is contaminated by cardiac and respiratory pulsations. Therefore, BFR signal is filtered using a moving averaging (MA) or an extended Kalman filter (EKF) to reduce the heart and respiratory comp-onents. Blood flow-rate measurements were repeated at least five times and the results were averaged to achieve a reliable measurement in each experiment.

The blood velocity response (BVR) was measured by a sim-ilar approach. First, we defined a velocity index which is the maximum/minimum velocity inside the bounding box when blood flow-rate value is positive/negative. The velocity signal represents the fluctuations in the axial blood velocity. Then,

the blood velocity was calculated by: BVR(t) = 100 V(t)−VBVB

,

where V(t) is the velocity signal at time t and VB is the baseline value for the velocity. The BVR signals undergo the same fil-tering and trial averaging as the blood flow-rate measurements.

2.3. Vessel diameter response

For vessel diameter measurements, we use OCT angiography which relies on the motion contrast to visualize moving par-ticles in the tissue. Details of OCT angiography is presented in [13], which is based on the phase-sensitive OCT angiog-raphy technique [30]. Briefly, the OCT images are stored in a first-in first-out memory buffer with the size of eight images. At each point in time, the buffer contains the most recent cross-sectional OCT images that were captured from the vessel cross-section. We compensate the effect of motion as described in [13]. For any two of randomly selected images from the buffer, we obtain a normalized difference measured

by: |B1(z,x)−B2(z,x)|b+|B1(z,x)|+|B2(z,x)| , where B1 and B2 are the selected OCT

images and b = 2× < |B1(z, x)|+ |B2(z, x)| >(z,x) is a posi-tive number that suppresses the noise when OCT signals are weak. The depth and lateral location across an OCT image are shown by z and x. The operator <... > (z,x) computes the mean value over z and x. By processing this normalized dif-ference for every possible permutation of selecting two OCT images from the buffer, we obtain 28 motion contrast images among which four of them with the least amount of noise were averaged to obtain the vessel angiogram at that moment [13]. Then, we apply a maximum intensity projection (MIP) and calculate the FWHM of the MIP signal to estimate the vessel diameter.

To obtain the MIP of an angiogram, we first apply a smoothing filter of size 3 × 3 pixels (depth and lateral) to the angiogram to reduce noise. At each lateral location, the average of the largest five values across the depth is obtained and assigned to that location in the MIP image. The vessel

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diameter response (VDR), defined by the percent change in the vessel diameter after the heart pulsation removal, is then calculated similar to BFR measurements.

Since OCT angiography is based on motion contrast, the measured value of vessel diameter might differ from the actual diameter of vessel lumen. With some other imaging modalities, such as multi-photon microscopy, it is possible to image vessel lumen and measure lumen diameter. Therefore, OCT and multi-photon microscopy diameter measurements might report slightly different diameter responses. Such a comparison between measurements in different modalities can be valuable for interpretation of diameter responses that are observed via OCT angiography.

2.4. Heart pulsation and noise removal

Figure 1(e) displays snapshots of typical Doppler velocity measurements and the corresponding blood flow-rate values, which are sequentially acquired within one cardiac cycle in a typical cerebral artery. As illustrated, blood flow-rate and velocity measurements are contaminated by the heart and res-piration pulsations. Also, the diameter of arteries exhibit some spontaneous fluctuations in the spectral range from 0.1–1.0 Hz [33]. To discern any changes in the vasodynamics caused by neurostimulation, it is essential to at least remove the effect of cardiac (and even respiratory) pulsations from the recorded traces (supplementary note 2). Cardiac induced alternations are sometimes an order of magnitude larger than other physio-logical sources of fluctuations. It is possible to readily remove the contribution of smaller terms by repeating the experi-ments and performing ensemble averaging over a sufficient number of trials. On the other hand, cardiac and respiration comp onents are usually attenuated by using a moving-average (MA) filter as displayed in figure 1(f). The performance of the MA filter further improves when we use the length-locked moving-averaging in which the filter window size is con-tinuously adjusted according to the cardiac period (supple-mentary note 6). In more delicate experiments, it is better to use advanced mathematical algorithms such as the extended Kalman filter (EKF) ([34], supplementary note 7).

2.5. Animal preparation

All animal procedures were approved by the University of Wisconsin Institutional Animal Care and Use Committee (IACUC). We used 6–14 weeks old transgenic mice (Thy1::ChR2/H134R-YFP) for this study. Each animal received a thinned-skull cranial window and a glass coverslip [35] and the brain was imaged during a single terminal ses-sion. During preparation, the mice were anesthetized with iso-flurane (1.5%–2.0% in oxygen) and were administered 0.25 ml of fluids (sterile saline solution 0.9%) and Dexamethasone (2 mg kg−1). In each animal, the scalp was retracted and the skull on top of the somatosensory cortex was thinned over an area of 3 mm in diameter and a 3 mm diameter coverslip was installed. The average heart rate of the animals during this time period was between 450–550 bpm. When the surgical portion of the experiment is finished and the animals heart

and breathing rates are stable, the anesthetic was switched to Ketamine (25–100 mg kg−1 SC) and dexmedetomidine (0.05–0.5 mg kg−1 SC) prior to imaging. After switching the anes-thetic and during the imaging session, the animals heart rate was 251 ± 37.4 bpm (mean ± SD, 10 animals). The periph-eral capillary oxygen saturation was 96.6 ± 2.6 (mean ± SD, 10 animals). Furthermore, the body temperature of the ani-mals was kept around 36.5–37.5 °C by using a heated blanket.

2.6. Optogenetic stimulation

In the experiments, unless otherwise mentioned, the photo-stimulation was pulsed at 15 Hz with 50% duty cycle (DC) and the simulated beam diameter on the tissue surface was set to 266 μm, 461 μm, or 800 μm. The length of stimulation duration was varied between 1 s to 12 s for impulse measure-ments and was 240 s for the closed-loop blood flow control mechanism. Evoked neuronal activity during optogenetic stimulation was confirmed by recording brain electrical sig-nals using a transparent electrocorticography device [36] in some animals (appendix A).

2.7. Light propagation simulation

Light distribution in the brain of animals was estimated by a 3D voxel-based Monte Carlo simulation [37–39]. The bulk of the tissue in the simulation had the size of 5 × 5 × 5 mm3 (xyz) with a voxel size of 20 × 20 × 20 µm3 and a total number of 5 × 106 photon packets were used. The brain tissue was assumed to be homogeneous with the optical proper-ties of white matter at 450 nm. The optical properties were set to 1 mm−1, 55 mm−1, and 0.9 for absorption coefficient (µa), reduced scattering coefficient (µs), and anisotropic factor (g), respectively [39]. The brain surface was illuminated by a beam which had the numerical aperture (NA) of 0.1. The sim-ulated beam had a uniform light distribution across its waist with three different waist diameters of W = 266 μm, 461 μm, and 800 μm.

2.8. Closed-loop blood flow control algorithm

We developed a closed-loop controller to increase vascular blood flow-rate in a targeted vessel cross-section to a user-defined level and maintain it for 5 min. Before the start of a control session, the baseline blood flow-rate of the cross-sec-tion is calculated by monitoring the flow-rate for 30 s. During the control session, a 15 Hz pulsed blue laser is delivered to neurons in the vicinity of the downstream capillaries of the targeted vessel. A proportional-integral-derivative compen-sator is then used to constantly adjust the stimulation pulse width (or equivalently its duty cycle) to minimize the differ-ence between measured blood flow-rate and the user-defined level.

To implement the controller, we utilized the developed plat-form and implemented three separate software routines that work hand in hand. First, an OCT routine periodically scans and calculates the blood flow-rate of the selected vessel cross-section(s) at the rate of 82 samples per second. To achieve

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this frame rate during on-line processing the data acquisi-tion is performed in Labview environment and dedicated dynamic-link library (DLL) packages are used to process the raw OCT data and calculate the vascular flow-rate value. The DLL packages are developed in the C programming language. The online measured flow-rate values are stored in a queue and passed to the digital filter routine. Secondly, the digital filter routine retrieves the latest blood flow-rate value from the queue and removes the pulsation (by applying the length-locked MA filter or the EKF). Lastly, before the compensator routine starts, the percent of change of current blood flow-rate, f[n], with respect to the baseline is calculated. Then, the duty cycle of the pulsed optogenetic stimulation waveform is updated according to the error between the user-defined blood flow-rate, fset[n], and the measured value by using a discrete form of a proportional-integral-derivative (PID) compensator:

U[n + 1] = KP × e[n] + KI ×n∑

i=0

e[i] + KD × (e[n]− e[n − 1]),

(1)where e[n] = fset[n]− f [n] is the error signal, and n is the cur-rent time index. The values of KP, KI, and KD are the pro-portional, integral, and derivative gains, respectively, and are adjusted empirically to achieve a performance close to a criti-cally damped system. The tuning procedure is discussed later in the results session. U is the duty cycle of the laser pulse which changes within the interval between 0 and 1. To avoid excessive light exposure, especially during the first few sec-onds of the control process, the value of U is upper bounded to 0.5. Any value of U larger than this threshold is set to 0.5.

Occasional interruption of the CPU can potentially cause the data processing loop to miss few frames. Once the system detects a missing frame(s), a representative flow-rate value(s) for the missed frame(s) is calculated by interpolating the time trace of blood flow-rate to reduce the artifact caused by skipped frames, which is proven to be an essential operation.

3. Results

3.1. Influence of spatial-temporal configuration of photostimulation

We employed a Monte Carlo simulation software ([37–39]) to model light distribution inside the brain when the optical power is delivered to a spot on the surface of the tissue. By using the simulation results, we estimated the volume of activation (VoA) when the irradiance threshold for effective activation of ChR2 molecules was adjusted at 1 mW mm−2 [40]. Based on this analysis, when the same light intensity is delivered to a larger area, the corresponding VoA is wider but shallower (figure 2(a)). Simulations show that the VoA is a semi-linear function of the light intensity (figures 2(b) and S3); however, when the intensity is constant, changing the diameter of the illuminating spot, from 266 μm to 800 μm, had no significant impact on the estimated VoA (figure 2(c)). To demonstrate this observation in practice, we studied the effect of light intensity and illumination spot size on the evoked vascular response in vivo. We observed a strong correlation between

the blood flow-rate response (BFR) and the light intensity, or equivalently, the VoA. Meanwhile, increasing the diam-eter of the illuminating spot from 266 μm to 800 μm does not cause any significant change in the blood flow-rate (fig-ures 2(e)–(g)) or blood velocity responses (figure S4(e)). The magnitude of the vascular response is quantified by averaging the percent changes in the blood flow-rate within the interval starting at the stimulation onset and extending for 20 s. The traces of blood flow-rate show a rapid response following the stimulation onset and a prolonged tail which extends to over 20 s after stimulation for intense stimulations of 4 mW and 5.7 mW (n = 1 vessel) (figures 2(e) and S4(b) and (c)).

The length of stimulation has similar impact on the shape of the evoked BFR. To assess the effect of stimulation dura-tion, we conducted a set of experiments in which we kept the photostimulation pulses constant (I = 5.7 mW, W = 800 μm, Freq. = 15 Hz and DC = 50%) but we changed the duration from 1 s to 12 s as we simultaneously monitored the cross-sections of three vessels marked in figure 2(h). Out of these three monitoring sites, two cross-sections (sites 1 and 2) are selected to be on the main branches of the middle cerebral artery (MCA) while the third site is on a daughter branch of vessel 2 and this vessel is feeding the area farther away from the stimulation location.

For vessels 1 and 2, which are feeding the nearby regions, the amplitude and duration of the flow-rate and velocity responses increases as a function of the stimulus duration (figure 2(i)). For short durations (i.e. 1 s and 2 s), the shape of the BFR at site 2, which is closer to the stimulation loca-tion, can be described as a biphasic signal with a strong fast peak followed by a second relatively weaker and slower peak. When the duration of stimulation increases beyond 4 s, the slower peak becomes stronger and at stimulation durations of 8 s and 12 s, the second peak evidently merge with the first one (figures 2(i) and (j)). Similar behavior was observed for ten vessels in four animals. For each vessel the duration of response is calculated as the period over which the flow-rate response stays above 20% of its maximum. Figure 2(j) demonstrates the duration calculation for the representative animal. For stimulus durations of 1 s and 2 s, the response lasts for about 26 s. Stimulus durations above this range led to the response duration that increases almost linearly with the duration of stimulation in this animal. Figure 2(k) summarizes duration measurements for all the vessels. The error bars rep-resent ± standard deviation. For short stimulation periods (1 and 2 s), the flow-rate response in some vessels was below the sensitivity of our device and those datapoints were excluded from this analysis.

In the typical test shown in figure 2(i), the blood flow-rate at the third monitoring site remains flat after stimulation while the velocity drops significantly (the rightmost graph in figure 2(i)). The drop in the velocity is potentially a side effect of the vessel dilation which retro-propagates from the point of stimulation to this cross-section [41–43]. This data shows that each individual vessel can respond differently to the same stimulation pulse depending on the relative position of the vessel and the photostimulation site.

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3.2. Vascular receptive field

Results from the previous experiments suggested that each individual vessel potentially responds differently to the same stimulation pulse depending on the relative position of the vessel and the site of photostimulation. To further study this dependency, we conducted experiments in which photo-stimulation pulses (6 s duration, Freq. = 15 Hz, DC = 33%, I = 5.7 mW, and W = 461 μm) were delivered at multiple dis-crete locations (25 locations in a 5 by 5 matrix) across the field of view. In an example animal shown in figure 3, we analyzed the evoked vascular response in a set of four arteries which are

the main branches of the MCA (figure 3(a)). More examples are provided in supplementary note 4, figures S8 and S9.

Generally, stimulations in the close proximity of a vessel evoke a strong biphasic BFR in the vessel which attenuates as the stimulus moves away from the vessel. To better visualize the spatial tie between the blood flow dynamics in a vessel and the activity in the nearby tissue, a sensitivity map is created for each vessel based on its BFR data. The value of each pixel in this map represents the percent change in the blood flow-rate of the vessel in response to the optogenetic stimulation that is being delivered to the position of that pixel (supplemen-tary note 3 and figure 3(b)). This map conceptually resembles

Figure 2. Stimulation configurations: (a) The light distribution profile (λ = 450 nm, I = 5.7 mW) estimated by Monte Carlo simulations for three different beam diameters: 266 μm, 461 μm, and 800 μm. The color code represents the photon density and the dark line represents the isoline at 1 mW mm−2. (b) Effect of light intensity on the volume of activation (VoA). (c) Effect of the beam diameter on the VoA. (d) The fluorescent image captured from the cortical tissue showing the vascular network. Areas of stimulation with different spot sizes are marked by different colors. (e) Effect of stimulation intensity on the blood flow-rate response (BFR), for illumination diameters of 266 μm, 461 μm, and 800 μm (from top to bottom, respectively). The gray line indicates the duration of stimulation (4 s). The shaded area shows mean ± SD. (f) The relationship between the stimulation light intensity and the average percent change in the blood flow-rate from stimulation onset to 20 s afterward (n = 1 vessel). (g) The relationship between the simulated VoA and the in vivo BFR measurements (n = 1 vessel). (h) The fusion of fluorescent image and the OCT angiogram shows the vasculature network. The blue circle marks the area under illumination (I = 5.7 mW, duration varied from 1 s to 12 s). The arrows indicate the vessel cross-sections to be monitored by the OCT. (i) The blood flow-rate (top) and blood velocity (bottom) responses in the target vessels. Blood flow-rate at the measurement sites 1 and 2 increases after the stimulation onset, but not at site 3. Longer stimulus duration causes stronger and lasting responses at sites 1 and 2. The shaded color marks mean ± SD. (j) The normalized BFR at site 2. Longer stimulations translate to enduring responses which take more time before returning to the baseline. The dashed line marks 20% threshold. (k) BFR duration as a function of the stimulation duration (n = 5, 8, 10, 10, 10 vessels for 1, 2, 4, 8, 12 seconds of stimulation across four animals). The error bars represent mean ± SD.

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the receptive field (RF) of a neuron. In this example, vessel 2 shows the largest flow-rate response (54%) among the ves-sels. The peak in the response happens when photostimula-tion pulses are delivered right on top of the vessel and drops quickly as the spot moves away from that position. The size of the RF for vessel 2 is estimated by fitting a two-dimen-sional Gaussian function to the image. The standard deviation

of the fitted Gaussian along and perpendicular to the vessel are σalong = 734 μm and σperp = 539 μm, respectively (figure S7). As we expected, the most sensitive area of the RF is in the vicinity of each vessel’s feeding territory. It is possible to obtain similar maps for velocity and diameter responses as well (supplementary note 3), which provides extra informa-tion that is not present in the RF of blood flow-rate.

Figure 3. Vascular receptive fields. (a) The vascular network in the animal under test (top) and the 25 stimulation locations (bottom) in a form of a 5 by 5 matrix. Diameters of the circles are 461 μm to represent the actual beam diameter on the tissue surface. The red lines mark the vessel cross-sections that are imaged as monitoring sites. (b) The color-coded receptive field (RF) of the arterial blood flow-rate for the four selected vessel cross-sections. The images belong to t ≈ 25 s after stimulation on-set. The dark red color shows strong increase, green color represents zero response, and blue color represents decrease in the blood flow-rate in each vessel. The recorded blood flow-rate response in each stimulation location is displayed in the color-coded image. The shaded area represent mean ± SD across five trials. The RF for the vessel 2 is 734 μm long and 539 μm wide. The side panels for each receptive field represent the measured increase in blood flow-rate at the marked rows and columns. The error bars show the standard deviation across five trials. (c) The RFs for blood flow-rate, blood velocity, and vessel diameter measured at t = 5 s. The curves show the time traces of blood flow-rate, blood velocity, and vessel diameter percent change for selected vessels when the stimulation was located on vessel 2 (marked by an asterisk). No significant blood flow-rate increase in vessel 1 was observed; however, simultaneous dilation of the vessel caused some drop in its blood velocity.

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The RFs of vessels provide great information to predict the behavior of each vessel and the correlation between dif-ferent vessels when the microvascular network responds to some form of neurostimulation. For instance, blood flow-rate in vessel 1 drops in response to stimulation on the right side of the field of view. Figure 3(c) shows the RF of all four vessels at the instant when the largest drop in the blood flow-rate of vessel 1 was detected (t = 5 s, figures S5 and S6). Based on this data, the area where photostimulation induces some nega-tive flow-rate response in vessel 1 overlaps with the area that causes dilation in the same vessel. Our previous observation in figure 2(i) have already shown that the traces of blood velocity and blood flow-rate can be different when responding to the stimulation. The new observations re-establishes that blood velocity, blood flow-rate, and vessel diameter (figures 3(c), B1 and S6) are three different aspects of the vascular response. The RF maps demonstrate that increase in blood velocity and flow-rate in response to stimulation at the vicinity of a vessel is mostly local. Nevertheless, the same maps demonstrate that the stimulation location which induces maximum flow-rate response might differ from the one causing maximum change in the velocity. In contrast to the velocity and flow-rate maps, the RF for the diameter response (figure B1(b)) reveals that a stimulus close to a branch may cause dilation in some other down- or up-stream branches which may be far from the stimulation location. For example, the stimulation

which dilates vessel 2 also causes dilation in vessel 1. This can explain the difference between blood flow-rate and blood velocity receptive fields since the flow-rate and velocity in a vessel are coupled variables determined by the vessel diam-eter (supplementary note 4).

3.3. Simultaneous multi-site photostimulation

Characterizing the response of the vascular network to simul-taneous multi-site stimulation based on the response of the same vessel to individual stimulus is an important step in developing network blood flow controllers. Previously, recep-tive fields of vessels were obtained by applying one stimulus at a time and scanning the position of stimulus across a desired area. However, the vascular response to multiple simultaneous stimulations was not investigated. Our strategy for this study was to conduct a sequence of experiments to individually measure the vascular response to two stimulations which are delivered to separate locations. Then, use this information to predict the vascular response when stimulation pulses of sim-ilar or different magnitudes are delivered simultaneously to the same sites and confirm the results experimentally. To conduct these experiments, we selected three branches of the MCA in a transgenic mouse where two selected vessels (branch 1 and 2) were daughter branches of the third parent vessel (figure 4(a)). Stimulation locations were selected such that applying

Figure 4. Simultaneous multi-site stimulation. Stimulation sites in each panel are marked by blue circles. (a) Fusion of the fluorescence and angiographic images of the vascular network in the animal under test. The vessels of interest (a parent and its daughter branches) are highlighted by the red color. In this experiment, the stimulation is applied only to site 1. (b) Time traces of blood flow-rate in the selected vessels. BFRs in three vessels respond differently to the photostimulation of site 1. The gray line shows the period that the stimulation was applied. Each recording was repeated at least four times and the results were averaged. The solid line is the average across trials and the shaded area represents the standard deviation. (c) In this experiment, the stimulation was delivered only to site 2. (d) Time traces of blood flow-rate in selected vessels following the stimulation of site 2. BFRs in all three vessels were responsive at different levels to photostimulation of site 2. (e) We simultaneously stimulated sites 1 and 2 at half of the power used in the last two experiments of panels (a) and (c). (f) Time traces of blood flow-rate in all selected vessels for simultaneous stimulation test. (g) A summary of the amount of BFR (blood flow-rate averaged over 60 s) under different stimulation scenarios for the parent vessel and its daughter branches. The error bars represent the standard deviation across trials. (h) Summary of the difference between the prediction (average of response in scenarios 1 and 2) and the measured overall response (scenario 3) (n = 15 vessels in five animals). In this figure the median of the data is indicated by the central mark, the 25th and 75th percentiles are shown by the bottom and top edges of the box, respectively. The whiskers extend to the maximum/minimum data points that are not considered outliers, while the outliers are displayed by the ‘+’ symbol.

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stimulation at each site predominantly induces activity in one daughter branch while the other daughter branch responds minimally (figures 4(a)–(d)).

Following the designed strategy, we recorded three data sets corresponding to three different stimulation scenarios. In the scenarios 1 and 2 (figures 4(a) and (c)), stimulation pulses (I = 4.7 mW, D = 4 s, Freq. = 15 Hz, DC = 32%, W = 461 μm) were delivered to sites 1 and 2, respectively, while the BFRs in all the three vessels were recorded. In the third scenario (figure 4(e)) the photostimulation was time shared between sites 1 and 2 by using the fast galvanometric mir-rors (stimulation at each site: I = 4.7 mW, D = 4 s, Freq. = 7.5 Hz, DC = 16%, W = 461 μm). Therefore, each site was receiving half of the power delivered to the sites in the pre-vious scenarios.

To compare BFRs in vessels under different stimulation configurations, we calculated the temporal average of the blood flow-rate over a period of 60 s after the stimulation onset. This result is graphically illustrated in figure 4(g). Error bars in this diagram show the standard deviation of the data for different trials for each scenario (minimum of five trials). Vessel cross-sections were chosen close enough so that all the blood flow in the parent cross-section flows through the daughter cross-sections. Stimulation sites 1 and 2 were chosen to be close to the feeding territory of vessels 1 and 2, respectively. As a result, we expected to detect larger response to photostimula-tion in vessel 1. Similarly, vessel 2 was expected to be more responsive to stimulation at site 2 which was confirmed in the experiment. After applying the photostimulation at site 1, the amount of blood flow-rate increase in the parent vessel and daughter branches 1 and 2 were 7.4 ± 2.5%, 12.7 ± 3.4%, and 2.8 ± 2.9% (mean ± SD), respectively. Stimulation at site 2, generated 14.1 ± 3.2%, 9.9 ± 3.3%, and 21.1 ± 5.4% change in the blood flow-rate of the same vessels. The weighted average of the responses predicts a blood flow-rate increase of ∼10.8%, ∼11.3%, and ∼12% for the parent vessel and the branches 1 and 2 during the third scenario, respectively. The actual measurements for blood flow-rate increase were 10 ± 3.9%, 10.6 ± 3.4%, and 12.2 ± 4%. Our observations match the initial intuition based on the linear superposition of responses to individual stimulation. While figures 4(a)–(g) are from one representative animal, figure 4(h) reports the predic-tion error measured from 15 vessels in five animals. The pre-diction error is calculated as the difference between the linear prediction versus the actual flow-rate measurements in sce-nario 3. Based on this data, we hypothesize that the vascular network behavior is spatially quasi-linear to the extent that the response to a set of stimulations can be estimated by the superposition of individual responses.

3.4. Closed-loop blood flow controller

To illustrate the flexibility of optogenetics in manipulating cortical flow by modulating brain activity, we implemented a proportional-integral-derivative (PID) closed-loop controller. This compensator strives to adjust and maintain blood flow-rate in any target artery(ies) at a user defined set-point by tuning the duty cycle of stimulating light pulses (I = 5.7 mW,

Freq. = 15 Hz, W = 800 μm) (figure 5(a)). In the designed tests, the closed-loop control process is engaged for 240 s, preceded by 30 s of baseline and followed by 60 s or 90 s of post-stimulus recordings (figures 5(b) and section 2.8). The average of flow-rate during the baseline period is used as a reference to calculate percent changes in the blood flow-rate during the control period. A length-locked MA or EKF filter (supplementary note 6 and supplementary note 7, figure 7) is used to attenuate the cardiac and respiratory components in the recorded data.

The error signal is defined as the difference between the desired and measured percent increases in the blood flow-rate. In this configuration, the proportional (KP), integrating (KI), and derivative (KD) gains are the variables that translate the error signal to the stimulation pulse duration and need to be chosen properly to achieve a reliable closed-loop controller.

To tune the gain values, the desired blood flow-rate is set to 15% above the baseline and the gain values are increased one-by-one until a near to critically-damped flow-rate response is observed. In a critically damped system the blood flow-rate reaches the set point quickly without significant oscillations. We start by a small value of KP and keep KI = KD = 0. As KP increases, the error decreases (figure 6). The reduction in steady-state error, that can achieve by increasing the gain beyond 3.2, comes at the cost of large overshoots. For KP = 3.1, we achieve a fast rise time but no large oscillation in the blood flow-rate. When increasing the derivative gain from KD = 0 s to KD = 25 s, the stability improves slightly. However, deriva-tive gains above KD = 25 s (e.g. KD = 50 s) result in slight oscillations in the blood flow-rate. Introduction of a small integrating gain (e.g. KI = 1.5 × 10−31/s) has pronounced impact on reducing the steady-state error. A larger integrating gain (e.g. KI = 7.5 × 10−31/s) reduces the steady-state error further although it causes a small overshoot at the beginning of the controller’s response. An integrating gain between KI = 1.5 × 10−31/s and KI = 7.5 × 10−31/s help to strike a proper balance between the steady-state error versus fluc-tuations. A large gain value (e.g. KI = 35 × 10−31/s) results in noticeable oscillations in the blood flow-rate which could potentially lead to the destabilization of the compensator. When using the optimal gain values (KP = 3.1, KD = 25 s, and KI = 1.5 × 10−31/s or KI = 7.5 × 10−31/s), near to critically-damped blood flow-rate response is observed (figure 6). At least three trials were recorded for each parameter set-tings to confirm the repeatability of the results.

The experiment are repeated in three separate animals using the same PID gain values for the controller and similar closed-loop performances are achieved. Based on this observation, at least for the MCA and its main branches, the same values can be used without the need for readjustments. By repeating the experiment, we notice that the closed-loop mechanism can readily lock on blood flow-rate increase percentages of 5%, 10% and 15%. In one animal, we even tested larger changes up to 25% and still desired response was achieved. As we increase the desired set-point further, the time-averaged pulse width (actu-ator value) as well as the time-averaged error between the set-point and the output also increased as displayed in figure 5(d). The zoomed-in window in this figure captures the close relation

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between the flow-rate and stimulation pulse width for a few selected trials. Whenever some drop in the blood flow-rate is detected, the controller increases the pulse width, which helps rise the blood flow-rate back to the desired set-point rapidly.

In this work, the cardiac pulsation removal is achieved by filtering the blood flow-rate response with a length-locked moving-averaging or an EKF. The Length-locked MA

algorithm is relatively simple with low computational cost. In contrast, EKF is more complex with ability to capture the state of the system when proper model is provided. To select the proper filtering mechanism for CLC applications, we compared the performance of the EKF versus the length-locked MA and no significant difference was observed in the performance of closed-loop controller (figure 7). Although

Figure 5. Optogenetic-based closed-loop control of blood flow. (a) Control protocol: The system records the blood flow-rate level in a target artery via SD-OCT imaging. The recorded data are processed in real-time and compared to a user-defined blood flow-rate level. Based on the difference between the recorded and the user-defined blood flow-rate level, the compensator calculates the pulse width and updates the stimulation waveform of a pulsed laser to adjust the level of induced blood flow-rate response and minimize the error. The fluorescence path (520 nm beam) is used to visualize the stimulation pattern or the vascular network. (b) Smoothed blood flow-rate (top) and optogenetic pulse width (bottom) during a control epoch (330 s). Data collection contains 30 s of baseline recording followed by 240 s of control period and 60 s (or 90 s) of post stimulation recording. The target blood flow-rate level is shown by a red solid line in the top plot. (c) Vascular network in the animal under test. The area of illumination is marked by the blue circle. The arrow points to the vessel cross-section under study. (d) Maintaining blood flow-rate at different set-points. Each experiment was repeated three times when the variables of the PID compensator were adjusted at KP = 3.1, KD = 25 s, and KI = 1.5 × 10−31/s. The first row shows the traces of BFR for three experiments each targeting a different set-point on same artery. The solid line represents the average of trials. The inset magnifies 30 s duration of each test to substantiate the correlation between the flow-rate (gray line) and the stimulation pulse width (blue line) for a typical trial. The second row displays the time trace of the pulse width in each test. The last row shows the distribution of blood flow-rate during the last 120 s of the control session. The center mark is the median, the whiskers are the maximum and minimum, and the box edges are the 25th and 75th percentiles of the data.

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at this stage no noticeable difference between the perfor-mance of the two methods, we anticipate that the EKF can offer a superior performance in more advanced controller mechanisms.

4. Discussion

In this study, we proposed several new methods to discern different temporal and spatial characteristics of the vascular response to direct brain stimulation. The potential of the new approach for capturing such characteristics was demonstrated by simultaneous measurement of blood flow-rate, blood velocity, and vessel diameter to obtain novel and comprehen-sive datasets to analyze the behavior of the vascular network. Since many of our observations were the first of this kind at

the vascular level, it is valuable to compare our findings with the results of preceding reports.

Our investigation of temporal characteristics of the blood flow dynamics following optical neurostimulation revealed a biphasic BFR comprised of an early fast transient (peaks at ∼5 s) and a slow prolong (peaks around 10 s–40 s) increase in blood flow-rate. Increasing the duration of photostimula-tion increased the length and amplitude of the measured BFR particularly at the slow phase of the response. Meanwhile, the response to short light exposures lasted for at least 25 s but exceeded 45 s for longer stimulus durations (e.g. 12 s). Typically, the slow phase of the response to longer light expo-sures was more persistent. Generally, BFRs were followed by a slight decrease in the blood flow-rate which is consistent with previous observations of post-stimulation vasoconstric-tion (e.g. see [12, 44]) or reduction in the blood volume (e.g.

Figure 6. Tuning the PID gain values when the system targets to adjust the BF of 15% above the resting state. KP = 3.1 resulted in fast response and low oscillations in the blood flow-rate. Larger values of KP led to large flow-rate overshoots. Flow-rate fluctuations decreased at KD = 25 s and increased when KD was set to 50 s. The steady state error was significantly reduced for KI = 1.5 × 10−31/s. At KI = 7.5 × 10−31/s, the steady state error reduced further and no large fluctuation in the blood flow-rate was observed. Larger KI values (35 × 10−31/s) caused some oscillations in blood flow-rate. The last column in this panel shows the distribution of the blood flow-rate values during the last 2 min of each control session. Longer whiskers correspond to stronger fluctuations in the blood flow-rate.

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[45]). Prior to our study, a biphasic change in total hemo-globin and oxyhemoglobin was reported by Kennerley et al [46]; however, the true cause of such early and late phases in hemodynamic response remains to be investigated.

We expected the blood flow-rate to respond to the collec-tive level of activity in nearby neurons. We observed that the BFR is a quasi-linear function of the volume of activation. Other researchers have also reported similar relations. For instance, Iordanova et al [10] measured an upward trend in the cerebral blood flow (CBF) response when the intensity of optogenetic stimulation was increased up to 10 mW. However, for light intensities above 10 mW, the CBF response saturated. Similarly, in peripheral stimulations, a quasi-linear relation between cerebral blood volume (CBV) and the level of local neural activity was reported (e.g. [47, 48]). While our obser-vations also show that changes in CBV are quasi-linearly proportional to the stimulation power, simultaneous measure-ments of the vascular flow-rate, CBV, and neural activity are required to obtain a complete model which captures all main features of the correlation between neural activity and the corre sponding hemodynamics.

To investigate the spatial extent of the correlation between neural activity and the response of pial vessels, we proposed a novel method to measure vessels’ receptive fields. For an artery of diameter 30 μm, the full width at half maximum (FWHM) extension of the receptive field was ∼1.4 mm wide. However, based on our simulations, the VoAs in our tests (figure 2(a)) spread about 1 mm in the lateral direction. While the VoA is comparable to the measured FWHM, it still implies that the spatial extent of the receptive field was over estimated. Prior to this study, findings of OHerron et al in cat visual cortex indicated a correlation between the dilation of parenchymal arterioles and the synaptic or spiking activity in neurons up to 200 μm farther away from the vessels [49]. Moreover, observations by Nishimura et al on rat cortex dem-onstrated that the blockage of a penetrating artery affects the blood flow in a region of radius ∼350 μm [50], which can cause a microinfarction in an area as large as 460 μm in diam-eter [51]. It is important to note that the latter study does not investigate the neuro-vascular correlation, rather it studies the region of physiological influence of penetrating arterioles. Although, our findings for pial artery (diameter of ∼30 μm), cannot be directly compared to the previous reports, due to the difference in the vessel size or the nature of the study; our results do not contradict with those observations either. The relatively large vessel under test in our study was feeding several penetrating arterioles which were widely distributed in the region. Evidently, a larger vessel diameter translates to a larger receptive field. Stimulating the territory of each penetrating arteriole affects the upstream flow and contributes to the shape and distribution of the receptive field for such a pial vessel. Practically, it is challenging to adapt the pre-vious methods to measure the influential region of an arbitrary vessel, since they are very invasive or are confined to measure-ments in the visual cortex. While, the proposed method does not require vessel disruption and is not limited to a specific region of the brain cortex of transgenic animals. Although, the current measurements are presented for arteries of size 30 μm

or larger, in combination with high-resolution OCT or multi-photon microscopy the same approach might be applicable to obtain the receptive field of parenchymal arterioles of smaller diameter as well.

In our experiments, we mainly observed blood flow ampli-fication at the vicinity of stimulation site; however, in the surrounding tissue, we occasionally detected some form of reduction in the flow-rate. This decrease in the blood flow-rate in the surrounding tissue is followed by some drop in blood oxygenation level in the region which was also observed by other research groups and considered as a center-surround hemodynamic response [52, 53]. Nonetheless, the sign-aling pathway and the mechanisms that mediate this form of response are not well-understood. We anticipate that meas-uring receptive fields of the main vessels over a large field of view and performing hemodynamic recording simulta-neously together with other imaging modalities (e.g. multi-spectral and metabolic imaging) can help elucidate details of the mechanisms that cast such center-surround hemodynamic responses.

We learned from our multi-site stimulation experiments that the blood flow-rate response following two simultaneous optogenetic stimulations can be estimated by the averaging blood flow-rate responses to the individual stimulations. On the other hand, extracting vascular receptive fields can help describe the correlation between the spatial distribution of neural activity and the corresponding vasodynamics. We can combine these two principles to predict the blood flow-rate response to any arbitrary illumination pattern by first decom-posing the pattern to a group of confined stimulations and then estimating the overall response as the weighted superposition of responses to each individual element. Considering this approach, it would become a possibility to use this informa-tion to design the spatial and temporal extent of our stimula-tion patterns to engineer desired distributions of blood flow in the cortical tissue.

Examining, validating, or generating new hypotheses and models via a closed-loop mechanism has become a common practice in recent years [17, 18]; however, no such method has been proposed for the cerebral blood flow. In this paper, we also demonstrated the ability of a closed-loop controller to manipulate the flow-rate of blood in the cortex of transgenic animals. The gain variables of the compensator were tuned to obtain a near to critically-damped response in the blood flow-rate of one animal. The same values were used later in other animals and yet near-critically damped responses were recorded which potentially implies that a similar circuit-model describes the relation between vascular flow and an exogenous input across different animals. Investigating the blood flow via a closed-loop mechanism opens an avenue to study long-term properties of the response of regional and global blood supply to long exogenous perturbation in neural activity.

Moreover, the closed-loop algorithm that we presented in this article can be expanded to form a distributed controller which maintains a desired spatial-temporal pattern of blood flow-rate in a large scale vascular network. For this purpose, the compensator should assimilate the spatial influence of a local perturbation on off-target vessels (figures 2(i) and 3, and

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[44]), which can be well estimated when the vascular recep-tive fields are measured. By upgrading to a model predictive controller (MPC), instead of the basic PID algorithm used in this work, the effect of long and biphasic vascular reaction to the stimulation can be incorporated in the control algorithm to improve the efficiency of photostimulation.

SD-OCT can provide depth-resolved information up to several hundred micrometers deep in the brain; however, in practice, the effective imaging range may be limited by the depth of focus (DOF) of the optical setup. To realize a fine lateral resolution (∼5 μm) in the shortwave infrared spectrum, an optical configuration with a moderate numerical aperture (∼0.1) should be used. Such a numerical aperture limits the optical DOF to ∼100 μm. The imaging resolution and signal to noise ratio degrades significantly outside this range. This limitation hinders simultaneous recording from vessels that are spread across the imaging depth. Some non-scanning optical imaging techniques, such as laser speckle imaging (LSCI) and intrinsic signal optical imaging (ISOI), provide informa-tion from up to several hundred micrometers deep in the brain ([54–56]) at a faster imaging frame rate than typical SD-OCT scanners. It is important to note that LSCI and ISOI provide an

en face image of the blood flow with no depth resolved infor-mation. The lateral resolution in these imaging modalities is typically larger than 20 μm and depending on the numerical aperture and the focal plane location of the imaging setup can exceed 100 μm ([54, 55]). Due to these factors LSCI and ISOI are less appropriate for the type of vasodynamic analysis that was proposed for small arteries in this work; however, we anticipate a combination of these imaging techniques with SD-OCT can provide information-rich data sets to investigate center-surround hemodynamic or negative blood oxygenation level dependent (BOLD) fMRI responses.

In multiple experiments, we showed that blood flow-rate and blood velocity respond differently to photostimulation pulses (figures 2(i) and 3). Such discrepancy is the result of the way these variables are related to changes in the vessel diameter which is controlled by muscle cells. Our observa-tions were mainly limited to small arteries but we did not study penetrating and parenchymal arterioles in this work. Investigation of small changes in a vessel diameter with OCT is challenging (supplementary note 5). Accompanying the OCT data with a second high resolution imaging modality, such as two-photon microscopy, can increase the accuracy of

Figure 7. Comparison between the Kalman and moving average pulsation removal filters used in the closed-loop brain control tests. (a) Maintaining blood flow-rate at three different levels after removing pulsations of cardiac cycle by a Kalman filter. Each experiment was repeated three times to ensure repeatability. The root mean square error between the desired and measured flow-rate is 2.09%. (b) The box plot of the percent blood flow-rate change for the last two minutes of each control trial. The center line shows the median, the whiskers are the maximum and minimum, and the box edges are the 25th and 75th percentiles of the data. (c) The same figures as (a) but for the case when we used length-locked MA algorithm to remove the heart pulsation. The root mean square error between the desired and measured flow-rate is 2.38%. (d) The box plots of the data for the last two minutes of control sessions.

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the vascular diameter detection and improve our insight into different aspects of vascular response. Nevertheless, studying mechanisms that regulate the flow of blood in the brain by using imaging techniques that solely measure vessel dilation/constriction can be misleading and interpretation of such data should be handled cautiously.

Acknowledgments

This project was supported by the Army Research Office (ARO) grant# 68750-LS-II, the National Science Foundation (NSF) Career Award grant# 1454300, the National Science Foundation (NSF) grant# 1830145, the Brain and Behavior Research Foundation (NARSAD) Young Investigator Award grant# 20610 and grant# 23620, and the University of Wisconsin research growth initiative (RGI) grant# 101X213 and grant# 101X254 to Ramin Pashaie, and the Defense Advanced Research Projects Agency MTO under the auspices of Dr J Judy through the Space and Naval Warfare Systems Center Grant #N66001-12-C-4025 to Justin C Williams.

Appendix A. Electrocorticography

The evoked brain activity during optogenetic stimulation was confirmed by electrocorticography (ECoG) for some of the animals. For this purpose, after thinning the skull, and prior to the installation of the coverslip, a carbon layered electrode array (CLEAR) device ([36, 57]) was placed on the region of interest. The CLEAR device offers >90% transmission in the optical spectrum from ultraviolet to infrared. It allows for concurrent optogenetic stimulation and electrocorticography [36]. Optogenetic stimulation applied by an optical pulse train for 4 s at an intensity of I = 4 mW, and pulse frequency of 15 Hz. The pulse width was set to 1.3 m s, 2.7 m s, or 5.3 m s. The data acquisition was performed by using a 32 Channel Tucker-Davis Technologies Neurophysiology System (Tucker-Davis Technologies, Alachua, FL) at the sampling rate of 3 KHz. Each recording was started 10 s before stimu-lation train and continued for at least 60 s and repeated five trials for each pulse duration. The recorded signals were then band-pass filtered between 0.05 Hz and 150 Hz (figure A1).

Appendix B. Vasodilation can be the cause of discrepancy between velocity and flow-rate responses

The flow-rate and velocity receptive fields of the vessels in figure 3 show some subtle differences. Since the blood velocity and blood flow-rate are two different measures which are related by the cross-sectional area of the vessel lumen, one postulation is that the vessel dilation/constriction, controlled by the smooth muscle cells, can cause the difference between two receptive fields (RFs). To verify whether the dilation can explain the dissimilarities between the flow-rate and velocity maps, we produced a spurious flow-rate receptive field by combining the RFs generated by the velocity and diameter

responses. The new RF matched the measured flow-rate RF (figure B1(d)), suggesting that the mismatch between flow-rate and velocity maps can in part be caused by the vessel dilation. The discrepancy between the flow-rate, velocity, and dilation implies that the analysis of the vascular response, through measuring only the vessel diameter, is insufficient and potentially misleading since dilations in some pial vessels coincide with a drop in the flow-rate.

Blood flow in penetrating arterioles is directly controlled by adjusting the vessel diameter. Even though pial arteries possess smooth muscle cells, their resistances are usually so small that fractional changes in their diameter does not mod-ulate the blood flow similar to the penetrating arterioles. In other words, blood flow in pial vessels is mainly a function of the flow in the downstream. As a result, in pial vessels, we can observe discrepancies between changes in blood flow-rate, blood velocity, and vessel diameter in response to stim-ulation. If penetrating arterioles are the main compartments that control blood flow in the network, then changes in their blood flow-rate and diameter should be coherent. On the other hand, there have been evidences which suggest that capillaries also contribute to blood flow regulation. If the contribution of

Figure A1. Brain electrical activity during optogenetic stimulation. (a) Average of 5 ECoG signal recorded during optogenetic stimulation (duration of 4 s). The blue line shows the stimulation period. A robust and strong electrical activity was detected at each optical pulse (b) Ensemble average (n = 60) of the electrical pulse evoked by optical neurostimulation for three different pulse widths. The dot indicates the stimulation start. The shaded area represents mean ± SD. The amplitude of brain activity potential increases as the stimulation pulse duration increases.

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Figure B1. Velocity, diameter, and flow-rate receptive fields. (a) velocity receptive fields of four vessels under study. The response in blood velocity is stronger when we stimulate the area closer to the territory of a vessel. The maximum velocity increase (31%) was observed in vessel 4. (b) Diameter receptive fields. Unlike blood velocity, we observed that the map of vessel dilation does not necessarily colocate with the territory of the vessels. Basically, we observed that the maximum dilation for vessel 1 and 4 happens when we stimulate the territory of vessel 2. Stimulating the territory of these vessels did not evoke a noticeable dilation. This can be justified by the endothelial signaling hypothesis [42]. (Since the lateral resolution of our OCT is ∼5 μm, accurate measurements of sub-micron changes in vessel diameters was quite challenging.) (c) flow-rate receptive fields. Vessel 2 shows the largest flow-rate response (54% increase). Similar to velocity receptive fields, the maximum response happens when the light illumination is on the vessel and the response drops quickly as we move away from the vessel. Despite this similarity, we observed some differences between the two receptive fields. For example, in vessel 1 and 2, we see that the shape of the receptive fields are different for blood flow-rate and velocity. Another example, is the vessel 4. This vessel shows the largest increase in its blood velocity, while the largest increase in the blood flow-rate is observed in vessel 2. The difference between the receptive fields of blood flow-rate and velocity is potentially due to the dilation in these vessels. (d) Estimated flow-rate receptive fields when we combined the diameter and the velocity fields to estimate the flow-rate response. The estimated flow-rate was calculated by (F̂RF = (1 + DRF)

2(1 + VRF)− 1, where VRF and DRF are the velocity and diameter receptive fields, and F̂RF is the estimated flow-rate receptive field. The estimated flow-rate receptive field matches the flow-rate measurements in panel (c).

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capillaries is significant, we expect to once again see some discrepancy between the traces of blood flow-rate and vessel diameter even in penetrating arterioles.

ORCID iDs

Ramin Pashaie https://orcid.org/0000-0002-4191-3872

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