Oxyhemoglobin and Cerebral Blood Flow Transients Detect Infarction in Rat Focal Brain Ischemia.

Spreading depolarizations (SD) refer to the near-complete depolarization of neurons that is associated with brain injuries such as ischemic stroke. The present gold standard for SD monitoring in humans is invasive electrocorticography (ECoG). A promising non-invasive alternative to ECoG is diffuse optical monitoring of SD-related flow and hemoglobin transients. To investigate the clinical utility of flow and hemoglobin transients, we analyzed their association with infarction in rat focal brain ischemia. Optical images of flow, oxy-hemoglobin, and deoxy-hemoglobin were continuously acquired with Laser Speckle and Optical Intrinsic Signal imaging for 2 h after photochemically induced distal middle cerebral artery occlusion in Sprague-Dawley rats (n = 10). Imaging was performed through a 6 × 6 mm window centered 3 mm posterior and 4 mm lateral to Bregma. Rats were sacrificed after 24 h, and the brain slices were stained for assessment of infarction. We mapped the infarcted area onto the imaging data and used nine circular regions of interest (ROI) to distinguish infarcted from non-infarcted tissue. Transients propagating through each ROI were characterized with six parameters (negative, positive, and total amplitude; negative and positive slope; duration). Transients were also classified into three morphology types (positive monophasic, biphasic, negative monophasic). Flow transient morphology, positive amplitude, positive slope, and total amplitude were all strongly associated with infarction (p < 0.001). Associations with infarction were also observed for oxy-hemoglobin morphology, oxy-hemoglobin positive amplitude and slope, and deoxy-hemoglobin positive slope and duration (all p < 0.01). These results suggest that flow and hemoglobin transients accompanying SD have value for detecting infarction.

Real-time tracking of brain oxygen gradients and blood flow during functional activation.

Significance: Cerebral metabolic rate of oxygen ( CMRO 2 ) consumption is a key physiological variable that characterizes brain metabolism in a steady state and during functional activation. Aim: We aim to develop a minimally invasive optical technique for real-time measurement of CMRO 2 concurrently with cerebral blood flow (CBF). Approach: We used a pair of macromolecular phosphorescent probes with nonoverlapping optical spectra, which were localized in the intra- and extravascular compartments of the brain tissue, thus providing a readout of oxygen gradients between these two compartments. In parallel, we measured CBF using laser speckle contrast imaging. Results: The method enables computation and tracking of CMRO 2 during functional activation with high temporal resolution ( ∼ 7 Hz ). In contrast to other approaches, our assessment of CMRO 2 does not require measurements of CBF or hemoglobin oxygen saturation. Conclusions: The independent records of intravascular and extravascular partial pressures of oxygen, CBF, and CMRO 2 provide information about the physiological events that accompany neuronal activation, creating opportunities for dynamic quantification of brain metabolism.

Blood flow response to orthostatic challenge identifies signatures of the failure of static cerebral autoregulation in patients with cerebrovascular disease.

BACKGROUND: The cortical microvascular cerebral blood flow response (CBF) to different changes in head-of-bed (HOB) position has been shown to be altered in acute ischemic stroke (AIS) by diffuse correlation spectroscopy (DCS) technique. However, the relationship between these relative ΔCBF changes and associated systemic blood pressure changes has not been studied, even though blood pressure is a major driver of cerebral blood flow. METHODS: Transcranial DCS data from four studies measuring bilateral frontal microvascular cerebral blood flow in healthy controls (n = 15), patients with asymptomatic severe internal carotid artery stenosis (ICA, n = 27), and patients with acute ischemic stroke (AIS, n = 72) were aggregated. DCS-measured CBF was measured in response to a short head-of-bed (HOB) position manipulation protocol (supine/elevated/supine, 5 min at each position). In a sub-group (AIS, n = 26; ICA, n = 14; control, n = 15), mean arterial pressure (MAP) was measured dynamically during the protocol. RESULTS: After elevated positioning, DCS CBF returned to baseline supine values in controls (p = 0.890) but not in patients with AIS (9.6% [6.0,13.3], mean 95% CI, p < 0.001) or ICA stenosis (8.6% [3.1,14.0], p = 0.003)). MAP in AIS patients did not return to baseline values (2.6 mmHg [0.5, 4.7], p = 0.018), but in ICA stenosis patients and controls did. Instead ipsilesional but not contralesional CBF was correlated with MAP (AIS 6.0%/mmHg [- 2.4,14.3], p = 0.038; ICA stenosis 11.0%/mmHg [2.4,19.5], p < 0.001). CONCLUSIONS: The observed associations between ipsilateral CBF and MAP suggest that short HOB position changes may elicit deficits in cerebral autoregulation in cerebrovascular disorders. Additional research is required to further characterize this phenomenon.

Noninvasive optical monitoring of critical closing pressure and arteriole compliance in human subjects.

The critical closing pressure ( CrCP) of the cerebral circulation depends on both tissue intracranial pressure and vasomotor tone. CrCP defines the arterial blood pressure ( ABP) at which cerebral blood flow approaches zero, and their difference ( ABP - CrCP) is an accurate estimate of cerebral perfusion pressure. Here we demonstrate a novel non-invasive technique for continuous monitoring of CrCP at the bedside. The methodology combines optical diffuse correlation spectroscopy (DCS) measurements of pulsatile cerebral blood flow in arterioles with concurrent ABP data during the cardiac cycle. Together, the two waveforms permit calculation of CrCP via the two-compartment Windkessel model for flow in the cerebral arterioles. Measurements of CrCP by optics (DCS) and transcranial Doppler ultrasound (TCD) were carried out in 18 healthy adults; they demonstrated good agreement (R = 0.66, slope = 1.14 ± 0.23) with means of 11.1 ± 5.0 and 13.0 ± 7.5 mmHg, respectively. Additionally, a potentially useful and rarely measured arteriole compliance parameter was derived from the phase difference between ABP and DCS arteriole blood flow waveforms. The measurements provide evidence that DCS signals originate predominantly from arteriole blood flow and are well suited for long-term continuous monitoring of CrCP and assessment of arteriole compliance in the clinic.

Pressure modulation algorithm to separate cerebral hemodynamic signals from extracerebral artifacts.

We introduce and validate a pressure measurement paradigm that reduces extracerebral contamination from superficial tissues in optical monitoring of cerebral blood flow with diffuse correlation spectroscopy (DCS). The scheme determines subject-specific contributions of extracerebral and cerebral tissues to the DCS signal by utilizing probe pressure modulation to induce variations in extracerebral blood flow. For analysis, the head is modeled as a two-layer medium and is probed with long and short source-detector separations. Then a combination of pressure modulation and a modified Beer-Lambert law for flow enables experimenters to linearly relate differential DCS signals to cerebral and extracerebral blood flow variation without a priori anatomical information. We demonstrate the algorithm's ability to isolate cerebral blood flow during a finger-tapping task and during graded scalp ischemia in healthy adults. Finally, we adapt the pressure modulation algorithm to ameliorate extracerebral contamination in monitoring of cerebral blood oxygenation and blood volume by near-infrared spectroscopy.

Modified Beer-Lambert law for blood flow.

We develop and validate a Modified Beer-Lambert law for blood flow based on diffuse correlation spectroscopy (DCS) measurements. The new formulation enables blood flow monitoring from temporal intensity autocorrelation function data taken at single or multiple delay-times. Consequentially, the speed of the optical blood flow measurement can be substantially increased. The scheme facilitates blood flow monitoring of highly scattering tissues in geometries wherein light propagation is diffusive or non-diffusive, and it is particularly well-suited for utilization with pressure measurement paradigms that employ differential flow signals to reduce contributions of superficial tissues.

Optical bedside monitoring of cerebral blood flow in acute ischemic stroke patients during head-of-bed manipulation.

BACKGROUND AND PURPOSE: A primary goal of acute ischemic stroke (AIS) management is to maximize perfusion in the affected region and surrounding ischemic penumbra. However, interventions to maximize perfusion, such as flat head-of-bed (HOB) positioning, are currently prescribed empirically. Bedside monitoring of cerebral blood flow (CBF) allows the effects of interventions such as flat HOB to be monitored and may ultimately be used to guide clinical management. METHODS: Cerebral perfusion was measured during HOB manipulations in 17 patients with unilateral AIS affecting large cortical territories in the anterior circulation. Simultaneous measurements of frontal CBF and arterial flow velocity were performed with diffuse correlation spectroscopy and transcranial Doppler ultrasound, respectively. Results were analyzed in the context of available clinical data and a previous study. RESULTS: Frontal CBF, averaged over the patient cohort, decreased by 17% (P=0.034) and 15% (P=0.011) in the ipsilesional and contralesional hemispheres, respectively, when HOB was changed from flat to 30°. Significant (cohort-averaged) changes in blood velocity were not observed. Individually, varying responses to HOB manipulation were observed, including paradoxical increases in CBF with increasing HOB angle. Clinical features, stroke volume, and distance to the optical probe could not explain this paradoxical response. CONCLUSIONS: A lower HOB angle results in an increase in cortical CBF without a significant change in arterial flow velocity in AIS, but there is variability across patients in this response. Bedside CBF monitoring with diffuse correlation spectroscopy provides a potential means to individualize interventions designed to optimize CBF in AIS.

Continuous optical monitoring of cerebral hemodynamics during head-of-bed manipulation in brain-injured adults.

INTRODUCTION: Head-of-bed manipulation is commonly performed in the neurocritical care unit to optimize cerebral blood flow (CBF), but its effects on CBF are rarely measured. This pilot study employs a novel, non-invasive instrument combining two techniques, diffuse correlation spectroscopy (DCS) for measurement of CBF and near-infrared spectroscopy (NIRS) for measurement of cerebral oxy- and deoxy-hemoglobin concentrations, to monitor patients during head-of-bed lowering. METHODS: Ten brain-injured patients and ten control subjects were monitored continuously with DCS and NIRS while the head-of-bed was positioned first at 30° and then at 0°. Relative CBF (rCBF) and concurrent changes in oxy- (ΔHbO2), deoxy- (ΔHb), and total-hemoglobin concentrations (ΔTHC) from left/right frontal cortices were monitored for 5 min at each position. Patient and control response differences were assessed. RESULTS: rCBF, ΔHbO2, and ΔTHC responses to head lowering differed significantly between brain-injured patients and healthy controls (P < 0.02). For patients, rCBF changes were heterogeneous, with no net change observed in the group average (0.3 ± 28.2 %, P = 0.938). rCBF increased in controls (18.6 ± 9.4 %, P < 0.001). ΔHbO2, ΔHb, and ΔTHC increased with head lowering in both groups, but to a larger degree in brain-injured patients. rCBF correlated moderately with changes in cerebral perfusion pressure (R = 0.40, P < 0.001), but not intracranial pressure. CONCLUSION: DCS/NIRS detected differences in CBF and oxygenation responses of brain-injured patients versus controls during head-of-bed manipulation. This pilot study supports the feasibility of continuous bedside measurement of cerebrovascular hemodynamics with DCS/NIRS and provides the rationale for further investigation in larger cohorts.

The challenge of connecting the dots in the B.R.A.I.N.

The Brain Research through Advancing Innovative Neurotechnologies (BRAIN) Initiative has focused scientific attention on the necessary tools to understand the human brain and mind. Here, we outline our collective vision for what we can achieve within a decade with properly targeted efforts and discuss likely technological deliverables and neuroscience progress.

Influence of probe pressure on the diffuse correlation spectroscopy blood flow signal: extra-cerebral contributions.

A pilot study explores relative contributions of extra-cerebral (scalp/skull) versus brain (cerebral) tissues to the blood flow index determined by diffuse correlation spectroscopy (DCS). Microvascular DCS flow measurements were made on the head during baseline and breath-holding/hyperventilation tasks, both with and without pressure. Baseline (resting) data enabled estimation of extra-cerebral flow signals and their pressure dependencies. A simple two-component model was used to derive baseline and activated cerebral blood flow (CBF) signals, and the DCS flow indices were also cross-correlated with concurrent Transcranial Doppler Ultrasound (TCD) blood velocity measurements. The study suggests new pressure-dependent experimental paradigms for elucidation of blood flow contributions from extra-cerebral and cerebral tissues.

Blood flow and oxygenation changes due to low-frequency repetitive transcranial magnetic stimulation of the cerebral cortex.

Transcranial magnetic stimulation (TMS) modulates processing in the human brain and is therefore of interest as a treatment modality for neurologic conditions. During TMS administration, an electric current passing through a coil on the scalp creates a rapidly varying magnetic field that induces currents in the cerebral cortex. The effects of low-frequency (1 Hz), repetitive TMS (rTMS) on motor cortex cerebral blood flow (CBF) and tissue oxygenation in seven healthy adults, during/after 20 min stimulation, is reported. Noninvasive optical methods are employed: diffuse correlation spectroscopy (DCS) for blood flow and diffuse optical spectroscopy (DOS) for hemoglobin concentrations. A significant increase in median CBF (33%) on the side ipsilateral to stimulation was observed during rTMS and persisted after discontinuation. The measured hemodynamic parameter variations enabled computation of relative changes in cerebral metabolic rate of oxygen consumption during rTMS, which increased significantly (28%) in the stimulated hemisphere. By contrast, hemodynamic changes from baseline were not observed contralateral to rTMS administration (all parameters, p>0.29). In total, these findings provide new information about hemodynamic/metabolic responses to low-frequency rTMS and, importantly, demonstrate the feasibility of DCS/DOS for noninvasive monitoring of TMS-induced physiologic effects.

Neurovascular coupling varies with level of global cerebral ischemia in a rat model.

In this study, cerebral blood flow, oxygenation, metabolic, and electrical functional responses to forepaw stimulation were monitored in rats at different levels of global cerebral ischemia from mild to severe. Laser speckle contrast imaging and optical imaging of intrinsic signals were used to measure changes in blood flow and oxygenation, respectively, along with a compartmental model to calculate changes in oxygen metabolism from these measured changes. To characterize the electrical response to functional stimulation, we measured somatosensory evoked potentials (SEPs). Global graded ischemia was induced through unilateral carotid artery occlusion, bilateral carotid artery occlusion, bilateral carotid and right subclavian artery (SCA) occlusion, or carotid and SCA occlusion with negative lower body pressure. We found that the amplitude of the functional metabolic response remained tightly coupled to the amplitude of the SEP at all levels of ischemia observed. However, as the level of ischemia became more severe, the flow response was more strongly attenuated than the electrical response, suggesting that global ischemia was associated with an uncoupling between the functional flow and electrical responses.

Effect of vagus nerve stimulation during transient focal cerebral ischemia on chronic outcome in rats.

The aim of this study was to investigate the effect of vagus nerve stimulation (VNS) on infarct volume and neurological recovery up to 3 weeks following transient focal cerebral ischemia. Transient ischemia was produced by filament occlusion of the proximal middle cerebral artery (MCA) in rats. The right vagus nerve was stimulated starting 30 min after MCA occlusion and consisted of 30-sec pulse trains (20 Hz) delivered to the animal's right vagus nerve every 5 min for a total period of 60 min (n = 10). All the procedures were duplicated, but no stimulus was delivered, in a control group (n = 10). Neurological evaluations were performed in all animals at 24 hr, 48 hr, 1 week, 2 weeks, and 3 weeks after MCA occlusion; animals were euthanized; and neuronal damage was evaluated in hematoxylin-eosin-stained sections. The ischemic lesion volume was smaller in the VNS-treated animals in comparison with the nonstimulated group (P < 0.02). Although the functional score in both treated and untreated groups improved over the 3-week observation period (P < 0.001), there was still a statistically significant improvement reszulting from VNS treatment compared with control animals (P < 0.05). Cerebral blood flow changes in the MCA territory during ischemia did not differ between the VNS-treated animals (31.9% ± 10.4% of baseline) and control animals (29.9% ± 9.1%; P = 0.6). Stimulation of the vagus nerve for only a brief period early in ischemia provides neuroprotection in transient ischemia, with neuroprotection persisting for at least 3 weeks.

Blood oxygen level dependent angiography (BOLDangio) and its potential applications in cancer research.

Clinically, development of anti-angiogenic drugs for cancer therapy is pivotal. Longitudinal monitoring of tumour angiogenesis can help clinicians determine the effectiveness of anti-angiogenic therapy. Blood oxygen level dependent (BOLD) effect has been widely used for functional imaging and tumour oxygenation assessment. In this study, the BOLD effect is investigated under different levels of oxygen inhalation for the development of a novel angiographic MRI technique, blood oxygen level dependent angiography (BOLDangio). Under short-term (<10 min) generalized hypoxia induced by inhalation of 8% oxygen, we measure BOLD contrast as high as 25% from vessels at 9.4T using a simple gradient echo (GRE) pulse sequence. This produces high-resolution 2D and 3D maps of normal and tumour brain vasculature in less than 10 minutes. Additionally, this technique reliably detects metastatic tumours and tumour-induced intracranial hemorrhage. BOLDangio provides a sensitive research tool for MRI of vasculature under normal and pathological conditions. Thus, it may be applied as a simple monitoring technique for measuring the effectiveness of anti-angiogenic drugs in a preclinical environment.

Magnetic resonance imaging of glutamate.

Glutamate, a major neurotransmitter in the brain, shows a pH- and concentration-dependent chemical exchange saturation transfer effect (GluCEST) between its amine group and bulk water, with potential for in vivo imaging by nuclear magnetic resonance. GluCEST asymmetry is observed ∼3 p.p.m. downfield from bulk water. Middle cerebral artery occlusion in the rat brain resulted in an ∼100% elevation of GluCEST in the ipsilateral side compared with the contralateral side, predominantly owing to pH changes. In a rat brain tumor model with blood-brain barrier disruption, intravenous glutamate injection resulted in a clear elevation of GluCEST and a similar increase in the proton magnetic resonance spectroscopy signal of glutamate. GluCEST maps from healthy human brain were also obtained. These results demonstrate the feasibility of using GluCEST for mapping relative changes in glutamate concentration, as well as pH, in vivo. Contributions from other brain metabolites to the GluCEST effect are also discussed.

The effect of right vagus nerve stimulation on focal cerebral ischemia: an experimental study in the rat.

BACKGROUND: The aim of this study was to determine the effect of vagus nerve stimulation (VNS) on infarct size after transient and after permanent focal cerebral ischemia in rats and to test the hypothesis that VNS-induced neuroprotection is due to changes in cerebral blood flow. METHODS: Ischemia was produced by either temporary proximal middle cerebral artery occlusion (TMCAO) or permanent distal middle cerebral artery occlusion (PMCAO). Stimulating electrodes were implanted on the cervical part of the right vagus nerve, and electrical stimulation was initiated 30 minutes after the induction of ischemia and delivered for 30 seconds every 5 minutes for 1 hour. All the procedures were duplicated but no stimulus was delivered in control groups. Cerebral blood flow in the MCA territory was continuously monitored with laser speckle contrast imaging. A neurologic evaluation was undertaken after 24 hours of ischemia, and animals were euthanized and neuronal damage evaluated. RESULTS: Ischemic lesion volume was smaller in VNS-treated animals in both the temporary and permanent ischemic groups (P<.01). VNS-treated animals in TMCAO had better functional scores at 24 hours as compared with control animals (P<.01), but there were no statistically significant differences in the neurobehavioral scores in PMCAO (P=.089). Cerebral blood flow changes in the MCA territory during ischemia did not differ between the VNS-treated animals and control animals in either group. CONCLUSIONS: VNS offers neuroprotection against stroke in both temporary and permanent ischemia. Although the precise mechanism of this effect remains to be determined, alterations in cerebral blood flow do not appear to play a role. VNS could readily be translated to clinical practice.

Absolute cerebral blood flow quantification with pulsed arterial spin labeling during hyperoxia corrected with the simultaneous measurement of the longitudinal relaxation time of arterial blood.

Quantitative arterial spin labeling (ASL) estimates of cerebral blood flow (CBF) during oxygen inhalation are important in several contexts, including functional experiments calibrated with hyperoxia and studies investigating the effect of hyperoxia on regional CBF. However, ASL measurements of CBF during hyperoxia are confounded by the reduction in the longitudinal relaxation time of arterial blood (T(1a) ) from paramagnetic molecular oxygen dissolved in blood plasma. The aim of this study is to accurately quantify the effect of arbitrary levels of hyperoxia on T(1a) and correct ASL measurements of CBF during hyperoxia on a per-subject basis. To mitigate artifacts, including the inflow of fresh spins, partial voluming, pulsatility, and motion, a pulsed ASL approach was implemented for in vivo measurements of T(1a) in the rat brain at 3 Tesla. After accounting for the effect of deoxyhemoglobin dilution, the relaxivity of oxygen on blood was found to closely match phantom measurements. The results of this study suggest that the measured ASL signal changes are dominated by reductions in T(1a) for brief hyperoxic inhalation epochs, while the physiologic effects of oxygen on the vasculature account for most of the measured reduction in CBF for longer hyperoxic exposures.

The biological effect of contralateral forepaw stimulation in rat focal cerebral ischemia: a multispectral optical imaging study.

Our group has already published the possible neuroprotective effect of contralateral forepaw stimulation in temporary focal ischemia in a study. However, the background is still unclear. In the present study we investigated the possible mechanism by monitoring focal ischemia with multispectral [laser speckle, imaging of intrinsic signals (OIS)] imaging. Sprague-Dawley rats were prepared using 1.2% isoflurane anesthesia. The middle cerebral artery was occluded by photothrombosis (4 mW) and the common carotid artery was ligated permanently. Physiological variables were constantly monitored during the experiment. A 6 x 6 mm area centered 3 mm posterior and 4 mm lateral to Bregma was thinned for laser speckle and OIS imaging. Nine circular regions of interests (0.3 mm in diameter) were evenly spaced on the speckle contrast image for the analysis of peri-infarct flow transients, blood flow, and metabolic changes. Both the sham (n = 7) and forepaw-stimulated animals (n = 7) underwent neurological examinations 24 h after ischemia at which point all animals were sacrificed and the infarct size was determined by triphenyltetrazolium chloride. The physiological variables were in normal range and the experimental protocol did not cause significant differences between groups. Both the neurological scores (sham: 3.6 +/- 1.7, stimulated: 4.3 +/- 1.4) and the infarct volume (sham: 124 +/- 39 mm(3), stimulated: 147 +/- 47 mm(3)) did not show significant differences between groups. The forepaw stimulation did not increase the intra-ischemic flow neither over the penumbral or the peri-ischemic area. However, the hemoglobin transients related metabolic load (CMRO(2)) was significantly lower (p < 0.001) while the averaged number of hyperemic flow transients were significantly (p = 0.013) higher in the forepaw (sham: 3.5 +/- 2.2, stimulated: 7.0 +/- 2.3) stimulated animals.

3-Monoiodothyronamine: the rationale for its action as an endogenous adrenergic-blocking neuromodulator.

The investigations reported here were designed to gain insights into the role of 3-monoiodothyronamine (T1AM) in the brain, where the amine was originally identified and characterized. Extensive deiodinase studies indicated that T1AM was derived from the T4 metabolite, reverse triiodothyronine (revT3), while functional studies provided well-confirmed evidence that T1AM has strong adrenergic-blocking effects. Because a state of adrenergic overactivity prevails when triiodothyronine (T3) concentrations become excessive, the possibility that T3's metabolic partner, revT3, might give rise to an antagonist of those T3 actions was thought to be reasonable. All T1AM studies thus far have required use of pharmacological doses. Therefore we considered that choosing a physiological site of action was a priority and focused on the locus coeruleus (LC), the major noradrenergic control center in the brain. Site-directed injections of T1AM into the LC elicited a significant, dose-dependent neuronal firing rate change in a subset of adrenergic neurons with an EC(50)=2.7 microM, a dose well within the physiological range. Further evidence for its physiological actions came from autoradiographic images obtained following intravenous carrier-free (125)I-labeled T1AM injection. These showed that the amine bound with high affinity to the LC and to other selected brain nuclei, each of which is both an LC target and a known T3 binding site. This new evidence points to a physiological role for T1AM as an endogenous adrenergic-blocking neuromodulator in the central noradrenergic system.

Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects.

We employ a hybrid diffuse correlation spectroscopy (DCS) and near-infrared spectroscopy (NIRS) monitor for neonates with congenital heart disease (n=33). The NIRS-DCS device measured changes during hypercapnia of oxyhemoglobin, deoxyhemoglobin, and total hemoglobin concentrations; cerebral blood flow (rCBF(DCS)); and oxygen metabolism (rCMRO(2)). Concurrent measurements with arterial spin-labeled magnetic resonance imaging (rCBF(ASL-MRI), n=12) cross-validate rCBF(DCS) against rCBF(ASL-MRI), showing good agreement (R=0.7, p=0.01). The study demonstrates use of NIRS-DCS on a critically ill neonatal population, and the results indicate that the optical technology is a promising clinical method for monitoring this population.