Laser Doppler flowmetry (LDF) and laser speckle flowmetry

Channels and stimulus

The chosen LDF channel sets the time base. A stimulus channel recorded faster is reduced to the LDF rate by taking the maximum over each LDF sample (short pulses are kept); a slower one is held. When the comments / event markers are the stimulus, each one becomes a pulse of height 1 lasting 0.5 s, so LDF Processing finds it with a threshold of 0.5; choose one comment text to use only those comments. The plots are titled with the channel names, and the methods text names the acquisition software and the channels.

Cropping

Sample k is at time (k − 1) / Fs. Cropping keeps samples round(Start·Fs)+1 to round(End·Fs)+1, with 0 ≤ Start < End ≤ duration. Loading a new file, or choosing other channels, discards the previous crop, so a stale crop can never be saved by mistake.

Filtering and downsampling

Downsampling decimates the LDF with an anti-aliasing filter and subsamples the stimulus. Filters are applied forwards and backwards (zero-phase), so responses are not shifted in time. Butterworth filters have a maximally flat pass-band^[19]; Chebyshev I filters are steeper with pass-band ripple; FIR filters are always stable but need a high order for a sharp cutoff. Cutoffs must lie below half the sampling rate after downsampling (1000 Hz / 10 → cutoffs below 50 Hz). Processing always starts from the loaded data, so new settings never filter an already filtered signal.

Trials

Onsets are the samples where the stimulus rises above the threshold; a crossing closer than the minimum interval to the last accepted onset is ignored, so a train of pulses gives one onset. Each trial runs from onset − pre to onset + post; trials that would run past the start or end of the recording are skipped. Files are pooled in the Average LDF Viewer only when their time axes are identical. Relative to baseline subtracts the mean of each trial's samples before t = 0.

Checks

After Segment trials, one row per check (the same checks run in Batch processing and, for the shared ones, on laser speckle and perfusion images):

• Trials: stimuli left out because their trial does not fit; fewer than 3 trials. Trial baseline: shorter than 2 s or 5 samples.
• Time resolution: one value every dt s after downsampling: Check above 0.5 s (latency and rise time known to within dt), Warning above 2 s.
• Baseline: the mean before the stimuli, usually 30–600 PU for a probe on tissue; outside that a Check (a large vessel under the probe, no contact or bone, or a channel not in PU), never a Warning, because tissue and devices differ.
• Filter: a low-pass below 0.5 Hz smooths the 1–2 s rise (Check); a high-pass above 0.02 Hz shrinks a response lasting several seconds (Check; above 0.1 Hz Warning).
• Baseline drift: a linear fit, in % of the baseline per minute, over the part before the first stimulus when it lasts 60 s or more, else over the trial baselines (4 or more trials over 120 s or more): Check above 3%/min, Warning above 10%/min; a Note when the recording is too short to tell.
• Movement artefacts (on the loaded trace, before filtering): jumps away from the 1 s moving median by more than 8 robust SDs and 25% of the baseline, with their times; Warning when they fall in a trial, Check otherwise.
• Signal range: more than 0.1% of the samples at 0 or below (probe lifted) or stuck at the top (device or export range saturated): Warning.

• Data: LabChart-style export, 8 channels, 300 s at 1000 Hz. Channel 6 = stimulus: 9 pulses of 5 s every 30 s from t = 30 s. Channel 8 = LDF: ~120 PU baseline with slow drift, vasomotion (0.13 Hz), a cardiac ripple (6 Hz) and noise.
• What you should see: after each stimulus pulse the LDF rises by about +30 PU, peaking about 4 s after the onset, and returns to baseline within ~12 s.
• Try: crop 20 to 280 s (this is exactly what the LDF Process demo file contains) and save; the cropped plots start at t = 0 with the first pulse at 10 s.
• Other formats: core/demo/demoLDFFormats.m writes the same recording at 100 Hz as a LabChart text export, a PeriSoft-style table, a Spike2 export, a table without a time column (type 100 Hz when asked) and an EDF+ file, so each one can be opened in Extract LDF and checked against the same answer.

• Data: the cropped demo recording (20–280 s of the LDF export, 1000 Hz): 9 stimulus pulses of 5 s, the first at 10 s, then every 30 s.
• Try: downsample 10x, low-pass ~1 Hz (removes the 6 Hz cardiac ripple), then segment with pre = 5 s and post = 20 s.
• What you should get: 8 complete trials (the last pulse is too close to the end for a 20 s window). The mean response rises after 0 s and peaks ~4 s after onset at ~+30 PU above a ~120 PU baseline.
• Checks: no warnings; one Check, Trials (1 of 9 stimuli left out: its trial does not fit); OK for the baseline (~120 PU), drift (about −1.4%/min from the 8 trial baselines), movement artefacts, signal range, the filter and the time resolution.
• Faults demo: load demo_ldf_faults.mat from the demo folder and segment with the same settings: Baseline drift is a Check (about +5.4%/min), Movement artefacts a Warning (jumps at 31 and 72 s, the second in trial 3) and Signal range a Warning (0.38% of the samples at 0).

• Data: the cropped demo LDF (1000 Hz). Besides the ~+30 PU responses it contains a slow drift (period 400 s), vasomotion at 0.13 Hz (±3 PU), a cardiac ripple at 6 Hz (±1.5 PU) and white noise.
• Low-pass 1 Hz (after 10x downsampling): the 6 Hz ripple and most noise disappear, the responses keep their shape and timing (zero-phase filtering: the peak stays ~4 s after onset).
• High-pass 0.2 Hz: removes drift and vasomotion but also shrinks and distorts the slow (~5 s wide) responses, a good example of a cutoff that is too high for LDF.

• Data: demo_ldf_trials.mat, 8 trials from −5 to 20 s at 10 Hz (0 = stimulus onset).
• What you should get: the grand average is flat before 0 s (at 0: the demo ticks Relative to baseline; untick it to see the ~122 PU baseline), rises after onset and peaks ~4 s after onset at ~+30 PU, then returns to baseline by ~12–15 s. The SD band shows the trial-to-trial vasomotion (a few PU).
• With Relative to baseline the curve starts at ~0 PU and peaks at ~+30 PU.

Speckle contrast

A surface lit by a laser shows a grainy speckle pattern. Moving red blood cells change it during the camera exposure, so the pattern is blurred: its contrast K = σ / mean of the intensity drops where blood flows faster (K near 1: still; near 0: fast flow).

• Spatial: K of the pixels in a window around each pixel (5 × 5 or 7 × 7), in every frame^{[32, 33]}. It keeps the time resolution but blurs the image by the window: small vessels look wider, and a region only gives its own contrast where the window stays inside it.
• Temporal: K of each pixel over N frames (15–25 usual)^[35]. The image stays sharp; the time resolution drops by N. Needs a still preparation.
• Frames per value (spatial): the K² of this many frames is averaged. Speckle is noisy; averaging frames is standard (commercial systems do it too).
• Dark level: the camera offset adds to the mean but not to the σ, so without subtracting it the contrast is too low.

Flow index

• 1/K² (speckle flow index): for exposures much longer than the decorrelation time τc, K² ≈ β τc / (2T), so 1/K² is proportional to 1/τc and to the speed of the red blood cells^[33]. Relative changes of 1/K² follow changes in flow closely; for a +25% flow change it shows about +24%.
• 1/τc (exposure model): solves K² = β (e^−2x − 1 + 2x) / (2x²), x = T/τc, for every value^{[34, 33]} and gives 1/τc in 1/s. It needs the exposure T; β (0–1) is the contrast of still speckle for your optics: it changes absolute values, not relative changes.
• Perfusion / flux images from a commercial system are used as they are (their own units).

ROIs, trials and the response map

• The K² (or perfusion) of a ROI's pixels is averaged in each frame, then converted to the flow index. Flow over time is relative to the baseline window (from the start to the first stimulus).
• Each trial is cut from Before to After the onset and expressed as % change from its own mean before 0 s. Average response is the mean ± SD over trials; the response is its mean in the response window (robust); the peak is its largest value after onset (noise makes it larger).
• Response map: in every pixel, the flow of the response window divided by the flow before the onsets (both averaged over trials), minus 1, in %.

Checks

One row per check (Result, Topic, Finding; click a row for why it matters and what to try).

• Raw images: Saturation (saturated pixels lower the contrast), Dark level (none subtracted, or pixels below it), Contrast window (smaller than 5 × 5), Speckle contrast (outside the usual range: static tissue, wrong exposure or already processed images; values above 1), Speckle size (width of the spatial autocorrelation of raw frames: below 1.5 px a Check, since below about 2 px per speckle each pixel averages several and K drops), Illumination (the mean raw intensity changes by more than 10%: laser or light path drift).
• Raw and contrast images: Exposure outside 1–20 ms (Check); Baseline contrast above K = 0.4 in a ROI (Check: static scattering through skull, dura or scar makes 1/K² underestimate relative changes; a thinned skull, a window or multi-exposure speckle imaging help); a Note on the flow index used.
• Perfusion images: Export range (more than 0.1% of the values at the top, e.g. 3000 PU: Warning), and Notes: values are in the device's units (compare relative changes only with the same device and settings), and the dark level and speckle checks need the raw images.
• Every input: Field shift between frames (blocks of frames registered against the first; Check above 1 px, Warning above 3 px), then the blood-flow checks shared with the needle probe, on the ROI traces: Trials, Trial baseline, Time resolution (one value every dt s: Check above 0.5 s, Warning above 2 s or with fewer than 2 values in the response window), Baseline drift, Movement artefacts and Signal range (see LDF Process for the rules). With several ROIs each check is one row, the worst ROI sets its result and the text names the ROIs.

OK is green, Check amber, Warning red, Note grey; the same tab is in every window that has checks.

• Data: demo_lsci.mat (or Try demo data): raw speckle images of a rodent cortex, 80 × 64 px (width × height), 900 frames at 10 Hz (90 s), exposure 5 ms, camera dark level 100 counts (uint16). Each pixel is an independent speckle whose contrast follows the exposure model with β = 1.
• Tissue: cortex (parenchyma) with τc = T/20 (K = 0.22), a vessel (x = 14–25 px) with τc = T/200 (K = 0.07, much faster flow) and a static corner (bone, K = 0.70, no flow).
• Stimuli: 5 s pulses at 10, 30, 50 and 70 s (stim in the file). In an activated disk (centre x = 52, y = 28, radius 12 px) the flow rises by 25% at 4 s after each onset and returns within about 12 s; nowhere else does the flow change.
• ROIs in the file: Activated area (inside the disk), Control cortex, Vessel.
• Run with the defaults (spatial 7 × 7, 5 frames per value = 2 Hz, dark level 100, 1/K²): 4 trials; Activated area about +21% in the 2–6 s window (the true mean flow change there is +21.9%; 1/K² sees +21.3%), peak about +28% near 4 s; Control cortex and Vessel about 0% (within ±3%). The response map shows an orange disk of about +20% at the activated area and 0 elsewhere.
• Show → Speckle contrast K: cortex 0.22, vessel 0.07 (light), static corner 0.70 (black). The vessel's edges look wider than 12 px because the 7 × 7 window mixes vessel and cortex there.
• Flow index → 1/τc (exposure model): about 4000 /s in the cortex and 40000 /s in the vessel; the activated area rises slightly more than with 1/K² (closer to the true flow change).
• Dark level 0 instead of 100: the contrast drops by about 5% everywhere and Checks has a Check row, Dark level, asking you to measure it; the relative responses hardly change.
• Checks with the defaults: no warnings. One Check, Speckle size (about 1 px): the demo makes each pixel an independent speckle, which a real camera should not do (2 px or more per speckle). Field shift, exposure, illumination, baseline contrast (K = 0.07–0.22), trials, trial baseline (10 samples), time resolution (2 Hz), movement artefacts and signal range are OK; Baseline drift is a Note: 10 s before the first stimulus and 4 trials over 60 s are too short to judge it.
• Faults demo (demo_lsci_faults.mat in the demo folder): Field shift is a Warning (the image moves by up to 4 px, first above 1 px at 46 s); Illumination (−22%), Exposure (25 ms), Baseline contrast (Thinned skull, K = 0.49) and Speckle size are Checks; the contrast is lower everywhere (two speckles per pixel: cortex K = 0.16).
• Perfusion demo (demo_perfusion_faults.mat, opens as perfusion images): Export range is a Warning (13% of the values at 3000 PU: the vessel), Time resolution a Check (one image per second), and three Notes, among them device units and that the dark level, saturation and speckle size checks need raw images. The activated area still rises by about +20%.