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Demo for how to track a single RBC from its kymogram and estimate the RBC’s speed

Demo for how to track a single RBC from its kymogram and estimate the RBC’s speed#

import matplotlib.pyplot as plt
import numpy as np

from sl2pm import track_rbc
from sl2pm.models import rbc
from sl2pm.misc import fitted_params

Load a kymogram, consisting of three consecutive line-scans

kymogram = np.load('rbc_linescans.npy')

Enter PMT parameters (known from the calibration)

ALPHA = 0.452
SIGMA = 6.0
GAIN = 3/ALPHA

Tracking a single RBC, visualising and inspecting the fits#

Fit three consecutive line-scans. After each fit, we show raw line-scan (black staircase curve) and its fit (blue curve), respectively.

x = np.arange(len(kymogram[0]))

rbc_loc = [] # Fitted RBC locations and their error bars

for i, linescan in enumerate(kymogram, start=1):
    
    print(f'Fitting line-scan {i}/{len(kymogram)}...')
    
    optim_res = track_rbc.mle_fit(linescan, 
                                 ALPHA, 
                                 SIGMA, 
                                 mu=0, 
                                 sigma_blur=1, 
                                 delta_s=4, 
                                 s_max=700, 
                                 minimize_options=dict(gtol=1e-3)
                                )
    
    print(optim_res.message)
    
    pars = fitted_params(optim_res, ['b', 'A', 's', 'xo'])
    rbc_loc.append(pars['xo'])

    ### Plot line-scans and their fits
    fig, ax = plt.subplots(figsize=(8, 3))
    
    ax.step(x, linescan/GAIN, c='k', where='mid', label='line-scan')
    ax.plot(x, rbc(x, *[val for val, err in pars.values()]), c='royalblue', label='fit', lw=2)
    ax.legend(frameon=False)
    ax.set_xlabel('Pixel #')
    ax.set_ylabel('Photon count')
    
rbc_loc = np.array(rbc_loc)

Fitting line-scan 1/3...
Optimization terminated successfully.
Fitting line-scan 2/3...
Optimization terminated successfully.
Fitting line-scan 3/3...
Optimization terminated successfully.
../../_images/d8e13ab2d513514ff8211887396c32e06b442ed95a4cbf681d126f6e8c676704.png ../../_images/96ae40f12fdb49429e3b9b96695e98c099b906778b4cd9da36bce60ef86a1010.png ../../_images/d04ec2db9b83bce296f557c1e146c906f99908eeec8778a49aa4bf346a2ab4d3.png

Estimating the RBC’s speed#

Estimate RBC speed [mm/sec] from the three estimated RBC locations

dt = 0.00166 # [sec] inverse sampling rate of line-scans
t = np.arange(3)*dt

pixel_width = 1e-4 # [mm]

result = track_rbc.rbc_speed(t, rbc_loc[:,0], rbc_loc[:,1])

print(f'RBC speed = {result["speed"]*pixel_width:.3f}+/-{result["speed_err"]*pixel_width:.3f} mm/sec')

RBC speed = 0.520+/-0.051 mm/sec
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