Single-kidney glomerular filtration rate

This examples illustrates the use of Kidney for measurement of single kidney glomerular filtration rate (SK-GFR). The script aims to replicate a validation study comparing MRI-derived measurement of SK-GFR against reference measurement performed with radio-isotopes Basak et al 2018). The study used 124 historical datasets collected in between the years 2000 and 2010 at 1 Tesla and 3 Tesla MRI. The study concluded that while the MRI-derived values were unbiased, the precision was low and significant improvements in data quality would be needed before this technique can be applied in clinical practice. The study was funded by Kidney Research UK.

Reference

Basak S, Buckley DL, Chrysochou C, Banerji A, Vassallo D, Odudu A, Kalra PA, Sourbron SP. Analytical validation of single-kidney glomerular filtration rate and split renal function as measured with magnetic resonance renography. Magn Reson Imaging. 2019 Jun;59:53-60. doi: 10.1016/j.mri.2019.03.005. [URL].

Setup

# Import packages and fetch data
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

import dcmri as dc

# Fetch the data
data = dc.fetch('KRUK')

Model definition

In order to avoid some repetition in this script, we define a function that returns a trained model for a single dataset:

def kidney_model(scan, kidney):

    # Get B0 and precontrast T1
    B0 = scan['field_strength']
    T1 = scan[kidney+' T1']
    T1 = dc.T1(B0, 'kidney') if T1 is None else T1

    # Set kidney model parameters
    model = dc.Kidney(
        aif = scan['aorta'],
        t = scan['time'],
        vol = scan[kidney+' vol'],
        R10 = 1/T1,
        R10a = 1/dc.T1(B0, 'blood'),
        sequence = 'SS',
        TR = scan['TR'],
        FA = scan['FA'],
        field_strength = B0,
        agent = scan['agent'],
        n0 = scan['n0'],
    )

    # Customize free parameter ranges
    model.set_free(
        pop = 'Ta',
        Fp = [0, 0.05],
        FF = [0, 0.3],
        Tt = [30, np.inf],
    )

    # Train the kidney model on the data
    xdata = scan['time']
    ydata = scan[kidney]
    model.train(xdata, ydata)

    return xdata, ydata, model

Check model fit

Before running the full analysis on all cases, lets illustrate the results by fitting the left kidney of the first subject:

time, signal, model = kidney_model(data[0], 'LK')

Plot the results to check that the model has fitted the data:

model.plot(time, signal)

Print the measured model parameters and any derived parameters and check that standard deviations of measured parameters are small relative to the value, indicating that the parameters are measured reliably:

model.print_params(round_to=3)

--------------------------------
Free parameters with their stdev
--------------------------------

Plasma flow (Fp): 0.035 (0.003) mL/sec/cm3
Plasma volume (vp): 0.278 (0.019) mL/cm3
Filtration fraction (FF): 0.103 (0.017)
Tubular mean transit time (Tt): 304.622 (149.971) sec

----------------------------
Fixed and derived parameters
----------------------------

Blood flow (Fb): 0.063 mL/sec/cm3
Tubular flow (Ft): 0.004 mL/sec/cm3
Plasma mean transit time (Tp): 7.239 sec
Extracellular volume (ve): 0.252 mL/cm3
Extraction fraction (E): 0.094
Single-kidney glomerular filtration rate (SK-GFR): 0.431 mL/sec
Single-kidney renal blood flow (SK-RBF): 7.58 mL/sec

The measured SK-GFR for this kidney (0.43) is somewhat higher than the radio-isotope reference value (0.28):

print('-----------------------------')
print('Comparison to reference value')
print('-----------------------------')
print('Radio-isotope SK-GFR: ', data[0]['LK iso-SK-GFR'])

-----------------------------
Comparison to reference value
-----------------------------
Radio-isotope SK-GFR:  0.2779460500963383

Fit all data

Now that we have illustrated an individual result in some detail, we proceed to determine SK-GFR for all datasets:

results = []

for scan in data:
    for kidney in ['LK', 'RK']:
        if kidney not in scan:
            continue
        xdata, ydata, model = kidney_model(scan, kidney)

        # Export parameters and add reference value
        pars = model.export_params()
        pars['iso-SK-GFR'] = [
            'Isotope single-kidney GFR',
            scan[kidney + ' iso-SK-GFR'],
            'mL/sec',
            0,
        ]

        # Convert to a dataframe
        pars = pd.DataFrame.from_dict(
            pars,
            orient = 'index',
            columns = ["name", "value", "unit", "stdev"])
        pars['subject'] = scan['subject']
        pars['kidney'] = kidney
        pars['visit'] = scan['visit']
        pars['parameter'] = pars.index
        pars['B0'] = scan['field_strength']

        # Append to results
        results.append(pars)

# Combine all results into a single dataframe
results = pd.concat(results).reset_index(drop=True)

Plot MRI values and reference values

# Validation
v1T = pd.pivot_table(results[results.B0==1], values='value', columns='parameter', index=['subject','kidney','visit'])
v3T = pd.pivot_table(results[results.B0==3], values='value', columns='parameter', index=['subject','kidney','visit'])

iso1T, iso3T = 60*v1T['iso-SK-GFR'].values, 60*v3T['iso-SK-GFR'].values
mri1T, mri3T = 60*v1T['SK-GFR'].values, 60*v3T['SK-GFR'].values

plt.title('Single-kidney GFR (SK-GFR)')
plt.plot(iso1T, mri1T, 'bo', linestyle='None', markersize=4, label='1T')
plt.plot(iso3T, mri3T, 'ro', linestyle='None', markersize=4, label='3T')
plt.plot(iso3T, iso3T, linestyle='-', color='black')
plt.ylabel("MRI SK-GFR (mL/min)")
plt.xlabel("Isotope SK-GFR (mL/min)")
#plt.xlim(0,100)
#plt.ylim(0,200)
plt.legend()
plt.show()

Compute bias and accuracy

v = pd.pivot_table(results, values='value', columns='parameter', index=['subject','kidney','visit'])

iso = 60*v['iso-SK-GFR'].values
mri = 60*v['SK-GFR'].values

diff = mri-iso
bias = np.mean(diff)
err =  1.96*np.std(diff)
bias_err = 1.96*np.std(diff)/np.sqrt(np.size(diff))

print('-----------------')
print('Single-kidney GFR')
print('-----------------')
print('95% CI on the bias (ml/min): ', bias-bias_err, bias+bias_err) # paper 0.56
print('95% CI on individual error (ml/min): ', bias-err, bias+err) # paper [-28, 29]

-----------------
Single-kidney GFR
-----------------
95% CI on the bias (ml/min):  7.391160008329153 13.99521953118509
95% CI on individual error (ml/min):  -39.166366228478346 60.55274576799258

As the results show, these data do not replicate the results from the original study exactly..

[ …more results coming soon… ]

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