An In Silico Modelling Approach to Predict Hemodynamic Outcomes in Diabetic and Hypertensive Kidney Disease

Abstract

Early diagnosis of kidney disease remains an unmet clinical challenge, preventing timely and effective intervention. Diabetes and hypertension are two main causes of kidney disease, can often appear together, and can only be distinguished by invasive biopsy. In this study, we developed a modelling approach to simulate blood velocity, volumetric flow rate, and pressure wave propagation in arterial networks of ageing, diabetic, and hypertensive virtual populations. The model was validated by comparing our predictions for pressure, volumetric flow rate and waveform-derived indexes with in vivo data on ageing populations from the literature. The model simulated the effects of kidney disease, and was calibrated to align quantitatively with in vivo data on diabetic and hypertensive nephropathy from the literature. Our study identified some potential biomarkers extracted from renal blood flow rate and flow pulsatility. For typical patient age groups, resistive index values were 0.69 (SD 0.05) and 0.74 (SD 0.02) in the early and severe stages of diabetic nephropathy, respectively. Similar trends were observed in the same stages of hypertensive nephropathy, with a range from 0.65 (SD 0.07) to 0.73 (SD 0.05), respectively. Mean renal blood flow rate through a single diseased kidney ranged from 329 (SD 40, early) to 317 (SD 38, severe) ml/min in diabetic nephropathy and 443 (SD 54, early) to 388 (SD 47, severe) ml/min in hypertensive nephropathy, showing potential as a biomarker for early diagnosis of kidney disease. This modelling approach demonstrated its potential application in informing biomarker identification and facilitating the setup of clinical trials.

Keywords: 1D modelling; Biomarkers; Chronic kidney disease; Diabetes mellitus; Hypertension; Renal circulation modelling.

Fig. 1

Workflow chart of the study methodology. Validation through comparison with in vivo data was performed for the baseline and healthy ageing model, whereas calibration was performed through comparison with in vivo data for the disease models

Fig. 2

Illustration of openBF whole-circulation network (centre) with the two renal networks (left and right). Measurement locations of the mean RBF rate were shown by a grey circular plane (I) at the main renal artery, and measurement locations for blood velocity waveforms and RI values were shown by grey circular planes (II) at the five segmental renal arteries in the enlarged representation of the left (L) renal network. Model flow rate waveforms for a typical individual were shown on the right hand side, a blood volumetric flow rate in ascending aorta imposed as inlet boundary condition, b renal blood volumetric flow rate predicted at location (I), c renal blood velocity at location (II)

Fig. 3

Validation of modelled data for a healthy, ageing population. a and b: Comparison of modelled systolic and diastolic blood pressure in the brachial artery against in vivo data [38]. c: Comparison of RI distributions in renal segmental arteries against ultrasound measurement data [71]. d: Comparison of modelled total mean renal blood flow rate (the sum of mean RBF rate in both kidneys) in main renal arteries against MRI-measured data [72]

Fig. 4

Comparison of RI values in segmental renal arteries with in vivo literature data for 20-79 yo healthy individuals [71], diabetic (Early.D/Severe.D) [70] and hypertensive (Early.H/Severe.H) patients [8, 70] at different disease stages. Simulation results are shown in black, and in vivo data are shown in grey. White solid lines represent mean values, while white solid circles represent median values

Fig.5

Scatter plot, showing RI and mean RBF rate distributions through single kidney for a 50-59 yo virtual population in presence of health, diabetes or hypertension at different disease stages

Fig.6

Box plot of modelled mean RBF rate through single kidney for 50 to 59 yo healthy individuals, DN and HN patients at different disease stages. White solid lines represent mean values, while white solid circles represent median values. Black solid star signs represent outliers defined as values that fall below the first quartile − 1.5 * interquartile range (IQR) or above the third quartile + 1.5 * IQR

Fig.7

ROC curves for 50 to 59 yo Early.D, Early.H, and Severe.D, Severe.H populations using RI and mean RBF rate classifiers. Solid black line represents the ROC curve for the early disease stage (Early.D/H) using RI. Dotted black line represents the ROC curve for the severe disease stage (Severe.D/H) using RI. Dashed black line represents the ROC curve for the early disease stage (Early.D/H) using mean RBF rate. Dash dotted black line represents the ROC curve for the severe disease stage (Severe.D/H) using mean RBF rate. Black solid dot on each ROC curve is the best cut-off point to classify between DN and HN in early and severe stages. Dashed grey line represents a random classifier