Anneloes de Boer1, Bashair Al Hummiany2, Kanishka Sharma3, and Steven Sourbron3
1University Medical Center Utrecht, Utrecht, Netherlands, 2University of Leeds, Leeds, United Kingdom, 3University of Sheffield, Sheffield, United Kingdom
Synopsis
Medullary perfusion potentially is an early marker of renal
damage, but cannot be measured using existing models in MR renography. In this
study a novel 7-compartment, 10-parameter model is proposed and evaluated in
synthetic and patient data. Robustness of an iterative fitting approach was
assessed by the coefficient of variation over multiple fits, resulting in
median values <2.5% both in synthetic and patient data. According to
simulations, medullary perfusion was underestimated by 5.3%, but in diabetic patients
medullary perfusion was relatively high (81 mL/100mL/min). Future studies will
be needed to determine this model’s sensitivity to pathophysiological changes
in medullary perfusion.
Introduction
MR Renography traces contrast passage through the kidneys
and uses subsequent modelling of the contrast enhancement curve to measure
renal perfusion and filtration. Existing models however do not allow for measurement
of medullary perfusion (Fmed).(1,2)
Since the renal medulla functions on the border of hypoxia,(3)
it is very sensitive to perfusion defects, rendering
a promising
marker of early stage renal damage.Theory
A 7-compartment model
(7CM) of renal perfusion and filtration was constructed (Figure 1), reflecting
renal physiology. The model involves 10 free parameters: for each compartment
X a time
constant
TX
, the filtration fraction
EPT,PA, the extraction fraction to the vasa
recta
EVR,PA, and cortical perfusion Fcor. Glomerular filtration rate (GFR) is derived
by
$$$E_{PT,PA}F_{cor}$$$ and
$$$F_{med}=E_{VR,PA}F_{cor}$$$.
Cortical and medullary enhancement are modelled separately
and mathematically described as:
$$C_{cor}(t)=\left[T_{PA}+ R_{PV}(1-E_{PT,PA}-E_{VR,PA})+R_{PV}*H_{VR}E_{VR,PA}+R_{PT}E_{PT,PA}+R_{DT}*H_{LH}*H_{PT}E_{PT,PA}\right]...$$
$$...*H_{PA}* F_{cor}C_{A}(t)$$
$$C_{med}(t)=\left[R_{VR}E_{VR,PA}+R_{LH}*H_{PT}E_{PT,PA}+R_{CD}*H_{DT}*H_{LH}*H_{PT}E_{PT,PA}\right]*H_{PA}*F_{cor}C_{A}(t)$$
Here,
$$$*$$$ denotes convolution and for each compartment
X, $$$R_{X}=e^{-\frac{t}{T_{X}}}$$$ and $$$H_{X}=\frac{1}{T_{X}}e^{-\frac{t}{T_{X}}}$$$.Methods
Implementation
The model was implemented in Matlab (R2019, MathWorks,
Natick, MA, USA). Medullary and cortical curves were fitted simultaneously
using a nonlinear least squares fit. Each timepoint was weighted by the inverse
of its magnitude (except baseline signal). The model fit was iterated 50 times
with random initial values (within bounds). Median values were used as
parameter estimations.
Simulations
Ten arterial input functions obtained
from patient data were used to generate 20 different ground-truth renal
enhancement curves using the 7CM. Ground truth parameter values were obtained
from the normal distribution with a standard deviation of 20% around values
obtained from explorative fits in patient data. Gaussian noise was added to
obtain curves visually resembling patient data (CNR 150). To determine accuracy
and precision, the iterated fit was repeated 60 times. Accuracy and precision were
calculated for
EPT,PA,
Fcor, GFR and
Fmed. Accuracy was defined as the
average deviation of the ground truth parameters over 60 repetitions of the
iterated fit. Precision was measured using the coefficient of variation (CoV,
the standard deviation of those 60 iterations divided by the mean).
Patient data
Patient data (type-2 diabetes, eGFR >30) was used from
the iBEAt study.(4)
Data was acquired on a 3T MR system (MAGNETOM Siemens, Erlangen, Germany),
using a 2D fast gradient echo with a non-selective 90 degree saturation pulse
prior to each slice readout. Scan parameters are provided in table 1. During
DCE MRI, a quarter dose 0.05 mL/kg of
Dotarem was infused at a rate of 2 mL/s followed by a 20mL saline flush.
Deformable motion correction was performed using model-driven registration.(5)
Enhancement curves were extracted after segmentation of renal cortex and
medulla by k-means clustering.(6)
Fitting stability was assessed by 20 iterated fits. Values
for GFR, TPA and FPA,A were compared to values obtained
using a two compartment model (2CM)(1)
using linear regression and the ICC.
Data are presented as median (interquartile range (IQR)).Results
Of the 24 datasets available, 4 were excluded because of heavy
variations of inflow effects in the arterial input function. A representative
example of the MR images is shown in Figure 2. In Figure 3a and b, an example
of the simulated time intensity curve and 7CM fit is shown alongside a measured
time intensity curve in Figure 3c and d. As shown in Figure 4a, precision of
estimation
(CoV 1.7(1.2-2.4)%) was slightly less compared to the other parameters (FPT,PA,
Fcor and GFR with an IQR <1%). Also, Fmed was underestimated by median 5.3(0.2-16)% (Figure
4b).
In patient data, median values for EPT,PA, Fcor, Fmed and GFR were 0.28(0.25-0.34),
238(188-309)mL/100mL/min, 81(58-111)mL/100mL/min and 67(59-86)mL/100mL/min,
respectively. Stability was excellent with a CoV of 0(0-0)% for
all four parameters of interest (Figure 4c). However, in some curves the fit
was less stable resulting in outliers with CoVs of max 13, 1.6, 50 and 13% for
EPT,PA, Fcor, Fmed and GFR, respectively.
Correlation of GFR and
Fcor to
values obtained by a 2CM fit yielded systematically higher values of GFR and lower
values of
Fcor (Figure
4d and e). ICCs were 0.86 and 0.57 in GFR and Fcor, respectively.Discussion
A 7CM capable of modelling
Fmed was developed
and tested both in synthetic and patient data. Although the model contains 10
free parameters, the fit was relatively stable both in synthetic and patient
data. However, iterative fitting with
varying initial values is recommended to avoid local minima. Based on
simulations,
Fmed could
be estimated reasonably accurate with an underestimation of only 5.3%.
Considering patient data however,
Fmed was
relatively high, around one third of
Fcor, while
Fcor was
underestimated compared to a conventional 2CM fit. Partly, this might be
explained by impaired cortical perfusion
in diabetes, while medullary perfusion is preserved.(7)
Additionally, the inability of the model to capture the first pass peak
correctly might play a role. It might therefore be indicated to incorporate a
delay before arrival of contrast agent in the cortex.
In conclusion, the 7CM model enables measurement of
Fmed using
a MR renography experiment, which might be helpful in detecting early stage
renal damage. In future studies the model’s sensitivity to pathological and
physiological changes in medullary perfusion has to be determined.Acknowledgements
The iBEAt study is part of the
BEAt-DKD project. The BEAt-DKD project has received funding from the Innovative
Medicines Initiative 2 Joint Undertaking under grant agreement No 115974. This
Joint Undertaking receives support from the European Union’s Horizon 2020
research and innovation programme and EFPIA with JDRF. For a full list of
BEAt-DKD partners, see www.beat-dkd.eu.
Anneloes de Boer was supported by stipends from the COST action PARENCHIMA (CA16103), "Stichting De Drie Lichten" and the "van Wijck-Stam-Caspers" foundation.
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