Marta Tibiletti^{1}, Jo Naish^{1,2}, Matthew J. Heaton^{1}, Paul JC Hughes^{3}, Jim Wild^{3}, and Geoff JM Parker^{1,4}

^{1}Bioxydyn Ltd, Manchester, United Kingdom, ^{2}Division of Cardiovascular Sciences, University of Manchester, Manchester, United Kingdom, ^{3}POLARIS, , Academic Radiology, Department of Infection, Immunity and Cardiovascular Disease, The University of Sheffield, Sheffield, United Kingdom, ^{4}Centre for Medical Image Computing, University College London, London, United Kingdom

Application of first pass imaging to the lung is a promising technique. The majority of works apply a Singular Value Decomposition (SVD) with or without a prior fit to a gamma variate function to the concentration-time curve. In this study we compare lung perfusion quantification with and without 2 versions of the gamma-variate fitting in data from 66 patients with Interstitial lung disease. We found that the presence and choice of gamma variate fitting has an influence on perfusion parameters, but this is generally very small, except for mean transit time, suggesting that these approaches are broadly equivalent in practice.

Signal curves within the lung ROI and the AIF were converted into concentration-time curves (C(t), C

$$$ \begin{equation}GV1(t) \begin{cases}0, & t<t_{start}\\\alpha(\frac{t-t_{start}}{t_{p}})^{\beta} e^{\frac{t-t_{start}}{t_{p}}} & t≥_{start}\end{cases}\end{equation} $$$

where parameters α, β, t

$$$ \begin{equation}GV2(t) \begin{cases}0, & t<t_{start}\\\frac{AUC}{\gamma^{\beta+1}\sqrt[]{2\pi\beta }\beta^{\beta}e^{-\beta+1/(12\beta)}}(t-t_{start})^{\beta}e^{\frac{t-t_{start}}{\gamma}} &t≥t_{start}\end{cases}\end{equation} $$$

where parameters β, γ define the shape of the curve. AUC is the area under the concentration-time curve, and is calculated, not fitted. Each curve fit was executed using a Levenberg-Marquardt algorithm (least_squares routine, Scipy Python package).

Blood volume was calculated as BV = $$BV = \frac{\int_{0}^{inf} C(t)dt }{\int_{0}^{inf} C_{AIF}(t)dt } $$ . On the basis of indicator dilution theory, a deconvolution of CAIF(t) from C(t) was performed by truncated SVD (tSVD, threshold of 20% of the largest SV). Blood Flow (BF) is defined as the maximum of the obtained impulse response function and the mean transit time as MTT = BV/BF.

Median and interquartile range (IQR) over the whole lung for BV, MTT and BF were obtained using C(t), and with C(t) and C

Parameters were compared using a repeated measure one-way ANOVA with Bonferroni correction. The median values of residuals were compared using a repeated measures two-tailed t-test. Spearman correlation coefficients were calculated between perfusion parameters and FEV1% pred, FVC pred%, DLCO and KCO. p<0.05 was considered significant.

Figure 1 presents box plots of BV, MTT and BF median values and the difference between the GV1 and GV2 fits and no fit results. Parameters obtained by the different methods are all significantly different, with the exception of BF obtained by GV1 and GV2. Figure 2 presents maps from one subject showing BV, MTT and BF derived using each of the three considered methods.

Table 2 presents the Pearson correlation between perfusion parameters and lung function tests. P-values are indicated when p<0.05. GV1 generates consistently slightly higher fitting residuals than GV2 (0.88 ± 0.06 vs 0.86 ± 0.06, p<0.0001).

The lack of a gold standard, independent measurement of lung perfusion parameters does not allow determination of which analysis method is most accurate. However, when comparing the perfusion parameters with lung function parameters, similar correlations exist between parameters extracted with no_fit and GV1. The only exception is MTT IQR, where a stronger correlation exists with KCO% when no fit is applied, than when the GV1 fit is applied. GV2 results generally show less evidence correlation with lung function.

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Table 1: summary of parameters for the considered MR acquisitions.

Figure 1: First line: boxplots representing the distribution
of BV, MTT and BF in the population, calculated with no gamma-variate fit and applying the gamma-variate fits considered (GV1, GV2). Second line: boxplots
representing the distribution of the difference between the parameter obtained
with and without gamma-variate fitting (GV1- no_fit, GV2 - no_fit).

Figure 2: examples of BV, MTT and BF parameter maps
calculated with the three methods in one subject, showing presence of lung
fibrosis in the lower left lobe. MTT is the only parameter presenting visible
differences.

Table 2:
Pearson correlation coefficients between MR perfusion
parameters (BV, BF and MTT) median and interquartile range (IQR) and lung function
tests (FEV1%, FVC%, TICO%, KCO%). P values are indicated only when p<0.05. Similar correlations exist between
parameters extracted with no_fit and GV1. The only exception is MTT IQR, where
a stronger correlation exists with KCO% when no fit is applied, than when the
GV1 fit is applied.