Susanne S. Rauh^{1,2}, Oliver J. Gurney-Champion^{2}, Uwe Oelfke^{2}, Frederik B. Laun^{1}, and Andreas Wetscherek^{2}

To use intravoxel incoherent motion (IVIM) modelling for clinical applications, the model parameters need to be determined accurately and precisely, which was found challenging. We studied the influence of signal-to-noise ratio (SNR), number of b-values and perfusion fraction on the accuracy of the recently introduced flow-compensated IVIM model parameters (tissue diffusivity, perfusion fraction, characteristic timescale and blood flow velocity). Simulations were performed for typical parameters obtained in healthy volunteers for pancreas and kidney and revealed that for an SNR of 20, 9 b-values and a perfusion fraction of more than 15% are needed for reliable parameter estimation in flow-compensated IVIM.

In the IVIM model, the DW signal attenuation S/S_{0}
is a function of tissue diffusivity D, perfusion fraction f, characteristic
timescale τ and blood flow velocity
v of the vascular network^{1,5}: $$\frac{S}{S_0} = (1-f)exp(-bD) + f \cdot F(b,T,τ,v)\cdot exp(-bD_b).$$

While in *classic *IVIM
modelling the perfusion-based attenuation F(b,T,τ,v) and self-diffusion (modelled here by D_{b}= 1.6 µm^{2}/ms)
of blood are approximated by exp(-bD*), in *flow-compensated* IVIM F(b,T,τ,v) is calculated using normalized phase
distributions^{5},
taking diffusion gradient scheme and diffusion time T (defined
in Fig. 1) into account.

We acquired abdominal DW MRI from three volunteers (each scanned twice) at 1.5T (Magnetom
Avanto, Siemens Healthcare, Germany) using an in-house developed single-shot
echo planar imaging sequence^{5}, which was respiratory triggered to exhalation.

The same protocol was used for volunteer experiments and simulations. It consisted of four series with constant T and varying b-values and three series with constant b-value and varying T, illustrated in Fig. 1.

In the simulations we examined the influence of Rician noise
(SNR 10-60 at b=0), employed b-values (4-18 b-values in range 0-600 s/mm^{2})
and the perfusion fraction (2-40%). Each simulation was repeated 100 times and
boxplots of the distribution of the relative error of the parameter estimates
were generated in MATLAB (The MathWorks, Inc., Natick). The median
of the box-plots is a measure of accuracy, the range is a measure of precision. Ground-truth values for the pancreas simulations were taken from
literature^{5} and values of the kidney were obtained from the volunteer
data.

Results of a typical volunteer measurement are shown in Fig. 2, which displays the measured signal attenuation and a fit of the flow-compensated IVIM model. The signal dependence on T was not well-resolved, which is crucial to determine τ and v accurately.

In the SNR simulations (Fig. 3) an increased random error was found at lower SNR for both pancreas and kidney data. For SNR ≥ 20 the inter-quartile range was below 20% for all parameters.

Figure 4 shows the dependency on the number of used b-values (SNR = 20). Using less than 7 b-values led to systematic errors (underestimation of D, overestimation of f). Starting with 9 b-values, the relative errors for D and f stayed below 10%, adding more b-values did not yield further gain in accuracy or precision for any of the model parameters.

The accuracy of the tissue diffusivity D was unaffected by the blood fraction, which can be seen in Figure 5 (top left). The other three parameters were strongly dependent on f: for very low perfusion fractions (f<5%), τ and v could not be determined precisely. Acceptable accuracy and precision were only found for f ≥ 15%.

The work at
hand was inspired by the challenges of applying the flow-compensated IVIM model
to in-vivo data. The simulations revealed, that for an SNR of 20, 9 b-values and a
perfusion fraction of f ≥ 15% are required to enable estimation of the
parameters τ and v. For the used protocol, this corresponds to reducing the
acquisition time by 50%. D and f could be measured accurately already from 7
b-values, which is in accordance with literature^{4,6}.

To overcome
the limitations of long breath holds, which were used in previous work^{5},
a respiratory-triggered acquisition was used. Despite the
fact that our experimental data fulfilled the requirements determined by the
simulations, signal variations were still obscuring the dependence of the
flow-compensated diffusion signal on T, which is needed to determine τ and v.

Registration
of the diffusion-weighted images would be one possibility to reduce the
observed variance. While adding to the complexity of the acquisition,
respiratory and cardiac gating might be necessary for reliable flow-compensated
IVIM, since a signal dependency on the cardiac cycle has been previously reported
for *classic *IVIM^{7}.

We acknowledge NHS founding to the NIHR Biomedical Research Centre and the Clinical Research Facility at The Institute of Cancer Research and The Royal Marsden NHS Foundation Trust and the CR UK Cancer Imaging Centre grant C1060/A16464. We acknowledge funding from CR UK programme grants C33589/A19727 and C7224/A23275. Funding by the DFG grant LA 2804/6-1 is gratefully acknowledged.

1. Le Bihan, D., Breton, E., Lallemand, D., Aubin, M., Vignaud, J., & Laval-Jeantet, M. (1988). Separation of Diffusion and Perfusion in Intravoxel Incoherent Motion MR Imaging. Radiology, 168(2):497-505.

2. Klauss, M., Mayer, P., Maier-Hein, K., Laun, F., Mehrabi, A., Kauczor, H., et al. (2016). IVIM-diffusion-MRI for the differentiation of solid benign and malign hypervascular liver lesion-Evaluation with two different MR scanners. European journal of radiology, 85(7):1289-94.

3. Pan, J., Zhang, H., Man, F., Shen, Y., Wang, Y., Zhong, Y., et al. (2017). Measurement and scan reproducibility of parameters of intravoxel incoherent motion in renal tumor and normal renal parenchyma: a preliminary research at 3.0 T MR. Abdominal Radiology, https://doi.org/10.1007/s00261-017-1361-7.

4. Gurney-Champion, O., Froeling, M., Klaassen, R., Runge, J., Bel, A., van Laarhoven, H., et al. (2016). Minimizing the Acquisition Time for Intravoxel Incoherent Motion Magnetic Resonance Imaging Acquisitions in the Liver and Pancreas. Investigative radiology, 51(4):211-20.

5. Wetscherek, A., Stieltjes, B., & Laun, F. (2015). Flow-Compensated Intravoxel Incoherent Motion Diffusion Imaging. Magnetic Resonance in Medicine, 74(2):410-9.

6. Lemke, A., Laun, F., Klauss, M., Re, T., Simon, D., Delorme, S., et al. (2009). Differentiation of pancreas carcinoma from healthy pancreatic tissue using multiple b-values: comparison of apparent diffusion coefficient and intravoxel incoherent motion derived parameters. Investigative radiology, 44(12):769-75.

7. Federau, C., Hagmann, P.,
Maeder, P., Mueller, M., Meuli, R., Stuber, M., et al. (2013). Dependence
of brain intravoxel incoherent motion perfusion parameters on the cardiac cycle.
PloS One, 8(8):e72856.

**Figure 1:** Diffusion schemes used in this study (left) and acquisition parameters
(right). Diffusion schemes: flow-compensated (top) and monopolar (bottom). Gradients
were placed symmetrically around the refocusing pulse to mitigate concomitant
field artifacts. The diffusion time T was defined as the duration of the
diffusion block and can be adjusted independently of the echo time. Acquisition parameter and series used in this work: One series was monopolar
(constant T, varying b-values), the others flow-compensated (FC). For diffusion times T=52/70 ms the maximum
b-value was 250/450 s/mm^{2}. The
repetition time varied with respiratory cycle, but was at least 1300 ms.