Appendix A: Simulation of reactivity measurement

Appendix A: Simulation of reactivity measurement

Authors: Lennart Geurts, Alex Bhogal, Jeroen Siero, Peter Luijten, Geert Jan Biessels, Jaco Zwanenburg

1 Introduction The smallest perforators in this study have diameters that are smaller than the acquired voxel size. This causes a partial volume effect between perforator blood signal and the surrounding tissue signal. The partial volume effect increases with a smaller diameter, lower blood flow velocity (through the T1-inflow effect), and higher tissue signal (Brown et al., 2014). This effect might lead to an underestimation of the measured blood flow velocity. Since a hypercapnic stimulus increases perforator diameter and blood flow velocity, it might decrease the amount of velocity underestimation. Unfortunately, this may cause a systematic error in the measured velocity reactivity (Rv). This effect would be most pronounced in the smallest perforators, which are located in the semi-oval center (CSO) for the current study. Due to the small dimensions of the perforators, it is not possible to directly measure the change in vessel diameter. Therefore, we performed simulations to estimate the confounding influence of velocity and diameter increases on Rv in the CSO as measured by 2D phase contrast at 7T. However, to simulate the measurement a baseline velocity, baseline diameter and diameter reactivity must be assumed. Since these values are unknown (for human CSO perforators), we assume that they are similar to values of similarly sized arterioles either at a different location in humans or from animal models.

2 Methods The blood vessel simulations were performed using the Bloch equations as described in our previous publications, with an additional component to simulate increased flow and diameter during the challenge (Bouvy et al., 2016; Geurts et al., 2017). To limit the multi-parametric landscape we divided the simulation into two steps. In the first step we aimed to find a realistic value for the true (unbiased) Rv for a single vessel, given a diameter reactivity (Rd) from the literature. In the second step this representative Rv and the literature Rd were used to simulate measured Rv, for vessels with a range of baseline diameters and velocities. First, to find a representative value of the true Rv for further simulations, a single vessel of 175 µm with a baseline blood flow velocity of 3.0 cm/s was simulated. The measured velocity (including partial volume effects) was simulated for baseline and for a 12 mmHg increase PetCO2 challenge, simulating the combined ranges of 25 Rv values and 25 Rd values (both ranging between 0 and 1%/mmHg). From the simulated velocity measurements during baseline and challenge, the corresponding simulated (biased) Rv was calculated. A line was fitted to the combinations of Rv and Rd simulation input values that yielded a simulated output Rv that was equal to the measured Rv obtained from our data in the CSO. A literature value of Rd for human retinal arterioles (0.5 %/mmHg) was then used to project the required true Rv, that would result in our measured Rv when combined with this literature Rd (Rose et al., 2014; Venkataraman et al., 2017). Retinal arterioles were chosen because they have diameters between tens and hundreds of micrometers, similar to CSO perforators. Second, blood vessels were simulated with a range of baseline velocities (plug flow, 0.5 to 4.0 cm/s) and diameters (50 to 300 µm) inside a 0.3x0.3x2.0 mm3 voxel, with excitation and read-out as

performed in the PC acquisition of the CSO. For each baseline velocity and diameter combination, a challenge velocity and diameter was calculated, using the projected true Rv obtained in the first step, and the Rd from the literature (0.5 %/mmHg), respectively. These velocity and diameter values were used to simulate the measured velocities during the challenge (including partial volume and saturation effects). The simulated measured velocities for baseline and challenge were then used to calculate the Rv, as it would be measured by the PC acquisition. The amount and distribution of Rv overestimation was then qualitatively assessed. The sensitivity of the Rv measurement to baseline diameter was analyzed by calculating the derivative of Rv with respect to baseline diameter. This was performed for a single vessel of 175 µm with a baseline blood flow velocity of 3.0 cm/s (realistic case) and one of 300 µm with a baseline blood flow velocity of 4.0 cm/s (best case). These sensitivities were extrapolated to the smaller baseline diameters of hypertension patients (-4.6 µm) compared to healthy controls (Ikram et al., 2004; Leung et al., 2003). This difference was calculated from literature values of retina arteriolar diameter dependency on blood pressure, for a difference in systolic pressure of 20 mmHg.

3 Results

Supplemental Figure A.1 shows the results for the simulation. The first simulation step yielded a true Rv of 0.4 %/mmHg for a vessel with diameter of 175 um and 3 cm/s velocity at baseline, using the literature value of 0.5 %/mmHg for the Rd and the measured Rv of 0.7 %/mmHg in the CSO. This projected true Rv is almost a factor of 2 lower than the measured Rv. Using this 0.4 %/mmHg as representative for the true velocity reactivity, the simulated Rv map suggests a considerable overestimation of the Rv, for every combination of baseline velocity and diameter. The simulated Rv measurements gradually increase further with smaller diameters and smaller velocities, with a maximum overestimation around 125 µm and 3.0 cm/s. The sensitivity of Rv to baseline diameter was -0.01 %/mmHg/µm for a vessel of 175 µm, corresponding to an additional overestimation of the reactivity of 0.04 %/mmHg for hypertensive patients compared to healthy controls. As expected, the sensitivity approached zero for a vessel of 300 µm with -0.0004 %/mmHg/µm, corresponding to an additional overestimation of only 0.002 %/mmHg for patients.

4 Discussion The results from the simulations showed that velocity reactivity as measured by 2D phase contrast at 7T may be an overestimation. Overestimation is more pronounced with smaller baseline vessel diameters. The additional overestimation in Rv for CSO perforators was estimated to be 0.04 %/mmHg when comparing hypertensive patients (with smaller vessel diameters) to healthy controls. The systematic error in Rv for BG perforators likely approaches zero, since BG perforator diameters approach the voxel size. However, the direction of the systematic error is opposite to the effect of interest. Since patients have smaller arteriolar diameters their reactivity is overestimated more than in healthy controls, while a study would expect to detect a lower reactivity in patients (Ikram et al., 2004; Leung et al., 2003). This means that lower reactivities measured in patients are likely to be true. The simulations were partly based on the choice of a single vessel with a given diameter and velocity, and on a diameter reactivity value taken from literature. The choice of the diameter and velocity of this vessel affects the result for the projected true velocity reactivity that was obtained in the first step of the simulations, and used in the subsequent simulation of the reactivity for a range of diameters and velocities. True Rd values in human perforating arteries might differ from human retinal arterioles, as higher Rd values (1.2-1.7 %/mmHg) are reported for rodent pial arterioles in several studies (Wang et al., 2015; Xu et al., 2016). Due to these assumptions, the exact amount of

overestimation is unknown, which limits the interpretability of the results. However, the overestimation should not hamper between-group comparisons when consistently using the same technique. Besides that, reactivity measurements in larger perforators such as in the basal ganglia should be decidedly less overestimated.

5 Conclusion Simulations showed that velocity reactivity in the CSO measured with 2D phase contrast might be an overestimation, because velocity underestimation decreases with the increased diameter and velocity during the breathing challenge. However, even under the liberal assumptions for the vessel diameter, velocity and diameter reactivity, the projected true reactivity is still within one standard error from the measured reactivity, for the vessel diameter and velocity chosen in the simulation. The systematic errors overestimate reactivity more in patients than in healthy controls, which means that lower reactivities measured in patients are likely to be true.

Figures

Figure A.1, simulated velocity reactivity measurements incorporating the partial volume effect, signal saturation and MRI sequence parameters. Left: The left graph shows simulations for a single perforator with a baseline diameter of 175 µm and a velocity of 3.0 cm/s. The solid black line shows the combinations of simulation input diameter reactivity (Rd input) and velocity reactivity (Rv input) combinations that result in a simulated velocity reactivity measurement, for this perforator, that corresponds to the average measured reactivity in the 10 healthy subjects in the CSO (Rv CSO). The vertical solid gray line shows the literature value for Rd for retinal arterioles(Rose et al., 2014) and the dashed gray line shows the projected true Rv. Right: The right graph color codes the simulated velocity reactivity measurements, output Rv, for a range of baseline velocity and diameter combinations, taking the literature Rd and the projected true Rv from the left graph as input reactivities. The dashed black line shows the iso-contour corresponding to Rv CSO.

References

Bouvy, W.H., Geurts, L.J., Kuijf, H.J., Luijten, P.R., Kappelle, L.J., Biessels, G.J., Zwanenburg, J.J., 2016. Assessment of blood flow velocity and pulsatility in cerebral perforating arteries with 7-T quantitative flow MRI. doi:10.1002/nbm.3306 Brown, R. w., cheng, Y. n., Haacke, M. e., Thompson, michael R., Venkatesan, R., 2014. Magnetic Resonance Imaging: Physical Principles and Sequence Design, 2nd ed. Wiley Blackwell. doi:10.1002/9781118633953 Geurts, L., Biessels, G.J., Luijten, P., Zwanenburg, J., 2017. Better and Faster Velocity Pulsatility Assessment in Cerebral White Matter Perforating Arteries With 7T Quantitative Flow MRI Through Improved Slice Profile, Acquisition Scheme, and Postprocessing. Magn. Reson. Med. Ikram, M.K., Jong, F.J. De, Vingerling, J.R., Witteman, J.C.M., Hofman, A., Breteler, M.M.B., Jong, P.T.V.M. De, 2004. Are Retinal Arteriolar or Venular Diameters Associated with Markers for Cardiovascular Disorders ? The Rotterdam Study 45. doi:10.1167/iovs.03-1390 Leung, H., Wang, J.J., Rochtchina, E., Tan, A.G., Wong, T.Y., Klein, R., Hubbard, L.D., Mitchell, P., 2003. Relationships between Age , Blood Pressure , and Retinal Vessel Diameters in an Older Population 44, 2900–2904. doi:10.1167/iovs.02-1114 Rose, K., Flanagan, J.G., Patel, S.R., Cheng, R., Hudson, C., 2014. Retinal blood flow and vascular reactivity in chronic smokers. Investig. Ophthalmol. Vis. Sci. 55, 4266–4275. doi:10.1167/iovs.14-14022 Venkataraman, S.T., Hudson, C., Rachmiel, R., Buys, Y.M., Markowitz, S.N., Fisher, J.A., Trope, G.E., Flanagan, J.G., 2017. Retinal Arteriolar Vascular Reactivity in Untreated and Progressive Primary Open-Angle Glaucoma 51. doi:10.1167/iovs.09-3630 Wang, C.X., Lin, Y.X., Xie, G. Bin, Shi, J.X., Zhou, M.L., 2015. Constriction and dysfunction of pial arterioles after regional hemorrhage in the subarachnoid space. Brain Res. 1601, 85–91. doi:10.1016/j.brainres.2015.01.012 Xu, H., Changyaleket, B., Valyi-Nagy, T., Dull, R.O., Pelligrino, D.A., Schwartz, D.E., Chong, Z.Z., 2016. The Role of HMGB1 in Pial Arteriole Dilating Reactivity following Subarachnoid Hemorrhage in Rats. J. Vasc. Res. 53, 349–357. doi:10.1159/000452412