Towards measuring the effect of flow in blood T₁ assessed in a flow phantom and in vivo

Quantitative myocardial tissue characterization has increasingly gained attention in cardiac magnetic resonance imaging (MRI) over the past several years for its ability to non-invasively study the myocardial tissue state (Ferreira et al 2014, Hamlin et al 2014, Moon et al 2013, Messroghli et al 2004). Myocardial T₁ mapping is sensitive to changes in the macro-molecular environment and has demonstrated clinical value in various ischemic and non-ischemic cardiomyopathies (Dall'Armellina et al 2012, Radenkovic et al 2017, Puntmann et al 2016). Additionally, extracellular volume (ECV) mapping is widely used as a marker for fibrotic remodeling of the myocardium in various pathologies (Moon et al 2013, Kim et al 2017, Haaf et al 2016, Messroghli et al 2017, Ntusi et al 2014). ECV maps are calculated based on native and post-contrast T₁ times in the myocardium and the blood-pool, and are normalized with the hematocrit (Hct). When hematocrit was not measured, or to achieve a more stream-lined process that does not require blood sampling and testing, it has been proposed to calculate a Hct estimate using blood T₁ times in a technique called synthetic Hct (Treibel et al 2016). Therefore, ECV and synthetic Hct values are highly dependent on the quality of blood T₁ measurements.

Several cardiac T₁ mapping sequences have been proposed and can be clinically used for native T₁ and ECV mapping (Messroghli et al 2004, Chow et al 2014, Weingärtner et al 2014, Piechnik et al 2010, Weingärtner et al 2015). Modified Look-Locker inversion recovery (MOLLI) (Messroghli et al 2004) is the most widely used method for myocardial T₁ mapping and yields precise T₁ maps but lacks accuracy compared to other T₁ mapping methods (Roujol et al 2014). In MOLLI multiple images with different T₁-weightings are acquired following a non-selective inversion pulse. This repeated image acquisition perturbs the magnetization which is corrected for in the reconstruction (Deichmann correction) (Look et al 1970, Deichmann et al 1992). Saturation recovery single-shot acquisition (SASHA) (Chow et al 2014) was proposed as an alternative for T₁ mapping with increased accuracy. In SASHA images are acquired every heartbeat following a non-selective saturation pulse with varying saturation time. Due to a reduced dynamic range and suboptimal sampling of the recovery curve for long T₁ times, SASHA T₁ maps suffer from reduced precision compared with MOLLI (Weingärtner et al 2016).

Accuracy and precision of myocardial T₁ mapping are integral to its clinical value and have been thoroughly investigated in several recent studies (Kim et al 2017, Haaf et al 2016, Roujol et al 2014, Weingärtner et al 2016, Kellman and Hansen 2014, Cameron et al 2018). It was shown that the dominant variability in blood T₁ comes from the biological constituents such as hematocrit, iron, and HDL cholesterol (Rosmini et al 2019). However, blood T₁ times often fall out of the range for which myocardial T₁ mapping techniques are validated and multiple confounding mechanisms have been proposed (Choi et al 2013, Shang et al 2018). In particular it has been suggested that various flow effects compromise T₁ measurement of the blood-pool (Kellman and Hansen 2014). Given the implicit clinical use of blood T₁ times, thorough investigation of the effect of flow is warranted. However, complex flow patterns in the ventricle as well as a multitude of parameters determining the relevant flow hamper the holistic evaluation of this confounder in vivo.

In this study, we aim to analyze the impact of certain aspects of flow on T₁ measurements with two commonly used myocardial T₁ mapping techniques in well controlled experimental settings in order to further our understanding of flow as a confounding factor. Bloch simulations are performed to shed light on the relative contribution of different flow effects. These effects are then validated in a controlled flow phantom comprising a peristaltic pump with linear flow. Finally, the combined flow dependency of T₁ measurements is studied in vivo by imaging the descending aorta as a proxy, where flow patterns are largely linear and consistently varying across the cardiac cycle.

2.1. Flow effects on blood T₁ measurements

Blood T₁ measurements can be subject to three main flow effects (Kellman and Hansen 2014, Chow et al 2014, Cameron et al 2018) depending on the myocardial T₁ mapping technique (figure 1).

• 1.  
  Non-prepared spins: In T₁ mapping multiple images are acquired with variable delay following a preparation pulse. During this delay spins that were not subject to the preparation (e.g. far outside the isocenter) can flow into the heart. This increases the signal intensity and therefore decreases the measured T₁ relaxation time.
• 2.  
  Beat-to-beat exchange: For sequences such as MOLLI the same magnetization preparation is read out over multiple heartbeats. Spins flowing into the imaging plane from beat-to-beat are not subject to partial saturation by repeated imaging readouts, but are influenced by one slice selective readout only.
• 3.  
  In- and out-flowing spins: Fast flowing spins that flow into the imaging plane during the readout lead to faster signal regrowth due to partial saturation by one train of imaging pulses.

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The Deichmann correction has been introduced to compensate for signal attenuation by continuous FLASH imaging pulses during inversion recovery of static tissue (Deichmann et al 1992) and is used in MOLLI to reduce the impact of the imaging readout on the T₁ time. However, in the presence of flow, the correction factor will also be subject to various flow-effects, including reduced effect of the repeated imaging readout and imperfect inversion due to in-flow of non-prepared spins.

In this study, we try to disentangle the relative contributions of the in-flow of non-prepared spins, beat-to-beat exchange and the flow effect during the imaging readout. We study the effect on the T₁ time, as well as the uncorrected $T_1^*$ for MOLLI and T₁ times calculated with 2- (Kellman et al 2014b) and 3-parameter models in SASHA.

2.2. Sequence parameters

2.3. Simulations

We used flow-sensitive Bloch-simulations to determine the relative contribution of the various flow effects for MOLLI and SASHA imaging sequences with bSSFP and GRE readout. All pulse sequences were simulated with the above listed sequence parameters.

For the no flow case, time periods of free relaxation/precession were simulated as

$$\begin{align} \begin{pmatrix}M_x(t+1)\\M_y(t+1)\\M_z(t+1) \end{pmatrix} = \begin{pmatrix}E_2 & 0 & 0\\ 0 & E_2 & 0\\ 0 & 0 & E_1 \end{pmatrix} \cdot \begin{pmatrix}M_x(t)\\M_y(t)\\M_z(t) \end{pmatrix} + \begin{pmatrix}0 \\ 0 \\ 1-E_1 \end{pmatrix}, \end{align} \tag{ 1 }$$

with $E_1 = \exp\left( t/T_1\right)$, $E_2 = \exp\left( t/T_2\right)$ and the time step t. Center of k-space was chosen to calculate the magnitude with $\sqrt{M_x^2 + M_y^2}$. Imaging and preparation pulses were simulated with corresponding rotation matrices. This magnitude is used for fitting MOLLI and SASHA relaxation curves. Along with the undisturbed relaxation curve without saturation by the readout pulses (no excitation pulses simulated), used as a reference relaxation curve, three different scenarios were simulated: 1) Stationary spins which are repeatedly saturated by the imaging pulses at every heartbeat. 2) Non-prepared spins flowing from the scan periphery into the imaging plane. 3) In-flow of unsaturated spins into the imaging plane during the readout at different flow velocities. For flow simulations, the magnetization vector was split in 1000 magnetization packages $(M_x, M_y, M_z)^T = 1/n \cdot \sum_i^n (M_{x_i}, M_{y_i}, M_{z_i})^T$. In-flow of unsaturated spins is simulated by exchanging magnetization packages with fully relaxed magnetization vectors (1, 0, 0)^T. All simulated spins are influenced by only one slice selective imaging readout, as fresh spins are flowing into the imaging plane from beat to beat. Therefore, between heartbeats the magnetization vectors are set to the magnetization of the undisturbed spins. The cardiac cycle was simulated with R-R intervals = 1000 ms and blood relaxation times were simulated as $T_1 = 2000\ \mathrm{ms}$ (Qin et al 2010, Varela et al 2011, Li et al 2017, Liu et al 2016) and $T_2 = 200\ \mathrm{ms}$ (Liu et al 2016, Chen et al 2009). For a given velocity the proportion of unsaturated spins flowing into the imaging plane per time step was calculated as follows:

$$\begin{equation} \text{percentage of in-flowing spins per time step} = \frac{\text{flow velocity}\cdot \text{time step}}{\text{slice thickness}\cdot\text{readout duration}}. \end{equation} \tag{ 2 }$$

This percentage is used to calculate the amount of magnetization vectors per time step, which are exchanged by the corresponding magnetization vector (all vectors in the magnetization package are the same) from the reference relaxation curve at that time step.

2.4. Phantom experiments

A 30 cm long peristaltic pump (Watson-Marlow-Bredel, 300 Series Laboratory Tube Pumps) was used to circulate gadolinium-doped water from a reservoir outside the scanner bore through a pipe into a dialysis filter (filter with increased diameter, consisting of small fibers). From there the water circulated back outside the bore to the reservoir (figure 2). A dialysis filter with a diameter of 6 cm was used. The dialysis filter and a reference probe (3 cm in diameter) with non-flowing solution were placed in a posterior imaging slice (figure 2). Additionally, imaging was performed in an anterior slice comprising only the dialysis filter. Imaging was performed at five different flow velocities in both flow directions. T₁ measurements were performed using IR, MOLLI T₁/$T_1^*$, MOLLIGRE T₁/$T_1^*$, SASHA and SASHA 2P. Additionally, MOLLI and SASHA were performed with a reduced slice thickness of 4 mm to evaluate the flow effect of in-plane saturation. Reference flow velocities were determined by velocity encoded (VENC) cine measurements in the dialysis filter.

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2.5. In vivo experiments

3.1. Simulations

Figure 3 demonstrates the effects of the previously described flow-induced phenomena studied in isolation with noise-free Bloch simulations for MOLLI and SASHA.

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3.1.1. In-flow of non-prepared spins

The simulation results in figure 3 show that in-flow of 2% non-prepared spins per heartbeat (purple lines in figure 3) leads to faster recovery and shortened apparent relaxation times. This effect is studied in greater detail for various degrees of in-flow in figure 4. Both MOLLI and SASHA show underestimation, which is increasingly pronounced with higher in-flow. Simulations indicate that for in-flow of 10% non-prepared spins, T₁ time accuracy is compromised by more than 30% and 15% for MOLLI and SASHA, respectively.

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3.1.2. Beat-to-beat exchange

Repeated application of imaging pulses leads to signal attenuation across heartbeats in stationary tissue (orange lines in figure 3). However, our results show that even slow flow velocities cause an exchange of the spins between heartbeats (beat-to-beat exchange), such that the imaging signal is just affected by a single set of imaging pulses for any given heartbeat (yellow lines in figure 3). Accordingly, the reduced signal attenuation from previous heartbeats leads to reduced underestimation of T₁ times compared with MOLLI values as commonly obtained in stationary tissue. Without Deichmann correction this leads to a major difference ($\triangle T_1^* > 200\ \mathrm{ms}$), but was largely mitigated when using Deichmann correction ($\triangle T_1^* \lt 60\ \mathrm{ms}$).

3.1.3. In-flow and out-flow during a readout

Flow during the imaging readout leads to further alteration of the magnetization signal as it leads to faster recovery during one imaging readout (i.e. between two imaging pulses, yellow lines in figure 3). This effect is studied in detail in figure 5 at various flow-velocities. Increased T₁ times are observed for SASHA 2P and increased $T_1^*$ times for MOLLI at slow flow up to 5 cm s⁻¹. However, the magnitude of this effect is small compared to the previously listed contributions (∼1%). Furthermore, the effect is strongly mitigated by using MOLLI with Deichmann correction or SASHA with a 3-parameter fit model. Of note, the consistent offset in T₁ observed with MOLLI is due to incomplete inversion efficiency caused by in-flowing spins. This is not due to its intrinsic well documented errors because we assume that all spins exchange from beat-to-beat and therefore no spins are affected by multiple readouts.

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3.2. Phantom experiments

Figure 6 shows the T₁ times measured in the flow phantom for various flow velocities. Negative flow direction for T₁ measurements in the posterior slice and positive flow for the anterior slice, lead to in-flow of spins from the reservoir outside the scanner bore, into the imaging plane. For these regimes (blue shaded area, figures 6(a) and (b)) T₁ times decrease by up to 125 ms with a decrease of 25 ms per 1 cm s⁻¹ for SASHA/SASHA 2P and up to 250 ms with a decrease of 50 ms per 1 cm s⁻¹ for MOLLI/MOLLIGRE with and without Deichmann correction. The highest deviation is observed at the largest velocity amplitude ($v \sim 5\ \mathrm{cm}\ \mathrm{s}^{-1}$).

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For absolute flow-velocities larger than $1-1.5\ \mathrm{cm}\ \mathrm{s}^{-1}$ all spins from the imaging readout can be assumed to have left the imaging plane during one heartbeat (beat-to-beat exchange). However, for slow absolute flow velocities ($-1.5\ \mathrm{cm}\ \mathrm{s}^{-1}$ to 1.5 cm s⁻¹) a varying degree of beat-to-beat exchange can affect the T₁ times. In this regime (gray shaded area, figures 6(a) and (b)) MOLLIs without Deichmann correction show a symmetrical peak for around $v = 0\ \mathrm{cm}\ \mathrm{s}^{-1}$, leading to $T_1^*$ deviation of more than 200 ms. This contribution is largely eliminated when using a Deichmann correction. SASHA shows only minor variation in this flow regime, which is expected as beat-to-beat exchange does not affect the SASHA signal due to the repeated saturation.

For large flow-velocities in the opposite flow direction, mostly prepared spins are flowing into the imaging plane. In this regime (white shaded area, figure 6(a) and (b)) varying amount of in-flow/out-flow during the readout is expected to be the dominant effect inducing flow susceptibility. MOLLI without Deichmann correction shows sensitivity to this flow effect, with increasing $T_1^*$ times for increasing flow magnitude. However, the effect is largely mitigated using Deichmann correction. No sensitivity to flow for SASHA or SASHA 2P can be discerned from the noise level in this regime. These findings are corroborated by the results of measurements with different slice thickness (figure 7), which also leads to difference in in-flow/out-flow during the readout. All T₁ methods yield excellent agreement for measurements at 4 mm and 8 mm slice thickness (absolute deviation less than 20 ms), except MOLLI without Deichmann correction. Substantial variation up to 80 ms is observed in the presence of flow, but excellent agreement is shown for the minimal flow case (deviation less than 26 ms).

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In the reference probe T₁ maps of SASHA/SASHA 2P achieved good agreement with IR yielding deviations less than 6% whereas MOLLI T₁/MOLLI $T_1^*$ underestimated the T₁ time of approximately 15%. MOLLIGRE underestimated the T₁ time by almost 20% and MOLLIGRE $T_1^*$ by 28%. All measurements resulted in standard deviations of less than 50 ms for SASHA, SASHA 2P, MOLLI, MOLLIGRE and less than 100 ms for MOLLI $T_1^*$ and MOLLIGRE $T_1^*$.

3.3. In vivo experiments

MOLLI T₁ maps were generated for an axial cross-section of the aorta at various time points throughout the cardiac cycle. Across all subjects, peak velocities up to 120 cm s⁻¹ were measured with an average peak velocity of $77\pm 24\ \mathrm{cm}\ \mathrm{s}^{-1}$. Figure 8 depicts the flow velocity and blood T₁ times as a function of time within the cardiac cycle of one healthy subject. A summary of T₁ times in the absence of flow and during peak velocity are given in table 1. T₁ times increased with decreasing velocity with differences up to 186 ms. Across all subjects MOLLI and MOLLIGRE measured during the diastole (slow flow) resulted in T₁ times comparable to the left ventricle in the SHAX measurement. Mean differences of T₁ times between peak flow and time point of minimal flow, and their corresponding standard deviations were $163 \pm 57\ \mathrm{ms}$ for MOLLI, $115 \pm 41\ \mathrm{ms}$ for MOLLIGRE, $424 \pm 192\ \mathrm{ms}$ for MOLLI $T_1^*$ and $362 \pm 181\ \mathrm{ms}$ for MOLLIGRE $T_1^*$. T₁ maps with Deichmann correction were more precise with standard deviations in the aorta of 107–252 ms over the cardiac cycle. Without Deichmann correction standard deviations vary from 203 ms for MOLLI up to 726 ms for MOLLIGRE respectively.

Table 1. Tabular of all in vivo blood T₁ values. Aortic blood T₁ times for MOLLI and MOLLIGRE with and without Deichmann correction for six healthy subjects. T₁ times for the time points in the cardiac cycle with no and maximum flow velocities are provided.

subject,		Deichmann	speed	min. flow T1	peak flow T1	diff. T1
gender	Sequence	correction	[cm s−1]	[ms]	[ms]	[ms]
1, f	MOLLI	on	76	1917±107	1759±66	158
		off		2126±384	1806±231	319
	MOLLIGRE	on		1838±375	1664±170	174
		off		2456±825	2041±649	415
2, m	MOLLI	on	64	1809 ± 252	1751 ± 121	58
		off		1898 ± 726	1965 ± 386	67
	MOLLIGRE	on		1757 ± 186	1737 ± 133	20
		off		2056 ± 843	1853 ± 656	203
3, m	MOLLI	on	63	1868 ± 123	1681 ± 209	186
		off		1839 ± 366	1159 ± 785	680
	MOLLIGRE	on		1757 ± 186	1737 ± 133	20
		off		2056 ± 843	1853 ± 656	203
4, f	MOLLI	on	54	1973 ± 222	1817 ± 424	156
		off		1921 ± 562	1430 ± 951	490
	MOLLIGRE	on		1930 ± 99	1844 ± 204	86
		off		2150 ± 330	1846 ± 675	304
5, m	MOLLI	on	87	1662 ± 162	1580 ± 410	82
		off		1607 ± 207	1039 ± 725	568
	MOLLIGRE	on		1639 ± 123	1552 ± 185	87
		off		1731 ± 457	1382 ± 627	349
6, m	MOLLI	on	120	1792 ± 174	1650 ± 301	142
		off		1638 ± 203	1297 ± 631	342
	MOLLIGRE	on		1734 ± 213	1650 ± 294	84
		off		1663 ± 452	1445 ± 671	218

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In this study we performed flow-dependent T₁ measurements using MOLLI and SASHA to evaluate different contributions of flow effects with simulations, phantom and in vivo measurements. Three flow effects were studied to play a role in blood T₁ measurements:

• In-flow of non-prepared spins from outside the scanner bore increase the signal magnetization and induce a faster T₁ relaxation.
• Sufficiently fast spins flowing outside the imaging plane from heartbeat to heartbeat eliminate the in-plane saturation effect and can result in decreased underestimation of MOLLI T₁ times compared with stationary tissue. However, the effect is small when Deichmann correction is used.
• Spins which flow inside and outside the imaging plane during one readout increase the signal intensity. This leads to higher $T_1^*$ for MOLLI but was mitigated when using Deichmann correction and did not affect SASHA.

Simulations and phantom measurements indicate that in-flow of non-prepared spins is the dominant flow effect. Our results show that this can lead to substantial deviations in the T₁ time, especially for large fractions of in-flowing non-prepared spins. The effect on SASHA T₁ times was substantially smaller compared with MOLLI because a non-selective saturation pulse erases the magnetization every heartbeat. For MOLLI T₁ times in-flow of non-prepared spins exacerbates T₁ underestimation.

The amount of non-prepared spins in blood T₁ measurements depends on a number of system and subject specific patterns. Besides the properties of the individual's circulation, the pulse type, the $B_1^+$ and B₀ inhomogeneity off the isocenter determine the reach of the preparation pulse. For the commonly used tan/tanh pulse as proposed by Kellman et al (Kellman et al 2014a) inversion efficiency of less than 0.5 is observed for around 1/3 of the peak B₁ amplitude. Our used body coil with 55 cm length has a 50% B₁ amplitude decrease 15 cm away from the iso-center. Therefore, spins outside the bore are negligibly influenced by the non-selective preparation pulses. Blood takes about 20 seconds for one circulation throughout the entire vascular system. Hence, throughout the inversion span of a typical MOLLI sequence, which reaches up to 5 seconds, non-negligible amounts of un-prepared spins can be expected to flow into the imaging plane.

The impact of the other two flow effects was relatively small compared to in-flow of non-prepared spins. Furthermore, the impact of the beat-to-beat exchange and the flow during the imaging readout were effectively mitigated using the Deichmann correction for MOLLI or using SASHA. We performed MOLLI experiments with and without Deichmann correction to fully understand the cause of flow susceptibility. Our simulations also showed that for increasing T₁ all flow effects increase. However, simulations and phantom measurements demonstrated higher resilience to flow effects in MOLLI with Deichmann correction, despite the known discrepancy between the assumptions underlying the correction and the MOLLI sequence (Shang et al 2018).

The effect of flow on the blood T₁ time plays a role in the calculation of ECV. However, our results indicate that the flow effects are more pronounced for longerT₁ times. The ECV calculation is more susceptible to changes in the post-contrast T₁ times, and thus shows stronger resilience to flow induced variations. Given the simulated effects from figure 4, errors about 5% can be expected for ECV. However, the synthetic Hct is inversely proportional to the native blood T1 times. Thus, decreasing blood T1 times increases the Hct. With flow induced T1 deviations of up to 20% synthetic Hct may vary by up to 17%. Hence, when using synthetic Hct for ECV calculation this error propagates to the ECV value linearly.

In vivo measurements confirm the flow effect of decreasing T₁ times by increasing flow velocity in the descending aorta. Due to the relatively high standard deviation in vivo, in-flow and out-flow of spins during a readout as observed in phantom can be assumed to be negligible. Flow susceptibility due to varying degrees of beat-to-beat exchange can also be assumed to be negligible due to the high ejection fraction in the aorta. Accordingly, our in vivo results in the aorta suggest a strong impact of in-flow of non-prepared spins on the T₁ time, indicating potential in vivo contribution of the dominant effect observed in phantom and simulations.

MOLLI T₁ mapping is well known to be susceptible to variations in prescribed or actual flip-angles (Cooper et al 2014, Kellman et al 2013). In-flow of spins during the readout, also impacts the amount of signal attenuation in tissue, although with different underlying principles. Therefore, we studied the contribution of flow to MOLLI T₁ times. Simulations suggested that the Deichmann correction is highly effective in mitigating the effects of variable signal saturation in the presence of flow. To further confirm this result, phantom experiments were conducted in a slow flow regime. In these experiments, in-flow during the readout is expected to affect T₁ times independent of the flow direction thus constituting a symmetrical peak. While this effect was observed the relative contribution compared with in-flow of non-prepared spins was almost negligible after Deichmann correction. This was further confirmed in scans with decreased slice thickness, which leads to increased in-flow/out-flow during the readout for a given flow velocity. As shown in our simulations, theoretically there is no need for correcting with Deichmann for sufficient fast flow. Nevertheless, our phantom measurements resulted in decreased T₁ times with higher standard deviations compared with using the Deichmann correction.

SASHA T₁ mapping showed substantially lower susceptibility to flow effects. However, residual changes in T₁ times were induced, primarily due to the in-flow of non-prepared spins. In simulations and phantom experiments, constant flow velocities were simulated throughout the heartbeat. However, in vivo in-flow of non-prepared spins is largely restricted to the systolic phase, potentially leading to even smaller flow susceptibility in the T₁ measurement. However, no SASHA imaging could be performed to study the flow effect in the aorta directly, as SASHA is incompatible with a variable readout timing with respect to the cardiac cycle.

Overall, our results demonstrate that under controlled conditions the T₁ times of moving fluids can be strongly dependent on flow velocities. These results are obtained in simplified and well controlled conditions. However, a multitude of factors likely determines the effect size on left ventriclualr blood T₁ as commonly performed. While this limits the feasibility, our results confirm the literature postulation that in-flow of non saturated spins is a potential confounder in blood T₁ measurement. The total in-flow and the flow velocity depends on a number of physiological parameters. The total stroke volume determines how much potentially non-prepared spins can flow in from the periphery. The patient size can affect the amount of blood in the periphery that is potentially not completely prepared. Ejection fraction can also be a confounding factor for blood T₁ measurements as this can variably affect the amount of beat-to-beat exchange. Hence, our results suggest that the use of blood T₁ as an independent parameter warrants careful consideration. Thorough control for flow determining physiology might potentially help to reduce variability (Becker et al 2019, Collis et al 2001, Barone-Rochette et al 2013). Due to the important role of blood T₁ in ECV mapping and due to its recent use in synthetic Hct numerous clinical studies evaluated cardiomyopathies based on blood T₁ based quantities (Haaf et al 2016, Kellman et al 2012, Ugander et al 2012, Ntusi et al 2014, Cameron et al 2018, Messroghli et al 2017, Moon et al 2013). As the effects observed in quantitative myocardial tissue characterization are often small it is paramount to understand potential confounders. Our results indicate that measurements in patients with largely varying flow-determining physiology could lead to increased variability in blood T₁ based biomarkers. This can potentially hamper the identification of pathological changes.

This study has several limitations. A number of simplifications had to be made in order to systematically analyze the impact of flow on myocardial T₁ mapping. These simplification limit the direct feasibility of the results to the measurements of blood T₁ times in the left ventricle. Firstly, the phantom setup was a simplified approach to measure the effects of different flow patterns in isolation. The reservoir was put outside the bore to create an environment where non-prepared spins flow into the imaging plane. However, the fraction of spins that is poorly polarized is likely smaller in vivo than as in this setting. Imaging of the descending aorta was performed as an in vivo model with controllable instantaneous flow velocities. However, different and more variable flow patterns are characteristic for the left ventricle potentially giving rise to different flow response of the T₁ time. A difference in local flow-patterns can potentially have minor impact on the effects of in-/out-flow during the readout. In our simulations we assumed 100% inversion efficiency with a rectangular slice profile without taking the distribution of flip angles into account. However, in-plane saturation only demonstrated minor effects on blood T1 times. For this reason we suspect that a distribution of flip angles as a result of the slice profile will only play a minor role. However, given our results indicate overall negligible contribution of this flow effect a detailed analysis of turbulent flow in dedicated phantoms or the ventricles might not be required.

T₁ times in moving fluids such as blood obtained with commonly used T₁ mapping techniques can be susceptible to flow-effects. In our simplified model analysis, we found the most significant flow effect due to in-flow of non-prepared spins. Other flow-induced effects showed minor impact and were well compensated for using either a Deichmann correction for MOLLI or SASHA. Overall, SASHA proved to be less prone to flow effects as the magnetization is saturated in every heartbeat compared with MOLLI, where a single inversion pulse spans up to five heartbeats. These results are suggestive that in-flow of non saturated spins could potentially be detrimental to blood T₁ measurements with potential implications for analysis of ECV and synthetic Hct, but thorough clinical investigation of the impact is warranted.