Novel T1 Analysis Method to Address Reduced Measurement Accuracy Due to Irregular Heart Rate Variability in Myocardial T1 Mapping Using Polarity-corrected Inversion Time Preparation

Abstract

Purpose

Polarity-corrected inversion time preparation (PCTIP), a myocardial T1 mapping technique, is expected to reduce measurement underestimation in the modified Look-Locker inversion recover method. However, measurement precision is reduced, especially for heart rate variability. We devised an analysis using a recurrence formula to overcome this problem and showed that it improved the measurement accuracy, especially at high heart rates. Therefore, this study aimed to determine the effect of this analysis on the accuracy and precision of T1 measurements for irregular heart rate variability.

Methods

A PCTIP scan using a 3T MRI scanner was performed in phantom experiment. We generated the simulated R-waves required for electrocardiogram (ECG)-gated acquisition using a signal generator set to 30 combinations. T1 map was generated using the signal train of the PCTIP images by nonlinear curve fitting using conventional and recurrence formulas. Accuracy against reference T1 and precision of heart rate variability were evaluated. To evaluate the fitting accuracy of both analyses, the relative fitting error was calculated.

Results

For the longer T1, the fitting error was larger than the short T1, with the conventional analysis showing 10.1 ± 2.0%. The recurrence formula analysis showed a small fitting error less than 1%, which was consistent for all heart rate variability patterns. In the conventional analysis, the accuracy, especially for longer T1, showed a large underestimation of the measurements and poor linearity. However, in the recurrence formula analysis, the accuracy improved at a long T1, and linearity also improved. The Bland–Altman plot showed that it varied greatly depending on the heart rate variability pattern for the longer T1 in the conventional analysis, whereas the recurrence formula analysis suppressed this variation.

Conclusion

T1 analysis of PCTIP using the recurrence formula analysis achieved accurate and precise T1 measurements, even for irregular heart rate variability.

Introduction

Cardiovascular MRI can provide detailed information about the characteristics of myocardial tissues.¹ Myocardial T1 mapping is useful for characterizing the myocardial tissue.² Moreover, T1 mapping and the extracellular volume fraction generated are useful for diagnosing diffuse fibrosis^3–6 and edema,^7–9 which are difficult to evaluate using qualitative findings from the late gadolinium enhancement (LGE) imaging.^10–13

Among the various myocardial T1 mapping strategies,^14–16 the most widely used is the modified Look-Locker inversion recovery (MOLLI) method introduced by Messroghli et al.¹⁷ This method acquires data at multiple inversion times (TI) for one inversion recovery pulse (Look-Locker experiment) using a steady-state free precession (SSFP) readout. This method reportedly provides highly precise T1 measurements and good reproducibility.^2,18 However, it has also been reported that various factors lead to the underestimation of the measurements.² This indicates that it may affect the discrimination between healthy and diseased myocardial tissues. Among them, the influence of heart rate variability is often reported as a physiological factor, which may compromise the accuracy and reproducibility of estimation of T1.^2,17,19 The two main factors that are affected by heart rate variability in the MOLLI method are the interval between multiple inversion recovery (IR) pulses and the effect of SSFP during image reading.² The interval between multiple IR pulses is reported to be the most dominant factor in the original scheme of the MOLLI method; however, improvements in the acquisition scheme have improved its effect.² However, because the Look-Locker experiment was used in the MOLLI method, the influence of the effect of SSFP during image reading remains. There is also a concern that heart rate variability affects the precision of measurement T1 because it relates to the ratio of data acquisition time for the Look-Locker experiment during longitudinal relaxation. Importantly, a T1 measurement method that overcomes both these factors is required.

Polarity-corrected inversion time preparation (PCTIP) is a T1 mapping technique that uses the fast-field echo (FFE) sequence of the gradient echo (GRE) readout.²⁰ This method is based on data acquisition in a single inversion recovery for a prepulse and restoration of the polarity of the longitudinal relaxation by polarity correction of the acquired complex signals. This technique is expected to reduce the underestimation of measured values and the effects of fluctuations owing to heart rate variability caused by multiple readouts in the Look-Locker experiment, which is a concern for the MOLLI.^21,22 However, measurement precision is reportedly reduced, especially for heart-rate variability. This is mainly due to potentially shorter (IR) pulse intervals and transient changes in the observed longitudinal relaxation due to shortening and fluctuations in the RR interval.^21,22 We devised an analysis using a recurrence formula to overcome this problem using the PCTIP method and reported its usefulness for heart rate variability at a constant RR interval.²³ However, in clinical situations, there are concerns about further complex RR fluctuations due to physiological RR interval variations caused by breath-holding and arrhythmias caused by diseases such as extrasystoles. It is speculated that the observed variation in longitudinal relaxation will be more transient than that at constant RR intervals and will greatly affect the T1 measurement results. The recurrence formula analysis can potentially be adapted to any RR interval during data collection; however, its effect has yet to be demonstrated. Therefore, this study aimed to determine the effect of this analysis on the accuracy of T1 measurements of irregular heart rate variability in phantom experiments.

Materials and Methods

PCTIP pulse sequence and T1 analysis

The PCTIP scheme is illustrated in Fig. 1. This method acquires a relaxation curve of longitudinal magnetization in the same cardiac phase (mostly from mid- to end-diastole) over several cardiac cycles in a single breath-hold. IR pulses were applied at the adjusted delay time after every R-wave of the electrocardiogram (ECG) trigger. Data were acquired with multiple TIs modulated against the R-wave trigger for longitudinal relaxation curve estimation. The trigger interval corresponds to a series of time units related to the data acquisition in a single TI. Shorter intervals were associated with shorter total data acquisition durations and used to acquire more data, whereas the imperfections of the longitudinal magnetization recovery increased. The TI and the number of points can be selected arbitrarily depending on the heart rate during the scan. Data were acquired using the FFE pulse sequence of a single slice. The benefits of phase-sensitive reconstruction for cardiac imaging are well accepted for LGE imaging²⁴ and phase-sensitive inversion recovery (PSIR) MOLLI.²⁵ The entire signal series restores the signal polarity, and the fitting of PCTIP signals with restored polarity is more efficient, leading to better T1 maps with fewer erroneous fluctuations. Phase correction uses a proton density (PD) image as a source for background phase estimation. For phase-sensitive LGE, an additional PD image was acquired in addition to the IR image. For PSIR MOLLI, the longest TI that sufficiently recovered magnetization without requiring extra acquisition was selected. Phase correction of PCTIP was performed as in PSIR MOLLI, according to a previous report.²¹ The polarity of the longitudinal relaxation curve was restored using the real component of the complex signals after correcting for the phase error, whereas T1 analysis was performed from the estimated T1 relaxation curve.

Fig. 1.

Scheme of the PCTIP sequence. The schematic representation depicts the data acquisition at five different inversion times gated by the ECG. These data were acquired in the same cardiac phase (mostly from mid- to end-diastole). The data acquisition interval (TR) is illustrated based on two heartbeats (2RR). Each single-shot data acquisition consisted of a ramp-up preparation followed by a fast-field echo readout. ECG, electrocardiogram; PCTIP, polarity-corrected inversion time preparation.

T1 values were estimated from images acquired using a PCTIP signal train. Phase error was determined from the final TI image with corrected positive and negative polarities. Nonlinear curve fitting based on the least-squares algorithm was performed using Equation (1):

$$S_{\left(T{I}_n\right)}=M_0\left(1-2exp\left(-\frac{T{I}_n}{T1}\right)+exp\left(-\frac{TR}{T1}\right)\right)$$ (1)

where $S_{\left(T{I}_n\right)}$, $M_0$, and TR denote signal intensity, equilibrium magnetization, and trigger interval, respectively. This formula indicates that the T1 relaxation is suitable for the PCTIP method derived from the Bloch equation. The second term of this equation corrects for the effect of the short TR described above on longitudinal magnetizati on recovery. This study applied this formula for nonlinear curve fitting for two parameters, M₀ and T1, as in the conventional analysis.

However, the correction term of this conventional method assumes correction of the longitudinal magnetization in the steady state when an IR pulse is continuously applied. Because it is difficult to adapt longitudinal magnetization in the transient state, such as for an early TI during data acquisition, we derived a novel T1 relaxation corresponding to this transient state from the Bloch equation and proposed an analysis formula to allow accurate fitting in such situations. The formula we have previously proposed²³ is given by Equation (2.1):

$$S_{\left(T{I}_n\right)}=M_0\left(1-2\times {\beta }_{n}exp\left(-\frac{T{I}_n}{T1}\right)\right)$$ (2.1)

$${\beta }_n=1-{\gamma }_n\times {\beta }_{n-1}$$ (2.2)

$${\gamma }_n=exp\left(-\frac{TR}{T1}\right)$$ (2.3)

where $\beta$ in Equation (2.2) was used to correct the transient response of the longitudinal magnetization. The transient response depends on T1 and TR, represented by $\gamma$ in Equation (2.3). This response inherits the state before the application each time an IR pulse is applied. In this analysis, the correction term when an IR pulse is applied is incorporated into the recurrence formula to address the correction. In other words, the correction term of the nth TI signal, ${\beta }_n$, is represented by the multiplication of the n-1th transient state, ${\beta }_{n-1}$, whereas the degree of the current influence of the transient response is represented by ${\gamma }_n$. Nonlinear curve fitting was performed for M₀ and T1 as the conventional formula. This previous study proposed the analysis to determine its usefulness for heart rate variability at a constant RR interval. In the current study, this recurrence formula analysis was used to verify its usefulness for fluctuations with irregular RR intervals.

MRI experiment in the phantom study

MRI was performed using a 3T whole-body clinical MRI system (Vantage Titan 3.0T; Canon Medical Systems, Otawara, Japan). A 16-channel head coil is used as the receiver coil. A T1 relaxation phantom (3T multi-CAGN [carrageenan, agarose, and gadolinium chloride], Kato Medience, Okayama, Japan)was used. An overview of the phantom is shown in Fig. 2. The reference T1 and T2 values of the phantom are measured in advance. The multi-CAGN phantom was placed in a shielded room at 22°C for 1 day, and T1 and T2 measurements were performed. Reference T1 measurements were established using a standard inversion-recovery fast-spin-echo sequence, with TI varying from 50 to 5000 ms and a TR of 10000 ms. Reference T2 measurements were established using a standard spin-echo sequence, with TE varying from 30 to 500 ms and TR of 2000 ms. The T1 and T2 maps were analyzed by nonlinear curve fitting based on each relaxation formula using a least-squares algorithm. For the acquired T1 and T2 maps, a circular ROI was placed on the T1 and T2 regions in the multi-CAGN phantom shown in Fig. 2, and the mean value in these regions was calculated as a reference. The relaxation constants and standard deviations within the ROIs at each location in the multi-CAGN phantom obtained from these measurements are shown in Table 1.

Fig. 2.

Structure of the multi-CAGN phantom. Phantom experiments were performed using a 3T multi-CAGN phantom (Kato Medience, Okayama, Japan). Small columnar rods containing substances with various T1 and T2 values were arranged in a larger columnar structure. This image shows the transverse axis of a cylinder. The numbers assigned to each region in the image correspond to T1 and T2 values, as shown in Table 1. CAGN, carrageenan, agarose, and gadolinium chloride.

Table 1.

Reference T1 and T2 values in each position of the multi-CAGN phantom

No.	T1 (ms)	T2 (ms)	No.	T1 (ms)	T2 (ms)
1	207 ± 6.2	49 ± 1.0	6	1644 ± 10	86 ± 1.1
2	250 ± 2.2	52 ± 0.6	7	324 ± 1.5	76 ± 0.6
3	412 ± 2.0	63 ± 0.4	8	141 ± 1.7	41 ± 0.4
4	657 ± 1.8	73 ± 1.2	9	223 ± 2.1	47 ± 0.5
5	1256 ± 8.0	83 ± 0.8	10	482 ± 7.0	61 ± 0.5

CAGN, carrageenan, agarose, and gadolinium chloride.

The PCTIP scan was performed using a dummy ECG generated by an MRI system. The scan parameters included TR = 5.0 ms, TE = 2.0 ms, flip angle (FA) = 13°, bandwidth (BW) = 488 Hz/pixel, number of averages = 1, parallel imaging factor = 2.0, FOV = 34.0× 34.0 cm², matrix = 114 × 240, and slice thickness = 10 mm. The initial TI was set to 50 ms, and the increment was 140 ms. The number of data points was set to 6, and the number of trigger interval was set to two heartbeats (two R-R triggers).

We generated simulated R-waves required for ECG-gated acquisition using an ECG generator and applied them to the ECG transmission module. To achieve an irregular heart rate variability, eight patterns of simulated R-waves, as shown in Fig. 3, were designed with four varying RR intervals as one unit. By varying the initial timings and repeating them periodically during the scan, 30 data combinations were acquired.

Fig. 3.

Scheme of irregular heart-rate patterns used in this study. The rectangle schematically shows the simulated R-wave required for ECG-gated acquisition. An ECG generator is generated and applied to the ECG transmission module. They are set to the pattern of four varied RR intervals and are periodically repeated. Thus, 30 different heart rate variability patterns are simulated in this experiment. ECG, electrocardiogram.

T1 map generation and data analysis

After correcting for the phase error determined from the longest TI image, the polarity of the longitudinal relaxation curve was restored using the real component of the complex signal. Then, T1 estimation was performed using the signal training of the PCTIP images along the TIs in a pixel-wise manner. Nonlinear curve fitting based on the least-squares algorithm using the simplex method²⁶ was performed using the conventional and recurrence formulas, and a T1 map was generated. The analyses were performed using MATLAB (MathWorks, Natick, MA, USA). For the acquired T1 maps, a circular ROI was placed on each rod of the phantom. The average T1 value of the phantom was then calculated. To evaluate the fitting accuracy of both analyses for the measured signals, the relative fitting error was calculated as the sum of the squares of the residuals normalized by the total signal strength.

Results

Performance on the analysis in T1 curve fitting accuracy in both analyses formulas

Figure 4 shows the acquired PCTIP images and curve fitting for both T1 analyses formulas. The left column (a) shows the phase-corrected images at each TI obtained using the PCTIP. The right column (b) shows the T1 relaxation observed from the PCTIP images in the region of T1 = 1644 ms for a certain heart rate variability pattern and the curve-fitted relaxation curves obtained using each analysis formula. The observed longitudinal relaxation showed complicated behavior. The curve-fitted results using the conventional formula (dashed line) and the observed signals (dots) exhibited poor correlation, resulting in poor accuracy in the fitting analysis. In contrast, the curve-fitted results using the recurrence formula (solid line) and the observed signals (dots) achieved good adaptivity, resulting in an accurate fitting analysis.

Fig. 4.

Acquired PCTIP images and curve fitting for both T1 analyses formulas. The left column (a) shows the phase-corrected images at each TI obtained using the PCTIP. The right column (b) shows the T1 relaxation observed from the PCTIP images in the region of T1 = 1644 ms for a certain heart rate variability pattern and the curve-fitted relaxation curves obtained using each analysis formula. The horizontal and vertical axes represent the inversion time and phase-corrected signals at each time point, respectively. The dots represent the measurement data, the dashed line represents the T1 relaxation formula used for the analysis of the conventional method, and the solid line represents the T1 relaxation formula of the recurrence formula analysis method. PCTIP, polarity-corrected inversion time preparation.

Table 2 shows the relative fitting errors of both analyses formulas as the sum of the squares of the residuals normalized by the total signal strength averaged across all heart-rate patterns. The objective T1 in the table is representative of the longest T1 in the phantom (T1 = 1644 ms). The results show the mean and standard deviation for all heart rate variability patterns at each reference T1. For the short T1, there was no difference in fitting accuracy between the two analyses formulas, with both showing small fitting errors less than 1%. For the long T1, the fitting error was larger than the short T1 with the conventional analysis formula showing 10.1 ± 2.0% with a maximum of 15%. Conversely, the recurrence formula analysis showed a small fitting error less than 1%, comparable to the short T1, which was consistent for all heart rate variability patterns.

Table 2.

Relative fitting errors of both analysis formulas as sum of the squares of the residuals normalized by the total signal strength averaged in all heart-rate patterns

Reference T1		Fitting error (%)
No.	T1 value	Conventional analysis	Recurrence formula analysis
1	207	0.16 ± 0.01	0.15 ± 0.01
2	250	0.22 ± 0.01	0.22 ± 0.01
3	412	0.04 ± 0.02	0.04 ± 0.01
4	657	0.44 ± 0.25	0.43 ± 0.25
5	1256	5.22 ± 1.56	0.05 ± 0.05
6	1644	10.1 ± 2.0	0.08 ± 0.04
7	324	0.07 ± 0.01	0.07 ± 0.01
8	141	0.23 ± 0.01	0.23 ± 0.01
9	223	0.10 ± 0.01	0.10 ± 0.01
10	482	0.04 ± 0.03	0.04 ± 0.03

T1 measurement accuracy and precision on heart-rate variability in both analyses formulas

Figure 5 shows the linearity of the mean estimated T1 in heart rate variability resulting from both analyses formulas to the reference T1. In the conventional analysis, the accuracy, especially for the longer T1, showed a significant underestimation of the measurements (1101 ms vs. reference T1 = 1644 ms) and poor linearity (y = 1.43 x−137 r = 0.976). The precision of the measured values among the heart rate variability patterns was also poor (±80 ms for T1 = 1644 ms). On the other hand, in the recurrence formula analysis, the accuracy was improved at a long T1 (1472 ms for T1 = 1644 ms), and linearity was also improved (y = 1.11 x−38.2r = 0.998), which was observed in the conventional analysis. Moreover, the precision of the measured values between heart rate variability patterns also improved to ±24 ms at T1 = 1644 ms.

Fig. 5.

Comparison of the linearity of mean estimated T1 in heart rate variability resulted with both analysis formulas to reference T1. The horizontal axis shows the reference T1 values estimated using the inversion-recovery fast-spin-echo sequence. The vertical axis shows the T1 values of the PCTIP for each analysis. On the left and right are the results of T1 acquired using the conventional and recurrence formula analysis, respectively. The error bar indicates the standard deviation of the mean value within heart rate variability. PCTIP, polarity-corrected inversion time preparation.

Figure 6 shows the Bland–Altman plot for the estimated T1 between both the conventional and recurrence formula analyses and the reference T1. In the conventional analysis, the bias was −75.1 ms, and the upper and lower 95% limit of agreement (LOA) was 263.0 ms and −413.3 ms, respectively. In the recurrence formula analysis, the bias was −23.0 ms, and the upper and lower 95% LOA was 86.8 ms and −132.8 ms, respectively.

Fig. 6.

Comparison of estimated T1 resulted for both analysis formulas to a reference T1 using Bland–Altman plots. The horizontal and vertical axes show the mean and difference in the measured T1 between the reference standard and the results of the PCTIP using each analysis formula. Solid and dashed lines denote bias and 95% limits of agreement. On the left and right are the results of T1 acquired using the conventional and recurrence formula analysis, respectively. PCTIP, polarity-corrected inversion time preparation.

Discussion

This study aimed to achieve T1 mapping using the PCTIP method, which is accurate and precise, independent of heart rate variability. Measurement precision is reduced, especially for heart-rate variability. This is mainly due to potentially shorter IR pulse intervals and two transient changes in the observed longitudinal relaxation due to shortening and fluctuations in the RR interval.^21,22 We devised an analysis using a recurrence formula to overcome this problem in the PCTIP method and showed that it improved the measurement accuracy, especially at high heart rates.²³ At the same time, that report did not clarify the effect of irregular heart rate variability, and this work examines the effect of this analysis method on this effect. This study acquired six TI images using two RRs as the data acquisition units. The total acquisition time varied depending on the sum of the RR intervals but was theoretically between 10.2 and 13.2s for the present heart rate variability pattern. The MOLLI method’s theoretical scan time of 5s(3s)3s scheme was 11s. No comparison of the measured precision accuracy with the MOLLI method was conducted in this study, and the relationship between the measurement accuracy and scan time is a matter of speculation.

The observed longitudinal relaxation for longer T1 values showed complicated behavior. This is mainly due to potentially shorter IR pulse intervals and transient changes in the observed longitudinal relaxation due to shortening and fluctuations in the RR interval.^21,22 From the curve fitting error results, accurate curve fitting was achieved for both analyses formulas at a short T1 (the range of T1 for typical normal myocardium in the delayed enhanced phase). The recovery of longitudinal magnetization during the trigger interval depends on heart rate and target T1. The shorter T1 allows relatively accurate curve fitting in both analyses formulas because the longitudinal magnetization recovers when the next IR pulse is applied, regardless of the short TR or its irregularity. For longer T1s such as native T1, the conventional analysis formula showed a greater increase in the curve fitting error, and the curve fitting results did not adapt to the behavior of complicated longitudinal relaxation curves collected using PCTIP under irregular heart rate variability. Conversely, the recurrence formula analysis achieved curve fitting that accurately adapted to the complicated longitudinal relaxation, and the error was as small as that in the shorter T1.

After the above curve fitting, the estimated T1 for short T1 showed good linearity with respect to the reference T1 in both the conventional and recurrence formula analyses and was consequently accurate. The Bland–Altman analysis also showed good precision for all irregular heart rate variability used in this experiment. In contrast, for a longer T1, the conventional method showed a large decrease in T1 accuracy and poor linearity with respect to the reference T1. Additionally, Bland–Altman analysis showed that measured T1 varied greatly, and precision was poor for irregular heart rate variability patterns. This result was worse than the results with regular heart rate variability reported in previous studies.²³ The recurrence formula analysis achieved higher accuracy than the conventional analysis and showed good linearity, although there was a decrease in accuracy compared to the short T1. The precision for the heart rate variability pattern also showed a greater improvement compared to the conventional analysis. The slight decrease in accuracy may be due to the residual factors caused by the single-shot readout. This is also one of the factors that may cause accuracy loss in the MOLLI due to heart rate variability, which is expected to be relatively small in the PCTIP because it does not use a Look-Locker experiment with multiple signal collection.^2,21–23 However, the TR, which affects the readout of the PCTIP, is slightly longer (TR = 5.0 ms) than that of cardiovascular MR (CMR) sequences with current high-speed data acquisition, such as the MOLLI method.^2,17 Optimization of the pulse sequence, including these factors, may contribute to further improvements in accuracy and should be considered in the future.

This study has some limitations. Human studies on healthy volunteers and patients with cardiovascular diseases should be conducted to validate the recurrence formula analysis. T1 mapping accuracy was evaluated using the final T1 values obtained by curve-fitting analysis. Furthermore, the average ROI on the uniform area of the T1 material in the multi-CAGN phantom was adopted for the measured T1. However, further examination of the precise differences in image quality is required for clinical adaptation, in which a more complicated tissue spatial distribution is important.

Conclusion

This phantom study aimed to determine the effect of the recurrence formula analysis on the accuracy of T1 measurements for irregular heart rate variability. Our results showed that the recurrence formula analysis achieves accurate curve fitting in the complicated behavior of the signals using the acquired PCTIP, and is consistent for all heart rate variability patterns. Furthermore, it was shown to improve accuracy independent of heart rate variability, even for longer T1. Our findings suggest that T1 analysis of PCTIP using the recurrence formula analysis achieved accurate and precise T1 measurements, even for irregular heart rate variability.