Quantitative myocardial perfusion in mice based on the signal intensity of flow sensitized CMR

The data acquisition scheme for this method consists of three scans: (i) Slice selective inversion-TI-acquisition, (ii) Non-select inversion-TI-acquisition, (iii) steady state acquisition with TR set to TI. The method as it was implemented in mice is depicted in Figure 1. A segmented k-space acquisition is assumed. A finite TR is assumed for (i) and (ii). We will derive an expression for magnetization for each of these cases in terms of perfusion in a two compartment model of tissue (Figure 2) where we assume myocardial tissue to be consisting of homogenous intra and extra-capillary space with respect to relaxation time. The rate of change of magnetization in the intra-capillary region m_c(t) depends on loss of magnetization due to T₁ relaxation, exchange of magnetic spins between intra and extra-capillary region and gain of magnetization due to in flow of blood. The magnetization in the extra-capillary region m_e(t) is unaffected by blood flow. The spin dynamics of the two compartments is described by the following modified Bloch equations.

Where T_lx, m_x(t), V_x and K_x are longitudinal relaxation time, magnetization, volume, spin exchange rate respectively with the subscript x=c for intra-capillary region and x=e for extra-capillary region. m_p(t) is the magnetization of the incoming blood. The total magnetization of tissue, M(t), is calculated as,

where λ is the blood tissue water partition coefficient [4], R B V = V c V t and V _T  = V _c  + V _e . Equations 13 describe the time evaluation of the total magnetization of tissue and can be solved for a given input magnetization, m_p(t), depending on the type of spin preparation. For slice-select inversion, m_p(t) is the equilibrium magnetization of capillary blood hence is equal to the constant m_c(0) in magnitude. For non-select inversion, at steady state, m p t = m c 0 1 − 2 e − T I T 1 c + m c 0 e − T R T 1 c, where TI and TR are the inversion and repetition times respectively (see Appendix).

The total magnetization for each spin preparation can be written in matrix from as follows:

for slice-select inversion and

for non-select inversion, where

Equations (5) and (6) can be solved to derive the magnetization for slice-select M_s(t=TI) and non-select inversion M_g(t=TI) using the initial condition that all magnetization within the selected slice is inverted at t=0 in both preparation schemes. The term R can be simplified following a series of steps proposed by Bauer et al. [1, 12] assuming fast exchange between intra and extra capillary regions i.e. Kc≈Ke≈∞. This assumption reduces the complexity of the model but is appropriate for myocardial tissue that has a high exchange rate compared to other tissues of the body [12]. The difference in the signal intensities between the two preparation schemes can now be defined as ΔM = M _g (t = TI) − M _s (t = TI). By combining the simplified expression for R and the solutions to equations (5) and (6) we obtain,

Where, μ = R B V λ 1 T 1 c + 1 − R B V λ 1 T 1 e + P λ

To remove the dependency on receiver characteristics, we normalize ΔM by the magnetization of a steady state gradient echo acquisition (M_s) with no spin preparation and with TR set to the same TI as in equation (7) (Figure 1). Since echo time of this acquisition is small (~ 1ms) we assume that M _s is not affected by perfusion. We also assume equilibrium magnetization of intra and extra-capillary regions to be similar i.e. m _c (0) ≈ m _e (0). Thus we obtain,

Where, μ 0 = R B V λ 1 T 1 c + 1 − R B V λ 1 T 1 e = 1 T 1

Here T ₁ is the myocardial longitudinal relaxation time without the in-flow effects. By dividing equation (7) by (8) we obtain an expression for the normalized magnetization difference, ΔM/M_s Then by taking the first order Taylor expansion of ΔM/M_s about TI we obtain,

Perfusion is derived for a non-exchangeable model of two compartments based on the same acquisition method as described above. The aim is to test the SI-method on a flow phantom. Since water exchange rates of tubing material is difficult to assess we chose material with zero permeability. This allows perfusion to be known exactly in terms of volume of fluid / volume of phantom / minute (i.e. min^-1), given a specific flow rate. The phantom will have two compartments, intra- and extra capillary, but with no exchange between them. Accordingly the SI-method is modified for this scenario by making K_c=0, K_e=0 in equations (2) and (3). The rest of the derivation is similar to as in the previous section.

The difference in the signal intensities between the two preparation schemes, ΔM, is obtained by first order Taylor expansion as in the previous section. By solving for perfusion we get,

Here we do not normalize ΔM by the signal intensity of a steady state acquisition, instead measure m_c(0), the equilibrium magnetization of the capillary fluid, using a spin echo sequence with long TR.

The aim is to compare the results of the T1-method with that of the SI-method using the flow phantom described above. The T1-method was originally developed by Bauer et al. [4] for a fast exchanging two compartment model of tissue. Here we modify it to reflect no exchange between compartments. Again we begin with setting K_c=0, K_e=0 in equations (2) and (3). In the T1-method we are interested in the apparent longitudinal relaxation times and not the magnitudes of magnetization. To make the derivation of relaxation times easier we normalize the magnetization of intra and extra-capillary regions at the time of inversion to one. The equilibrium magnetization on the other hand is set to zero i.e. m_c(0)=m_e(0)=0 in equations (2) and (3). The total magnetization of tissue, M(t), is given by equation (4) as before. Modified Equations 24 can be solved for a given input magnetization, m_p(t), depending on the type of spin preparation. According to the normalizing scheme introduced here the input magnetization, m_p(t), for slice-select inversion is zero and m p t = e − t T 1 c, for non-select inversion.

By taking into account the mean relaxation time approximation that T₁ = ∫ ₀ ^∞ M(t)dt, [4, 13], we obtain the following expressions for apparent relaxation times

for slice-select inversion, and

for non-select inversion. From equations (11) and (12) we derive an expression for perfusion in a two compartment model of tissue with no exchange.

The RBV in the context of the said phantom is equal to the volume ratio V_c/V_T, where V _c is the volume of capillary tube and V _T is the total volume of the phantom as measured from a cross section of the phantom.

A phantom was prepared by placing 12 loops of capillary tube (Cole Parmer # EW 06492–02) with inner diameter 0.51 mm, inside a 3cc syringe. One end of the capillary tube was fitted to a syringe infusion pump (Model R-99E, Razel Scientific Instruments, St. Albans, VT). The space between capillary tubes was filed with a mixture of Gadolinium and Poly Vinyl Alcohol solution. Diluted Gd solution was used as the capillary liquid. Intra and extra-capillary liquids were prepared to have approximately similar longitudinal relaxation times of blood and tissue at 7 Tesla (T _1-intra = 1896 ms, T _1-extra = 1344 ms). Perfusion was calculated using equation (10) for the SI-method and equation (13) for the T1-methods for the following flow velocities 0.03, 0.07, 0.09, 0.1, 0.18, 0.3, 0.35 cm s^-1. The average signal intensity of a region covering the phantom was considered for calculation of ΔM and for curve fitting of T ₁ .

Cardiovascular magnetic resonance (CMR) was performed on a 7T Bruker Biospec system using an inversion recovery FLASH sequence consisting of a sinc3 excitation pulse and a hyperbolic secant pulse (sech) for inversion. For the T1-method, slice select inversion and non-select inversion prepared images were acquired at a constant repetition time, varying the inversion time, TI, in twelve steps between 50 and 5500 ms. TR/TE = 6000 ms/ 2.6 ms field of view = 2.5 × 2.5 cm², flip angle = 30°, slice thickness = 4 mm, a matrix size = 256 × 64. For the SI-method, TR = 1000 ms and TI = 100 ms, flip angle = 90°, All other imaging parameters were set similar to that of the T1-method. Imaging was performed perpendicular to the direction of flow. For both methods, the average signal intensity of a region of interest covering a cross section of the phantom was considered for calculations. T _1s and T _1g were calculated by fitting to a mono exponential function of the form A e − T I T 1 + B. Spin density of intra (ρ_i) and extra-capillary (ρ_e) liquids were obtained by a spin echo pulse sequence with TR=20 sec and with all other imaging parameters including receiver gains fixed. Perfusion was calculated using equation (10) for SI-method and equation (13) for T1-method taking λ = (ρ _i  + ρ _e )/ρ _i and m _c (0) = ρ _i .

The study was conducted under a protocol approved by the Institutional Animal Care and Use Committee. To compare the proposed SI-method with the conventional T1-method, we measured myocardial perfusion of healthy ten weeks old C57BL/6 mice (n=12) using both methods. Mice were anesthetized with continuous inhaled Isoflurane (2% by volume) administered via a nose cone. Constant body temperature of 37°C was maintained using a thermocouple/heater system. Both SI and T1 methods were performed in the same session. To test the reproducibility of the SI-method three perfusion measurements were made on the same mouse. Each measurement was performed on a separate session (often on a different day). Three C57BL/6 mice were used for this study. Finally we used the SI-method to quantify perfusion in a mouse model of ischemia-reperfusion (IR). Four C57BL/6 mice were anesthetized with isoflurane and intubated through the mouth and ventilated. The left coronary artery was ligated with a silk ligature following thoracotomy. The animals were maintained in the ligated state for 30 minutes, after which the externalized silk was pulled to release the constriction and hence allowing full reperfusion. IR mice were scanned within 24 hours of surgery. The in vivo study was performed on a 7T Bruker Biospec system using a custom made solenoid coil having a single turn consisting of a wide conductive sheet (diameter =3.0 cm, length =3.5 cm). The sensitivity of the coil covered approximately 80%- 90% of the mouse’s body. In IR mice, in addition to myocardial perfusion measurement, LGE experiment was performed 30 minutes after injecting a bolus of Gd-DTPA (0.3-0.6 mmol/kg) intraperitonealy. T1 weighted cine imaging was performed in the short axis using a segmented FLASH sequence to highlight enhancement. Slice thickness=1.0 mm, matrix size=256x256, in-plane resolution=117x117 μm2. TE/TR=3/5.2ms, flip angle=30º. Image acquisition was prospectively ECG gated using pediatric ECG probes attached to the paws. A pneumatic pillow was used for respiratory gating (SA Instruments, Stony Brooks, NY).

The acquisition schemes for T1 and SI methods are shown in Figure 1. A gated, Look-Locker sequence [5] was implemented for the T1-method. A 5ms hyperbolic secant pulse was used for inversion. For the T1-method, for each inversion, the relaxation curve was sampled at twelve different inversion times at every third cardiac cycle i.e. TI = 3 × n × RR, n = 1,.12 with R ≈ 50 × RR, that is approximately 6 seconds. For the SI-method the same sequence was used with data acquired at a single TI time of 10×RR with TR=16×RR, that is approximately 2 seconds. In both methods the acquisition block comprised a single excitation pulse followed by one line of k space. For the SI-method an additional steady state gradient echo image was acquired without the inversion pulse with TR=10×RR. All images were acquired in the short axis plane at end diastole. The following common imaging parameters were used: TE = 1.73 ms, field of view = 2.5 × 2.5 cm², slice thickness = 2.0 mm, matrix size = 128 × 64, flip angle = 90° and 10° were used for SI and T1 method respectively. For slice select inversion, the slice thickness of the inversion pulse was set to twice that of the excitation slice to eliminate effects from imperfect edges of both the inversion and the imaging pulse profiles

For the in vivo study we assumed myocardial tissue to consist of fast exchanging two compartments. Therefore we used equation (9) for the SI-method, and equation (1) for the T1-method for calculating perfusion. Following constant values were used: T₁ of blood, T_1c = 1800 ms, T₁ of myocardial tissue in the absence of flow effects, T₁ = 1400 ms, λ=0.95 ml/g [14]. Perfusion was calculated on a pixel-by-pixel basis. The mean value was calculated from an ROI drawn within the left ventricle wall. Pixel values less than −5 ml/g/min and greater than 15 ml/g/min were set to zero and also threshold limit was set to obtain a noise free perfusion map. The apparent T ₁ values obtained by the Look Locker acquisition was corrected for saturation effects as previously described [5].

Results are expressed as mean ± standard deviation. Statistical differences were assessed with the unpaired 2-tailed Student’s t test for two experimental groups. A nonparametric test was applied when the data were not normally distributed. A 2-tailed P value of less than 0.05 was considered statistically significant.