MRI Contrast Calculator: TR, TE, Flip Angle and Scan Time

The conventional short-TE spin-echo approximation is

It assumes ideal 90° excitation and 180° refocusing with TE small compared with TR; the change in longitudinal recovery caused by the refocusing pulse is neglected. See Sung, UCLA M219 (2024), slide 25.

For a completely spoiled gradient echo in steady state,

The fixed point before excitation follows from $M_z^-=M_0(1-E_1)+E_1\cos\alpha\,M_z^-$. Maximizing the signal with respect to angle gives $\alpha_E=\arccos E_1$. See Hargreaves 2012, Eq. 5 (https://doi.org/10.1002/jmri.23742) and Karakuzu 2022, Eqs. 2.5–2.6 (attached s4, pages 56–58). The Ernst result applies to each tissue separately, not to maximum tissue contrast.

Signed contrast is $\Delta S=S_A-S_B$; absolute contrast is $|\Delta S|$. All amplitudes use the same arbitrary reference. The flip-angle chart evaluates spoiled GRE at TE = 0 on a 0.25° grid; its contrast peak is only a sampled demonstration.

Single-echo Cartesian scan time is $t=TR\,N_{phase}\,N_{avg}\,N_{extra}$, after converting TR to seconds. $N_{extra}$ is sequential 2D packages or acquired 3D partitions. Sung, slide 35, gives the independent 1000 ms × 256 × 1 = 4:16 example.

The isolated-pulse animation starts at equilibrium: $M_z/M_0=1-(1-\cos\alpha)e^{-t/T_1}$ and $M_{xy}/M_0=\sin\alpha\,e^{-t/T_2}$. It uses a uniform field, no refocusing and an arbitrary slowed precession rate. Its pulse is 90° for spin echo, or the selected flip angle for GRE; it is separate from the steady-state echo calculation.

• One uniform, monoexponential compartment per tissue, identical receiver sensitivity and a common relative-signal scale. Proton density inputs are user assumptions; equal defaults isolate relaxation contrast.
• T1 and T2 preset means are the “This study” columns of Stanisz et al. (2005), Table 1, printed p. 509 (attached s2, page 3). Measurements were in vitro at 37 °C: mouse liver/muscle/heart, rat kidney/spinal cord, bovine cartilage/brain/optic nerve, and human blood. These are not patient reference ranges.
• The 1.5 T / 3 T choice changes the preset relaxation times only. It does not scale M0 with B0 or predict SNR.
• T2 defaults of 40 and 50 ms are illustrative editable assumptions, not published tissue presets. GRE requires T2 ≤ T2. A physical Bloch compartment also requires T2 ≤ 2T1.
• Ideal instantaneous RF pulses, complete spoiling and established GRE steady state. No inflow, diffusion, magnetization transfer, chemical shift, exchange, B0/B1 errors or receiver noise.
• One acquired phase line per TR; each 3D partition is acquired, while 2D slices can be interleaved within one TR. Package count is supplied by the user. No timing overhead or acceleration is inferred.

Educational use for ideal spin echo and completely spoiled GRE with 0°–90° excitation. It does not model balanced SSFP, unspoiled GRE, inversion recovery, EPI or fast/turbo spin-echo contrast. For the approximate spin-echo formula use TE ≤ TR/10; longer ratios show a warning because the neglected refocusing effect on longitudinal recovery matters. TE = 0 and flip = 0 are mathematical limits, not practical protocols.

Displayed signal is relative amplitude, not scanner intensity, image quality, SNR or CNR. The swatches use a common grayscale and are not an image simulation. Clinical relaxation times depend on tissue condition, species, temperature, measurement technique and magnetic field; the preset means have experimental uncertainty and are not exact constants.

The scan-time estimate covers conventional single-echo Cartesian acquisitions only. It excludes preparation and dummy cycles, calibration, gating delays, phase oversampling, acceleration, partial Fourier and echo trains. Real package packing and hardware timing must come from the scanner. The animation uses a separate isolated pulse and intrinsic T2, rather than a free-induction T2* decay or a simulated repeated pulse train. Precession phase and speed are illustrative, not a Larmor-frequency prediction.

Use for learning, not diagnosis, clinical protocol prescription, implant/SAR assessment or contrast-agent dosing.