Image Contrast: TR, TE, TI & Flip Angle

Why the Same Anatomy Looks Different

A single slice of brain contains a fixed distribution of protons, T1 values and T2 values. Yet the radiologist can make cerebrospinal fluid (CSF) appear jet black on one image and brilliant white on the next, without moving the patient. Nothing about the tissue changed. What changed is when and how often we sampled the magnetization. The scanner offers a small set of timing knobs, principally the repetition time (TR), the echo time (TE), the inversion time (TI), and the flip angle, and these knobs are the clinician control surface that selects which tissue property dominates image contrast.

This lesson assembles the spin-echo signal equation from first principles, maps the TR-TE plane into its four diagnostic corners, predicts how the major tissues behave in each, and then verifies those predictions on real co-registered T1-, T2- and proton-density (PD) data. We close with the practical trade-offs among contrast, signal-to-noise ratio (SNR) and scan time, and the role of gadolinium.

Assembling the Spin-Echo Signal Equation

Consider a conventional spin-echo sequence: a 90 degree excitation pulse, a 180 degree refocusing pulse at time TE/2, and an echo read at time TE, with the whole block repeated every TR. Three physical processes set the echo amplitude.

Proton density. The equilibrium magnetization $M_0$ is proportional to the concentration of mobile hydrogen protons (PD). All else being equal, more protons means more signal.

Longitudinal recovery between excitations. After the 90 degree pulse tips magnetization into the transverse plane, the longitudinal component $M_z$ must regrow before the next excitation. With repetition time TR, the fraction recovered follows the T1 relaxation law. For the steady state of repeated 90 degree pulses, the available longitudinal magnetization is proportional to $1 - e^{-TR/T1}$. Short TR does not let long-T1 tissues recover, so they start the next cycle depleted and appear dark.

Transverse decay during the echo time. Once tipped, the transverse magnetization decays. The 180 degree pulse refocuses static field inhomogeneity, so true spin echo decays with the tissue T2 (not T2*). At echo time TE the surviving signal is proportional to $e^{-TE/T2}$. Long TE lets short-T2 tissues fade while long-T2 tissues persist and appear bright.

Multiplying the three independent factors gives the workhorse equation for spin-echo contrast.

The TR-TE Plane and Its Four Corners

Because TR sits in the T1 term and TE in the T2 term, the two knobs are nearly orthogonal. We can plot every protocol as a point on a plane whose axes are TR and TE, and each corner produces a recognizable weighting. The trick is to drive the unwanted term toward a constant: make $1 - e^{-TR/T1} \to 1$ by choosing TR much greater than T1, or make $e^{-TE/T2} \to 1$ by choosing TE much less than T2.

| Weighting | TR | TE | Dominant term in Eq. 7.1 | Typical 1.5 T values | | --- | --- | --- | --- | --- | | T1-weighted | Short | Short | T1 recovery differences | TR approximately 400 to 700 ms, TE approximately 8 to 15 ms | | T2-weighted | Long | Long | T2 decay differences | TR approximately 3000 to 6000 ms, TE approximately 80 to 120 ms | | Proton density | Long | Short | Spin density (both relaxation terms suppressed) | TR approximately 2000 to 4000 ms, TE approximately 10 to 30 ms | | Mixed or poor | Short | Long | T1 and T2 oppose each other | Avoided; low SNR, confusing contrast |

The fourth corner, short TR with long TE, is deliberately avoided. Short TR suppresses long-T1 tissue while long TE suppresses short-T2 tissue, so the two effects fight, contrast is unpredictable, and the long TE on top of a short TR throws away signal for no diagnostic gain.

Predicting Tissue Appearance

To predict an image, look up each tissue's T1, T2 and PD, then evaluate Equation 7.1 at the chosen TR and TE. Representative brain values at 1.5 T are shown below; absolute numbers rise with field strength (T1 lengthens at 3 T) but the rank order that drives contrast is stable.

| Tissue | T1 (ms, 1.5 T) | T2 (ms) | Relative PD | T1W | T2W | PDW | | --- | --- | --- | --- | --- | --- | --- | | CSF | approximately 3000 to 4000 | approximately 1500 to 2000 | High | Dark | Bright | Intermediate to bright | | White matter | approximately 550 to 650 | approximately 70 to 90 | Lower | Bright | Dark(ish) | Intermediate | | Gray matter | approximately 900 to 1100 | approximately 90 to 110 | Higher than WM | Intermediate | Brighter than WM | Bright | | Fat | approximately 250 to 350 | approximately 60 to 100 | High | Very bright | Intermediate (bright on FSE) | Bright |

Work through CSF as the canonical example. CSF has a very long T1, so on a short-TR T1-weighted scan its longitudinal magnetization barely recovers between excitations and $1 - e^{-TR/T1}$ is small; CSF is dark. CSF also has a very long T2, so on a long-TE T2-weighted scan $e^{-TE/T2}$ stays near 1 while solid tissue has decayed; CSF is bright. This flip from dark to bright is the single most reliable cue for naming a sequence at a glance.

Fat is the mirror image: short T1 means rapid recovery and bright fat on T1-weighted images, which is why orbital and marrow fat glow on T1. Note that on modern fast spin-echo (FSE/TSE) T2-weighted images fat also appears relatively bright because of magnetization-transfer and J-coupling effects, a frequent source of confusion that motivates fat saturation.

Explore the TR-TE Plane Interactively

Use the playground below to vary TR and TE and watch the predicted signal of each tissue track Equation 7.1. Try moving to each corner of the plane in turn and confirm the rank order of CSF, gray matter, white matter and fat against the table above.

Notice three behaviors. First, sliding TR while holding TE short separates tissues purely by T1; the curves fan out at short TR and converge as TR exceeds a few times the longest T1. Second, sliding TE while holding TR long separates tissues purely by T2. Third, at long TR and short TE all curves bunch close together at their PD-determined heights, the low-contrast hallmark of a PD image, where the only remaining differences are spin density.

Inversion Recovery and Flip Angle

Two further knobs extend the control surface. Inversion recovery (IR) prepends a 180 degree inversion pulse, then waits an inversion time TI before exciting. The longitudinal magnetization recovers from $-M_0$ through zero and back, so a tissue whose recovery curve crosses zero exactly at TI contributes no signal. Choosing TI to null a tissue is the basis of STIR (short TI, nulls fat) and FLAIR (long TI, nulls CSF). The null condition follows from setting the recovered magnetization to zero.

For CSF with T1 approximately 3500 ms, Equation 7.2 predicts a nulling TI of roughly 2400 ms, close to the TI used on clinical brain FLAIR. The same logic gives a fat-nulling TI near 150 to 170 ms at 1.5 T for STIR.

Flip angle is the dominant contrast knob in gradient-echo imaging, where short TR makes a full 90 degree pulse wasteful. A smaller flip angle preserves longitudinal magnetization between rapid excitations. The flip angle that maximizes steady-state signal for a given TR is the Ernst angle.

Verify on Real Data

Predictions are only worth what the scanner confirms. The viewer below holds three co-registered volumes of one subject, acquired as T1-, T2- and PD-weighted images. Switch among them and watch CSF in the ventricles and sulci. It should be dark on T1, bright on T2, and intermediate on PD, exactly as Equation 7.1 demands.

Trade-offs: Contrast, SNR and Scan Time

No knob is free. Longer TR linearly lengthens scan time because acquisition time scales as TR times the number of phase-encode lines times the number of signal averages (and divided by any parallel-imaging or multislice efficiency). Longer TE always discards transverse signal, so a heavily T2-weighted image with TE of 120 ms has intrinsically lower SNR than the same scan at TE of 20 ms. The art of protocol design is buying the contrast you need while spending the least signal and time.

Signal averaging (NEX or NSA) is the standard lever for recovering SNR. Averaging $N$ acquisitions adds signal coherently while noise adds in quadrature, so SNR improves as the square root of N, at a cost of N-fold longer scan time.

Gadolinium and T1 Shortening

Gadolinium-based contrast agents are paramagnetic and act predominantly by shortening the T1 of nearby water protons through dipolar relaxation. A tissue that takes up gadolinium (because of a leaky or absent blood-brain barrier, hypervascularity, or interstitial accumulation) recovers its longitudinal magnetization faster, so its $1 - e^{-TR/T1}$ term rises and it brightens on a T1-weighted sequence.

The effect is captured by adding the agent's relaxivity to the native relaxation rate. Because contrast agents shorten T1 far more, in relative terms, than they shorten T2 at clinical doses, enhancement is read on T1-weighted images, which is why post-contrast brain protocols are almost always short-TR, short-TE T1 sequences (often with fat saturation).

Putting It Together

Image contrast is not magic; it is Equation 7.1 evaluated at a chosen point in timing space. Pick short TR and short TE to read T1 differences, long TR and long TE to read T2 differences, long TR and short TE to read proton density, and add inversion pulses, flip-angle choices, or gadolinium to sculpt the result further. Once you can write down the signal equation and recall a tissue's relaxation times, you can predict any clinical image and, just as importantly, recognize when a contrast choice is fighting you.