07 MRI
Contrast-agent relaxivity
R1 = R10 + r1 C, so T1 falls as gadolinium concentration rises.
Listen
Listen · English
Simulation
Contrast-agent relaxivity — Change the numbers; the scene follows.
Where it works
MRI scanner
Patient in bore
In the tissue inside the bore — relaxation, fat/water, contrast, flow, magic angle.
Open this machineFormula
Variables
Results
R₁
Relaxation rate
3.0833s⁻¹
T₁
T1 with contrast
324.3ms
Curve
Explanation
What it means
Gadolinium shortens T1 (and T2) linearly: R1 = R10 + r1 C. Typical r1 is ~4 s⁻¹ mM⁻¹ at 1.5 T. After a standard dose the blood T1 can drop from ~1200 ms to a few hundred ms, bright on T1-w GRE. This is a working relation in MRI physics.
Where it is used
Clinically it sits on the MRI scanner — Patient in bore. In the tissue inside the bore — relaxation, fat/water, contrast, flow, magic angle. MRI physics lives in the magnet, the gradient, and the voxel: Larmor, Ernst, diffusion, and SAR. These relations decide whether a sequence is possible, safe, and worth the time.
MRI scanner · Open this machineHow to use it
C is millimolar in tissue (not the injected vial). r1 falls somewhat at 3 T vs 1.5 T and depends on protein binding (blood-pool agents). Change one input and watch the curve and the simulation follow.
Symbols
- T_{10}Native T11,200 ms
- r_1Relaxivity4.5 s⁻¹ mM⁻¹
- CConcentration0.5 mM
Worked example
A typical case from the default values: T_{10} = 1,200 ms (Native T1); r_1 = 4.5 s⁻¹ mM⁻¹ (Relaxivity); C = 0.5 mM (Concentration). Substituting into the relation gives R₁ = 3.0833 s⁻¹; T₁ = 324.3 ms. These are teaching numbers — align them with your machine.
Typical values give
- R₁ = 3.0833s⁻¹
- T₁ = 324.3ms
Where it comes from
The displayed formula is the working relation. R1 = R10 + r1 C, so T1 falls as gadolinium concentration rises. Usual reference: Hashemi / Gd package inserts. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Hashemi / Gd package inserts
Assumptions & limits
Fast water exchange, uniform compartment. High C also shortens T2/T2* (dark on long-TE). NSF / deposition risk is a clinical constraint, not in the formula.
Pitfalls
γ for ¹H is not γ for ¹³C. Ernst angle needs the true T1 at that field, not a 1.5 T table used at 3 T. SAR scales with B₀² and flip² — a 3 T copy of a 1.5 T protocol is not automatically legal. Fast water exchange, uniform compartment. High C also shortens T2/T2* (dark on long-TE). NSF / deposition risk is a clinical constraint, not in the formula.
Keep this
Name the nucleus and the field before you quote a Larmor frequency. Fast water exchange, uniform compartment. High C also shortens T2/T2* (dark on long-TE). NSF / deposition risk is a clinical constraint, not in the formula.
In this specialty