07 MRI
Relative SAR
SAR ∝ B₀² θ² / TR × (duty of the RF train). Doubling B₀ quadruples SAR at the same flip.
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Simulation
Relative SAR — Change the numbers; the scene follows.
Where it works
MRI scanner
RF coil
At the RF coil — flip angle, SAR, SNR, receive bandwidth, and the pulse sequence.
Open this machineFormula
Variables
Results
SAR₂/SAR₁
Ratio
4
(B₂/B₁)²
Field term
4
Explanation
What it means
RF power deposited in tissue is the Joule heating of induced E-fields. For a given pulse shape SAR scales as B₀² (because ω = γ B₀ and induced E ∝ dB/dt ∝ ω) and as θ² (voltage × time to reach a bigger flip) and as 1/TR (more pulses per second). That is why 3 T body TSE is SAR-hungry, why we drop flip angles on the refocusing train (hyperechoes, TRAPS), and why IEC whole-body limits (2 W/kg normal, 4 W/kg first-level) bite first at 3 T. This is a working relation in MRI physics.
Where it is used
Clinically it sits on the MRI scanner — RF coil. At the RF coil — flip angle, SAR, SNR, receive bandwidth, and the pulse sequence. 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
Enter two scenarios (B₀, θ, TR). Read the ratio SAR₂/SAR₁. 1.5 T → 3 T at the same sequence is ×4. Halving TR doubles SAR. A 180° pulse is 4× a 90° of the same duration. Change one input and watch the curve and the simulation follow.
Symbols
- B_{0,1}Field 11.5 T
- θ₁Flip 1180 °
- TR₁TR 14,000 ms
- B_{0,2}Field 23 T
- θ₂Flip 2180 °
- TR₂TR 24,000 ms
Worked example
A typical case from the default values: B_{0,1} = 1.5 T (Field 1); θ₁ = 180 ° (Flip 1); TR₁ = 4,000 ms (TR 1); B_{0,2} = 3 T (Field 2); θ₂ = 180 ° (Flip 2); TR₂ = 4,000 ms (TR 2). Substituting into the relation gives SAR₂/SAR₁ = 4; (B₂/B₁)² = 4. These are teaching numbers — align them with your machine.
Typical values give
- SAR₂/SAR₁ = 4
- (B₂/B₁)² = 4
Where it comes from
The displayed formula is the working relation. SAR ∝ B₀² θ² / TR × (duty of the RF train). Doubling B₀ quadruples SAR at the same flip. Usual reference: IEC 60601-2-33 / McRobbie. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: IEC 60601-2-33 / McRobbie
Assumptions & limits
Same pulse shape, same body coil, same patient. Parallel transmit, B1 shimming, and dielectric shading at 3 T make local SAR a different (and harder) number. Does not compute absolute W/kg.
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. Same pulse shape, same body coil, same patient. Parallel transmit, B1 shimming, and dielectric shading at 3 T make local SAR a different (and harder) number. Does not compute absolute W/kg.
Keep this
Name the nucleus and the field before you quote a Larmor frequency. Same pulse shape, same body coil, same patient. Parallel transmit, B1 shimming, and dielectric shading at 3 T make local SAR a different (and harder) number. Does not compute absolute W/kg.
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