Table 1 Design factors when developing a T₁ mapping phantom

Bottle magnetostatics and B ₀ distortion

The ideal phantom would be uniform and ellipsoidal to avoid susceptibility-induced magnetostatic field perturbation. Such a phantom would permit sphere of Lorentz uniformity but this is not easily mass produced. Many phantoms are cylindrical with the long axis along the static field, B ₀ but there is usually off-resonance at the z-ends of such objects [7].

An outer phantom body with a smooth surface and soft rounded-edges, placed inside B ₀ still distorts some of the imposed magnetic field lines at its z-ends so we prescribed scanning halfway along the length of the bottle.

Long term gel stability and risk of moulding

Phantoms with long-term stability could assure the stability of methods applied to patients against scanner alternations and across multiple centers.

Moulding was prevented by aseptic manufacturing, the toxicity of Ni²⁺ ions, and the absence of nutrients in the type of agarose used. Tap water might contain microbial contamination and metal ions so high purity water was used. The main risk is from contraction of gel on loss of water leading to gaps and water condensation but NiCl₂-doped agarose gel phantoms can be stable over a 1-year period [17].

Seal, leakages, air trapping for aqueous fill

Air pockets in the agarose gel phantom will give rise to susceptibility artifacts on account of the large mismatch in static magnetic susceptibility between air and surrounding gel producing a local distortion in magnetic field strength.

The main phantom was sealed by a black polypropylene screw cap fitted with a polyethylene foam insert. Each internal digestive tube was sealed by a tight screw cap. Gel preparation with warm, degassed water reduced air bubble formation. Note the tube “base-upward” setting procedure and subsequent “top-up” of the contracted gel in each tube after setting, described in the text.

Adjustments of B ₀ and reference frequency

Adjustments of B ₀ and scanner reference frequency over the phantom have the ability to impact T₁estimates.

We specified a constant shim volume for each scan. This is manufacturer-dependent—see the T1MES manual [23]. Consistency between repeat scans is the main point.

Gel diamagnetism

In the T1MES model system, because the impact of the paramagnetic ions is so small, we can conceptually treat the main phantom box as if it had no tubes, as if it were just filled with uniform gel throughout

The T1MES system has partly paramagnetic and partly diamagnetic constituents, but the impact of the paramagnetic Ni²⁺ ions is small, around 10 % (because concentrations are small) so the overall interaction is diamagnetic, considering the ~9 parts per million diamagnetism of most tissues relative to air from Lenz electronic diamagnetism.

Gibbs artifact ringing and other inplane effects

Truncating artifacts appear as lines of alternating brightness and darkness in the read-out and phase encode direction. Some effects also from asymmetric readout and ky coverage.

Large diameter digestive tubes to house the 9 agarose doped solutions, so that central regions of each tube are sufficiently distant (a number of pixels away) from regions impacted by artifacts from abrupt signal intensity transitions at the tube edges.

1.4 T, 1.5 T, 3 T performance

Many paramagnetic relaxation modifiers, including Mn²⁺ and Cu²⁺, exhibit significant frequency dependence.

We used Ni²⁺[13].

T₁|T₂ ranges: blood/myocardium, pre/post-GBCA

The T₁|T₂ values were carefully modelled for native and post-gadolinium based contrast agent, blood and myocardium.

5 common tubes, 4 tubes specific to 1.5 T, 4 tubes specific to 3 T. There was no macromolecular addition (no magnetisation transfer modelling) [22].

Tube arrangement

The phantom corners are more prone to inhomogeneities of the B ₀ and B ₁ magnetic fields.

Longer T₁ tubes were placed nearer the middle of the phantom layout and avoided the corners.