Yifan Zhang^{1}, Andre F Martins^{2}, Dean A Sherry^{2}, Christian E Anderson^{1}, and Chris A Flask^{1}

In this initial* in vitro *study, we used Magnetic Resonance
Fingerprinting (MRF)-based T_{1} and T_{2} relaxation time maps
to estimate the linear relationship between pH and relaxivity (r_{1}
and r_{2}) for a previously-described dysprosium (Dy) MRI contrast
agent. These relaxivity estimates were then used to calculate MRF-based estimates
of pH for each solution for comparison with gold-standard measurements by pH electrode at 7.0T (R = 0.93, p = <1e-6) and 9.4T (R =
0.68, p = 0.004). Results show
MRF can be used in combination with a pH-sensitive paramagnetic MRI
contrast agent to accurately estimate pH independent of agent
concentration.

Magnetic Resonance
Fingerprinting has been shown to provide the capability to simultaneously and
dynamically generate T_{1} and T_{2} relaxation time maps. This dynamic MRF approach has been shown
previously to provide the capability to accurately and simultaneously detect
two paramagnetic MRI contrast agents with differing magnetic relaxivities using
a multi-agent relaxation model.^{1-2} Recently, dysprosium (Dy) MRI
contrast agents have been shown to exhibit differential and approximately linear
pH sensitivity in their magnetic relaxivities (r_{1} and r_{2})
over a physiologic range (pH range = 6-8).^{3} Established linear models for the T_{1}
and T_{2} relaxation times as a function of magnetic relaxivities and
contrast agent concentration are shown in Equations 1a and 1b below.

1/T_{1}
= 1/T_{10} + r_{1} * [A] Eq.
1a

1/T_{2}
= 1/T_{20} + r_{2} * [A] Eq.
1b

If we model r_{1}
and r_{2} as linear functions of pH (e.g., r_{1} = a*pH + b; r_{2}
= c*pH + d), these two equations can be simplified to a single equation
independent of the concentration of the contrast agent.

ΔR_{2}/ΔR_{1} = r_{2}/r_{1}
= [c*pH + d] / [a*pH + b] Eq. 2

where ΔR_{2}
(= 1/T_{2} – 1/T_{20}) and ΔR_{1}
(= 1/T_{1}-1/T_{10}) are directly measured by MRF, while a, b,
c, and d are constants to be determined *a
priori* for each contrast agent. In
this initial *in vitro* study, we used
MRF to model the relaxation characteristics of a pH-sensitive MRI contrast
agent (Eq. 2) on a Bruker Biospec 7.0T and a 9.4T MRI scanner. These
pH-relaxivity models were then used to compare MRF-based estimates of with
gold-standard measurements obtained with a pH electrode.

**Discussion & Conclusion**

1. Gu Y, Wang CY, Anderson CE, Liu Y, Hu H, Johansen ML, Ma D, Jiang Y, Ramos-Estebanez C, Brady-Kalnay S, Griswold MA, Flask CA, Yu X. Fast magnetic resonance fingerprinting for dynamic contrast-enhanced studies in mice. Magn Reson Med. 2018 May 9. doi: 10.1002/mrm.27345. [Epub ahead of print] PubMed PMID: 29744935.

2. Anderson CE, Donnola SB, Jiang Y, Batesole J, Darrah R, Drumm ML, Brady-Kalnay SM, Steinmetz NF, Yu X, Griswold MA, Flask CA. Dual Contrast-Magnetic Resonance Fingerprinting (DC-MRF): A Platform for Simultaneous Quantification of Multiple MRI Contrast Agents. Scientific reports. 2017 Aug 16;7(1):8431.

3. Zhang L, Martins AF,
Zhao P, Wu Y, Tircsó G, Sherry AD. LanthanideāBased
T_{2}ex and CEST Complexes Provide Insights into the Design of pH Sensitive MRI
Agents. Angewandte Chemie. 2017 Dec
22;129(52):16853-7.

4. Luo Y, Kim EH, Flask CA, Clark HA. Nanosensors for the Chemical Imaging of Acetylcholine Using Magnetic Resonance Imaging. ACS Nano. 2018 Jun 6. doi: 10.1021/acsnano.8b01640. [Epub ahead of print] PubMed PMID: 29851460

Figure 1 : pH-sensitive contrast agent
structure used in this study.

Figure 2 : MR fingerprinting T_{1} T_{2} maps
of Dysprosium contrast *in vitro* at Bruker 7T. The pH of the agents
varied from 6 to 7.5 with step size of 0.5 in each row and [Dy]
varied from 1 to 4mM in each column. Units : ms.
T_{1} maps shows low linear trends with pH
while T_{2} shows significant linear trend with pH.

Figure 3 : MR fingerprinting T_{1} T_{2} maps
of Dysprosium contrast* in vitro* at Bruker 9.4T. The pH of the agents
varied from 6 to 7.5 with step size of 0.5 in each row and [Dy]
varied from 1 to 4mM in each column. Units : ms.
T_{1} maps shows little linear trends with
pH while some T_{2} maps show significant linear trend with pH.

Figure 4 : Linear pH dependencies for r_{1}
and r_{2}, measured at 7T and 9.4T Bruker systems. The relaxivity
parameter r_{1} and r_{2} for 16 samples were determined from R_{1}=r_{1}*[Dy]+R_{10}, and R_{2}=r_{2}*[Dy]+R_{20}, respectively.

Figure 5 : Algebraic solutions to predict
the pH from MRF estimated ΔR_{1} and ΔR_{2} versus
pH meter measurement of all 16 *in vitro* [Dy]
contrast agent samples. ΔR_{1} and ΔR_{2} are
derived from R_{1} - R_{10 }and R_{2 }- R_{20}, respectively.