NMR spectroscopy is often described as a quantitative analytical technique. Strictly, only the simple pulse-acquire experiment is universally quantitative, but the poor signal resolution of the ¹H NMR pulse-acquire experiment frequently complicates quantitative analysis. Pure shift NMR techniques provide higher resolution, by reducing signal overlap, but they are susceptible to a variety of sources of site-dependent signal loss. Here, we introduce a new method that corrects for signal loss from such sources in band-selective pure shift NMR experiments, by performing different numbers of iterations of the same pulse sequence elements before acquisition to allow extrapolation back to the loss-free signal. We apply this method to both interferogram and semi-real-time acquisition modes, obtaining integrals within 1 % of those acquired from a pulse-acquire experiment for a three-component mixture.

NMR spectroscopy is often described as a quantitative analytical technique. Strictly, only the simple pulse-acquire experiment is universally quantitative, but the poor signal resolution of the ¹H NMR pulse-acquire experiment frequently complicates quantitative analysis. Pure shift NMR techniques provide higher resolution, by reducing signal overlap, but they are susceptible to a variety of sources of site-dependent signal loss. Here, we introduce a new method that corrects for signal loss from such sources in band-selective pure shift NMR experiments, by performing different numbers of iterations of the same pulse sequence elements before acquisition to allow extrapolation back to the loss-free signal. We apply this method to both interferogram and semi-real-time acquisition modes, obtaining integrals within 1 % of those acquired from a pulse-acquire experiment for a three-component mixture.

"Rationalising spin relaxation during slice-selective refocusing pulses"Experimental data for six doped water samples [/Experimental_doped_water/]===========
These data were used to generate Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S7, Figure S11, Figure S12, Tables S5-S11 and Table S13 in the Supporting Information.
These data were analysed using the "UoM_RSR_lsqcurvefit" and "UoM_queue_RSR_lsqcurvefit" MATLAB functions.

Experimental_doped_water_integrals - Spreadsheet containing the absolute integrals obtained from slice-selective spin echo experiments performed on doped water samples 1-6
Directory structure for experimental data for doped water samples 1-5 (see Table 1 in main manuscript):
4 - 1H pulse-acquire NMR experiment5 - 1H inversion recovery NMR experiment (GNAT data in "GNAT" subfolder)6 - 1H Carr-Purcell Method A NMR experiment (GNAT data in "GNAT" subfolder)101-110 - Slice-selective spin echo NMR experiments using an rSNOB refocusing pulse of varying duration111-120 - Slice-selective spin echo NMR experiments using a REBURP refocusing pulse of varying duration121-130 - Slice-selective spin echo NMR experiments using a Gaussian refocusing pulse of varying duration131-140 - Slice-selective spin echo NMR experiments using a rectangular refocusing pulse of varying duration

Directory structure for experimental data for doped water sample 6 (see Table 1 in main manuscript):
4 - 1H pulse-acquire NMR experiment5 - 1H inversion recovery NMR experiment (GNAT data in "GNAT" subfolder)6 - 1H Carr-Purcell Method A NMR experiment (GNAT data in "GNAT" subfolder)101-113 - Slice-selective spin echo NMR experiments using an rSNOB refocusing pulse of varying duration121-133 - Slice-selective spin echo NMR experiments using a REBURP refocusing pulse of varying duration141-153 - Slice-selective spin echo NMR experiments using a Gaussian refocusing pulse of varying duration161-173 - Slice-selective spin echo NMR experiments using a rectangular refocusing pulse of varying duration

==========Simulated data for the six doped water samples [/Simulation_doped_water/]=========
These data were used to generate Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S10, Tables S5-S11, Table S13 and Table S14 in the Supporting Information.
These data were analysed using the "UoM_RSR_lsqcurvefit" and "UoM_queue_RSR_lsqcurvefit" MATLAB functions.

The data from each simulation is contained within a numbered folder. Three parameters are varied across the 252 simulations, in following order of precedence: pulse duration, sample (i.e., T1 and T2 time constants), and pulse shape. The T1 and T2 relaxation time constants matched those of the experimental samples.
1-63 - Slice-selective spin echo NMR Spinach simulations using an rSNOB refocusing pulse of varying duration performed on doped water samples 1-664-126 - Slice-selective spin echo NMR Spinach simulations using a REBURP refocusing pulse of varying duration performed on doped water samples 1-6127-189 - Slice-selective spin echo NMR Spinach simulations using a Gaussian refocusing pulse of varying duration performed on doped water samples 1-6190-252 - Slice-selective spin echo NMR Spinach simulations using a rectangular refocusing pulse of varying duration performed on doped water samples 1-6

==================================================================================================================================================================================Analysis of the experimental and simulated doped water data [/Analysis_doped_water/]===========
Analysis of the experimental and simulated doped water data were used to generate Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S12 and Tables S5-S14 in the Supporting Information.
The two functions used to perform this analysis were the "UoM_RSR_lsqcurvefit" and "UoM_queue_RSR_lsqcurvefit" functions. The specific functions used to perform each analysis maybe found, along with the analysis output, in the subfolders of this directory.
UoM_RSR_lsqcurvefit: MATLAB function used to perform global fitting of the data from slice-selective spin echo NMR experiments and Spinach simulations performed on the six doped water samples to various proposed relaxational attenuation modelsUoM_queue_RSR_lsqcurvefit: MATLAB function used to queue calls to the "UoM_RSR_lsqcurvefit" function and provide input parameters for the processing and analysis. These input parameters may be found in the "params.mat" files.

ModelFitting - Global fitting of the experimental and simulated doped water data to seven different models of relaxational attenuation (Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S7 and Tables S5-S11 in the Supporting Information)OnRes - Global fitting of the simulated doped water data from an on-resonance frequency-selective spin echo simulation (Figure S8 and Table S12 in the Supporting Information)Residuals - An examination of the residuals surface when performing global fitting (Figures S9-S12 in the Supporting Information)OppositeFitting - An examination of the residuals when fitting the simulated data with the optimal alpha and beta values determined for the experimental data, and vice versa (Table S13 in the Supporting Information)Fidelity - An investigation into the fidelity of the Spinach simulations performed by performing global fitting with different offset spacings (Table S14 in the Supporting Information)

========Simulated data in the linear attenuation regime [/Simulation_linear_attenuation/]=========
These data were used to generate Figure 3 and Table 3 in the main manuscript.
UoM_RSR_r1r2_offset_dependence - MATLAB function used to analyse the data from Spinach simulations of slice-selective spin echo experiments in the linear attenuation regime
1-4 - Slice-selective spin echo NMR Spinach simulations using a 10 ms rSNOB refocusing pulse, performed on single-spin systems with small differences in T1 and T2 5-8 - Slice-selective spin echo NMR Spinach simulations using a 10 ms REBURP refocusing pulse, performed on single-spin systems with small differences in T1 and T2 9-12 - Slice-selective spin echo NMR Spinach simulations using a 10 ms Gaussian refocusing pulse, performed on single-spin systems with small differences in T1 and T2 13-16 - Slice-selective spin echo NMR Spinach simulations using a 10 ms rectangular refocusing pulse, performed on single-spin systems with small differences in T1 and T2Analysis - Contains the output of the analysis of these data performed using the "UoM_RSR_r1r2_offset_dependence" function

=========Diffusional attenuation analysis [/Diffusional_attenuation/]==========
These data were used to generate Figure S13 in the Supporting Information.
UoM_RSR_diffusional_atten - MATLAB function used to predict the HDO signal loss due to diffusional attenuation in the slice-selective spin echo NMR experiments performed on the six doped water samples

=========Bloch sphere simulations [/Bloch_spheres/]==========
These data were used to generate Figure 1 in the main manuscript and Table S15 in the Supporting Information.
UoM_RSR_Bloch_spheres - Mathematica notebook used to calculate magnetisation trajectories in the Bloch sphere by numerical integration
UoM_RSR_diffusional_atten - MATLAB function used to predict the HDO signal loss due to diffusional attenuation in the slice-selective spin echo NMR experiments performed on the six doped water samples

=========Bloch sphere simulations [/Bloch_spheres/]==================================================================================================================================================================================
These data were used to generate Figure 1 in the main manuscript and Table S15 in the Supporting Information.
UoM_RSR_Bloch_spheres - Mathematica notebook used to calculate magnetisation trajectories in the Bloch sphere by numerical integration

"Rationalising spin relaxation during slice-selective refocusing pulses"Experimental data for six doped water samples [/Experimental_doped_water/]===========
These data were used to generate Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S7, Figure S11, Figure S12, Tables S5-S11 and Table S13 in the Supporting Information.
These data were analysed using the "UoM_RSR_lsqcurvefit" and "UoM_queue_RSR_lsqcurvefit" MATLAB functions.

Experimental_doped_water_integrals - Spreadsheet containing the absolute integrals obtained from slice-selective spin echo experiments performed on doped water samples 1-6
Directory structure for experimental data for doped water samples 1-5 (see Table 1 in main manuscript):
4 - 1H pulse-acquire NMR experiment5 - 1H inversion recovery NMR experiment (GNAT data in "GNAT" subfolder)6 - 1H Carr-Purcell Method A NMR experiment (GNAT data in "GNAT" subfolder)101-110 - Slice-selective spin echo NMR experiments using an rSNOB refocusing pulse of varying duration111-120 - Slice-selective spin echo NMR experiments using a REBURP refocusing pulse of varying duration121-130 - Slice-selective spin echo NMR experiments using a Gaussian refocusing pulse of varying duration131-140 - Slice-selective spin echo NMR experiments using a rectangular refocusing pulse of varying duration

Directory structure for experimental data for doped water sample 6 (see Table 1 in main manuscript):
4 - 1H pulse-acquire NMR experiment5 - 1H inversion recovery NMR experiment (GNAT data in "GNAT" subfolder)6 - 1H Carr-Purcell Method A NMR experiment (GNAT data in "GNAT" subfolder)101-113 - Slice-selective spin echo NMR experiments using an rSNOB refocusing pulse of varying duration121-133 - Slice-selective spin echo NMR experiments using a REBURP refocusing pulse of varying duration141-153 - Slice-selective spin echo NMR experiments using a Gaussian refocusing pulse of varying duration161-173 - Slice-selective spin echo NMR experiments using a rectangular refocusing pulse of varying duration

==========Simulated data for the six doped water samples [/Simulation_doped_water/]=========
These data were used to generate Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S10, Tables S5-S11, Table S13 and Table S14 in the Supporting Information.
These data were analysed using the "UoM_RSR_lsqcurvefit" and "UoM_queue_RSR_lsqcurvefit" MATLAB functions.

The data from each simulation is contained within a numbered folder. Three parameters are varied across the 252 simulations, in following order of precedence: pulse duration, sample (i.e., T1 and T2 time constants), and pulse shape. The T1 and T2 relaxation time constants matched those of the experimental samples.
1-63 - Slice-selective spin echo NMR Spinach simulations using an rSNOB refocusing pulse of varying duration performed on doped water samples 1-664-126 - Slice-selective spin echo NMR Spinach simulations using a REBURP refocusing pulse of varying duration performed on doped water samples 1-6127-189 - Slice-selective spin echo NMR Spinach simulations using a Gaussian refocusing pulse of varying duration performed on doped water samples 1-6190-252 - Slice-selective spin echo NMR Spinach simulations using a rectangular refocusing pulse of varying duration performed on doped water samples 1-6

==================================================================================================================================================================================Analysis of the experimental and simulated doped water data [/Analysis_doped_water/]===========
Analysis of the experimental and simulated doped water data were used to generate Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S12 and Tables S5-S14 in the Supporting Information.
The two functions used to perform this analysis were the "UoM_RSR_lsqcurvefit" and "UoM_queue_RSR_lsqcurvefit" functions. The specific functions used to perform each analysis maybe found, along with the analysis output, in the subfolders of this directory.
UoM_RSR_lsqcurvefit: MATLAB function used to perform global fitting of the data from slice-selective spin echo NMR experiments and Spinach simulations performed on the six doped water samples to various proposed relaxational attenuation modelsUoM_queue_RSR_lsqcurvefit: MATLAB function used to queue calls to the "UoM_RSR_lsqcurvefit" function and provide input parameters for the processing and analysis. These input parameters may be found in the "params.mat" files.

ModelFitting - Global fitting of the experimental and simulated doped water data to seven different models of relaxational attenuation (Figure 2 and Table 2 in the main manuscript, as well as Figures S1-S7 and Tables S5-S11 in the Supporting Information)OnRes - Global fitting of the simulated doped water data from an on-resonance frequency-selective spin echo simulation (Figure S8 and Table S12 in the Supporting Information)Residuals - An examination of the residuals surface when performing global fitting (Figures S9-S12 in the Supporting Information)OppositeFitting - An examination of the residuals when fitting the simulated data with the optimal alpha and beta values determined for the experimental data, and vice versa (Table S13 in the Supporting Information)Fidelity - An investigation into the fidelity of the Spinach simulations performed by performing global fitting with different offset spacings (Table S14 in the Supporting Information)

========Simulated data in the linear attenuation regime [/Simulation_linear_attenuation/]=========
These data were used to generate Figure 3 and Table 3 in the main manuscript.
UoM_RSR_r1r2_offset_dependence - MATLAB function used to analyse the data from Spinach simulations of slice-selective spin echo experiments in the linear attenuation regime
1-4 - Slice-selective spin echo NMR Spinach simulations using a 10 ms rSNOB refocusing pulse, performed on single-spin systems with small differences in T1 and T2 5-8 - Slice-selective spin echo NMR Spinach simulations using a 10 ms REBURP refocusing pulse, performed on single-spin systems with small differences in T1 and T2 9-12 - Slice-selective spin echo NMR Spinach simulations using a 10 ms Gaussian refocusing pulse, performed on single-spin systems with small differences in T1 and T2 13-16 - Slice-selective spin echo NMR Spinach simulations using a 10 ms rectangular refocusing pulse, performed on single-spin systems with small differences in T1 and T2Analysis - Contains the output of the analysis of these data performed using the "UoM_RSR_r1r2_offset_dependence" function

=========Diffusional attenuation analysis [/Diffusional_attenuation/]==========
These data were used to generate Figure S13 in the Supporting Information.
UoM_RSR_diffusional_atten - MATLAB function used to predict the HDO signal loss due to diffusional attenuation in the slice-selective spin echo NMR experiments performed on the six doped water samples

=========Bloch sphere simulations [/Bloch_spheres/]==========
These data were used to generate Figure 1 in the main manuscript and Table S15 in the Supporting Information.
UoM_RSR_Bloch_spheres - Mathematica notebook used to calculate magnetisation trajectories in the Bloch sphere by numerical integration
UoM_RSR_diffusional_atten - MATLAB function used to predict the HDO signal loss due to diffusional attenuation in the slice-selective spin echo NMR experiments performed on the six doped water samples

=========Bloch sphere simulations [/Bloch_spheres/]==================================================================================================================================================================================
These data were used to generate Figure 1 in the main manuscript and Table S15 in the Supporting Information.
UoM_RSR_Bloch_spheres - Mathematica notebook used to calculate magnetisation trajectories in the Bloch sphere by numerical integration

This archive contains all raw experimental data files, macros, pulse sequence code, shaped pulse definitions and Mathematica notebooks to support the article "Convection-compensated pure shift NMR: how to stop convection ruining experiments."

This archive contains all raw experimental data files, macros, pulse sequence code, shaped pulse definitions and Mathematica notebooks to support the article "Convection-compensated pure shift NMR: how to stop convection ruining experiments."