Technical note: Temperature and concentration dependence of water diffusion in polyvinylpyrrolidone solutions

Abstract

The goal of this work is to provide temperature and concentration calibration of water diffusivity in polyvinylpyrrolidone (PVP) solutions used in phantoms to assess system bias and linearity in apparent diffusion coefficient (ADC) measurements. Method: ADC measurements were performed for 40 kDa (K40) PVP of six concentrations (0%, 10%, 20%, 30%, 40%, and 50% by weight) at three temperatures (19.5 • C, 22.5 • C, and 26.4 • C), with internal phantom temperature monitored by optical thermometer (±0.2 • C). To achieve ADC measurement and fit accuracy of better than 0.5%, three orthogonal diffusion gradients were calibrated using known water diffusivity at 0 • C and system gradient nonlinearity maps. Noise-floor fit bias was also controlled by limiting the maximum b-value used for ADC calculation of each sample. The ADC temperature dependence was modeled by Arrhenius functions of each PVP concentration. The concentration dependence was modeled by quadratic function for ADC normalized by the theoretical water diffusion values. Calibration coefficients were obtained from linear regression model fits. Results: Measured phantom ADC values increased with temperature and decreasing PVP concentration, [PVP]. The derived Arrhenius model parameters for [PVP] between 0% and 50%, are reported and can be used for K40 ADC temperature calibration with absolute ADC error within ±0.016 µm 2 /ms. Arrhenius model fit parameters normalized to water value scaled with [PVP] between 10% and 40%, and proportional change in activation energy increased faster than collision frequency. ADC normalization by water diffusivity, D W , from the Speedy-Angell relation accounted for the bulk of temperature dependence (±0.035 µm 2 /ms) and yielded quadratic calibration for ADC PVP /D W = (12.5 ± 0.7) ⋅10 −5 ⋅[PVP] 2 − (23.2 ± 0.3)⋅10 −3 ⋅[PVP]+1, nearly independent of PVP molecular weight and temperature. Conclusion:The study provides ground-truth ADC values for K40 PVP solutions commonly used in diffusion phantoms for scanning at ambient room temperature. The described procedures and the reported calibration can be used for quality control and standardization of measured ADC values of PVP at different concentrations and temperatures.

Time‐dependent diffusion tensor imaging and diffusion modeling of age‐related differences in the medial gastrocnemius and feasibility study of correlations to histopathology

“…The apparent diffusion coefficient (ADC, also referred to as mean diffusivity) value was an average of 2.04 ± 0.03 μm 2 /ms (ambient temperature 20 °C) at the lowest diffusion time and remained fairly constant over the range of diffusion times investigated; this is consistent with a free medium (Figure 1). The ADC value is also close to that reported in the literature for 20 °C 28 . Fractional anisotropy (FA) values were as anticipated for an isotropic, unrestricted medium such as water and unaltered as a function of diffusion time Δ (30 to 603 ms).…”

Evaluation of Apparent Diffusion Coefficient Repeatability and Reproducibility for Preclinical MRIs Using Standardized Procedures and a Diffusion-Weighted Imaging Phantom

“…Physical phantoms with known properties are essential for technical performance assessments in the quality control (QC) programs [ 11 , 12 , 13 , 14 ]. Several diffusion phantom materials have been developed over the years, although aqueous solutions of polyvinylpyrrolidone (PVP) are popular and comprise diffusion coefficient standards within homemade and commercially available phantoms [ 15 , 16 , 17 , 18 ]. PVP is stable and exhibits monoexponential diffusion that is tunable over the full tissue ADC range, although internal phantom temperature must be known and controlled to ≈0.5 °C to measure diffusion coefficients to within 1% accuracy [ 15 , 19 ].…”

“…Several diffusion phantom materials have been developed over the years, although aqueous solutions of polyvinylpyrrolidone (PVP) are popular and comprise diffusion coefficient standards within homemade and commercially available phantoms [ 15 , 16 , 17 , 18 ]. PVP is stable and exhibits monoexponential diffusion that is tunable over the full tissue ADC range, although internal phantom temperature must be known and controlled to ≈0.5 °C to measure diffusion coefficients to within 1% accuracy [ 15 , 19 ]. Ice-water-based diffusion phantoms provide an effective inexpensive means for absolute temperature control and a precisely known true diffusion value for MRI system bias assessment [ 20 , 21 , 22 ].…”

Diffusion‐Weighted Imaging of the Abdomen: Correction for Gradient Nonlinearity Bias in Apparent Diffusion Coefficient

“…Ice‐water phantoms have been typically used and are listed in the Quantitative Imaging Biomarkers Alliance 1 and National Institute of Standards and Technology (NIST) 33 . However, they require a long MRI preparation time to achieve and maintain the equilibrium temperature at 0 °C 34 and in longer MRI experiments, researchers need to refill the ice and water mixture. The size of the ice‐water phantoms is limited to about 20‐cm diameter and is mainly used in the intracranial studies.…”