Quantitative theory for the transverse relaxation time of blood water

• Published in: NMR in biomedicine 2020-05, Vol.33 (5), p.e4207-n/a
• Main Authors: Li, Wenbo, Zijl, Peter C.M.
• Format: Article
• Language: English
• Subjects: Albumin; Albumins; Biological products; Blood; Blood plasma; blood T2; Cell membranes; Constants; Curve fitting; Data acquisition; Deoxygenation; Diamagnetism; Diffusion; Diffusion effects; Diffusion rate; Error correction; Erythrocytes; exchange; Exchanging; Field strength; Functional magnetic resonance imaging; Hematocrit; Hemoglobin; Magnetic fields; Oxygenation; oxygenation fraction; Physical properties; Physiology; Protons; Relaxation time; τcp dependence
• ISSN: 0952-3480; 1099-1492
• DOI: 10.1002/nbm.4207

An integrative model is proposed to describe the dependence of the transverse relaxation rate of blood water protons (R2blood = 1/T2blood) on hematocrit fraction and oxygenation fraction (Y). This unified model takes into account (a) the diamagnetic effects of albumin, hemoglobin and the cell membrane; (b) the paramagnetic effect of hemoglobin; (c) the effect of compartmental exchange between plasma and erythrocytes under both fast and slow exchange conditions that vary depending on field strength and compartmental relaxation rates and (d) the effect of diffusion through field gradients near the erythrocyte membrane. To validate the model, whole‐blood and lysed‐blood R2 data acquired previously using Carr‐Purcell‐Meiboom‐Gill measurements as a function of inter‐echo spacing τcp at magnetic fields of 3.0, 7.0, 9.4 and 11.7 T were fitted to determine the lifetimes (field‐independent physiological constants) for water diffusion and exchange, as well as several physical constants, some of which are field‐independent (magnetic susceptibilities) and some are field‐dependent (relaxation rates for water protons in solutions of albumin and oxygenated and deoxygenated hemoglobin, ie, blood plasma and erythrocytes, respectively). This combined exchange‐diffusion model allowed excellent fitting of the curve of the τcp‐dependent relaxation rate dispersion at all four fields using a single average erythrocyte water lifetime, τery = 9.1 ± 1.4 ms, and an averaged diffusional correlation time, τD = 3.15 ± 0.43 ms. Using this model and the determined physiological time constants and relaxation parameters, blood T2 values published by multiple groups based on measurements at magnetic field strengths of 1.5 T and higher could be predicted correctly within error. Establishment of this theory is a fundamental step for quantitative modeling of the BOLD effect underlying functional MRI. An integrative model is presented to describe the transverse relaxation of blood. It combines the contributions from two protein solutions (hemoglobin and albumin) with those from exchange and diffusion effects to describe the echo spacing (τcp) dependence of R2 = 1/T2 of blood on hematocrit and oxygenation. Using this model and the determined physiological time constants and relaxation parameters, blood T2 values at magnetic field strengths of 1.5T and higher could be predicted correctly within error, as demonstrated by comparing with existing experimental literature values.