A General Model to Calculate the Spin-Lattice Relaxation Rate (R1) of Blood, Accounting for Hematocrit, Oxygen Saturation, Oxygen Partial Pressure, and Magnetic Field Strength Under Hyperoxic Conditions

Abstract

Background: Under normal physiological conditions, the spin-lattice relaxation rate (R1) in blood is influenced by many factors, including hematocrit, field strength, and the paramagnetic effects of deoxyhemoglobin and dissolved oxygen. In addition, techniques such as oxygen-enhanced magnetic resonance imaging (MRI) require high fractions of inspired oxygen to induce hyperoxia, which complicates the R1 signal further. A quantitative model relating total blood oxygen content to R1 could help explain these effects.

Purpose: To propose and assess a general model to estimate the R1 of blood, accounting for hematocrit, SO₂ , PO₂ , and B0 under both normal physiological and hyperoxic conditions.

Study type: Mathematical modeling.

Population: One hundred and twenty-six published values of R1 from phantoms and animal models.

Field strength/sequence: 5-8.45 T.

Assessment: We propose a two-compartment nonlinear model to calculate R1 as a function of hematocrit, PO₂ , and B0. The Akaike Information Criterion (AIC) was used to select the best-performing model with the fewest parameters. A previous model of R1 as a function of hematocrit, SO₂ , and B0 has been proposed by Hales et al, and our work builds upon this work to make the model applicable under hyperoxic conditions (SO₂ > 0.99). Models were assessed using the AIC, mean squared error (MSE), coefficient of determination (R² ), and Bland-Altman analysis. The effect of volume fraction constants $W_{\mathrm{RBC}}$ and $W_{\text{plasma}}$ was assessed by the SD of resulting R1. The range of the model was determined by the maximum and minimum B0, hematocrit, SO₂ , and PO₂ of the literature data points.

Statistical tests: Bland-Altman, AIC, MSE, coefficient of determination (R² ), SD.

Results: The model estimates agreed well with the literature values of R1 of blood (R² = 0.93, MSE = 0.0013 s^-2 ), and its performance was consistent across the range of parameters: B0 = 1.5-8.45 T, SO₂ = 0.40-1, PO₂ = 30-700 mmHg.

Data conclusion: Using the results from this model, we have quantified and explained the contradictory decrease in R1 reported in oxygen-enhanced MRI and oxygen-delivery experiments.

Level of evidence: 3 TECHNICAL EFFICACY: Stage 1.

Keywords: R1; blood; hyperoxia; longitudinal relaxation; oxygen; oxygen-enhanced MRI.