Rat Brain Global Ischemia-Induced Diffusion Changes Revisited: Biophysical Modeling of the Water and NAA MR "Diffusion Signal"

PURPOSE

To assess changes in intracellular diffusion as a mechanism for the reduction in water ADC that accompanies brain injury. Using NAA as a marker of neuronal cytoplasmic diffusion, NAA diffusion was measured before and after global ischemia (immediately postmortem) in the female Sprague-Dawley rat.

METHODS

Diffusion-weighted PRESS spectra, with diffusion encoding in a single direction, were acquired from large voxels of rat brain gray matter in vivo and postischemia employing either pairs of pulsed half-sine-shaped gradients (in vivo and postischemia, b_max  = 19 ms/μm² ) or sinusoidal oscillating gradients (in vivo only) with frequencies of 99.2-250 Hz. A 2D randomly oriented cylinder (neurite) model gave estimates of longitudinal and transverse diffusivities (D_L and D_T , respectively). In this model, D_L represents the "free" diffusivity of NAA, whereas D_T reflects highly restricted diffusion. Using oscillating gradients, the frequency dependence of D_T [D_T (ω)] gave estimates of the cylinder (axon/dendrite) radius.

RESULTS

A 10% decrease in D_L,NAA followed global ischemia, dropping from 0.391 ± 0.012 μm² /ms to 0.350 ± 0.009 μm² /ms. Modeling D_T,NAA (ω) provided an estimate of the neurite radius of 1.0 ± 0.6 μm.

CONCLUSION

Whereas the increase in apparent intraneuronal viscosity suggested by changes in D_L,NAA may contribute to the overall reduction in water ADC associated with brain injury, it is not sufficient to be the sole explanation. Estimates of neurite radius based on D_T (ω) were consistent with literature values.

Noninvasive Quantification of Axonal Loss in the Presence of Tissue Swelling in Traumatic Spinal Cord Injury Mice

Neuroimaging plays an important role in assessing axonal pathology after traumatic spinal cord injury. However, coexisting inflammation confounds imaging assessment of the severity of axonal injury. Herein, we applied diffusion basis spectrum imaging (DBSI) to quantitatively differentiate and quantify underlying pathologies in traumatic spinal cord injury at 3 days post-injury. Results reveal that DBSI was capable of detecting and differentiating axonal injury, demyelination, and inflammation-associated edema and cell infiltration in contusion-injured spinal cords. DBSI was able to detect and quantify axonal loss in the presence of white matter tract swelling. The DBSI-defined apparent axonal volume correlated with the corresponding histological markers. DBSI-derived pathological metrics could serve as neuroimaging biomarkers to differentiate and quantify coexisting white matter pathologies in spinal cord injury, providing potential surrogate outcome measures to assess spinal cord injury progression and response to therapies.

Diffusion fMRI detects white-matter dysfunction in mice with acute optic neuritis

Optic neuritis is a frequent and early symptom of multiple sclerosis (MS). Conventional magnetic resonance (MR) techniques provide means to assess multiple MS-related pathologies, including axonal injury, demyelination, and inflammation. A method to directly and non-invasively probe white-matter function could further elucidate the interplay of underlying pathologies and functional impairments. Previously, we demonstrated a significant 27% activation-associated decrease in the apparent diffusion coefficient of water perpendicular to the axonal fibers (ADC⊥) in normal C57BL/6 mouse optic nerve with visual stimulation using diffusion fMRI. Here we apply this approach to explore the relationship between visual acuity, optic nerve pathology, and diffusion fMRI in the experimental autoimmune encephalomyelitis (EAE) mouse model of optic neuritis. Visual stimulation produced a significant 25% (vs. baseline) ADC⊥ decrease in sham EAE optic nerves, while only a 7% (vs. baseline) ADC⊥ decrease was seen in EAE mice with acute optic neuritis. The reduced activation-associated ADC⊥ response correlated with post-MRI immunohistochemistry determined pathologies (including inflammation, demyelination, and axonal injury). The negative correlation between activation-associated ADC⊥ response and visual acuity was also found when pooling EAE-affected and sham groups under our experimental criteria. Results suggest that reduction in diffusion fMRI directly reflects impaired axonal-activation in EAE mice with optic neuritis. Diffusion fMRI holds promise for directly gauging in vivo white-matter dysfunction or therapeutic responses in MS patients.

Manganese-enhanced MRI (MEMRI) via topical loading of Mn(2+) significantly impairs mouse visual acuity: a comparison with intravitreal injection

Manganese-enhanced MRI (MEMRI) with topical loading of MnCl2 provides optic nerve enhancement comparable to that seen by intravitreal injection. However, the impact of this novel and non-invasive Mn(2+) loading method on visual function requires further assessments. The objective of this study is to determine the optimal topical Mn(2+) loading dosage for MEMRI and to assess visual function after MnCl2 loading. Intravitreal administration was performed to compare the two approaches of MnCl2 loading. Twenty-four hours after topical loading of 0, 0.5, 0.75, and 1 M MnCl2 , T1 -weighted, T2-weighted, diffusion tensor imaging and visual acuity (VA) assessments were performed to determine the best topical loading dosage for MEMRI measurements and to assess the integrity of retinas and optic nerves. Mice were perfusion fixed immediately after in vivo experiments for hematoxylin and eosin and immunohistochemistry staining. Topical loading of 1 M MnCl2 damaged the retinal photoreceptor layer with no detectable damage to retina ganglion cell layers or prechiasmatic optic nerves. For the topical loading, 0.75 M MnCl2 was required to see sufficient enhancement of the optic nerve. At this concentration the visual function was significantly affected, followed by a slow recovery. Intravitreal injection (0.25 μL of 0.2 M MnCl2 ) slightly affected VA, with full recovery a day later. To conclude, intravitreal MnCl2 injection provides more reproducible results with less adverse side-effects than topical loading.

White-matter diffusion fMRI of mouse optic nerve

Non-invasive assessment of white-matter functionality in the nervous system would be a valuable basic neuroscience and clinical diagnostic tool. Using standard MRI techniques, a visual-stimulus-induced 27% decrease in the apparent diffusion coefficient of water perpendicular to the axonal fibers (ADC(perpendicular)) is demonstrated for C57BL/6 mouse optic nerve in vivo. No change in ADC(||) (diffusion parallel to the optic nerve fibers) was observed during visual stimulation. The stimulus-induced changes are completely reversible. A possible vascular contribution was sought by carrying out the ADC(perpendicular) measurements in hypercapnic mice with and without visual stimulus. Similar effects were seen in room-air-breathing and hypercapnic animals. The in vivo stimulus-induced ADC(perpendicular) decreases are roughly similar to literature reports for ex vivo rat optic nerve preparations under conditions of osmotic swelling. The experimental results strongly suggest that osmotic after-effects of nerve impulses through the axonal fibers are responsible for the observed ADC decrease.

A system for endoscopic mechanically scanned localized proton MR and light-induced fluorescence emission spectroscopies

Molecular and near-cellular modalities offer new opportunities in assessing living tissue in situ, and multimodality approaches, which offer complementary information, may lead to improved characterization of tissue pathophysiology benefiting diagnosis and focal therapy. However, many such modalities are limited by their low penetration through tissue, which has led to minimally invasive trans-cannula approaches to place the corresponding sensors locally at the area of interest. This work presents a system for performing localized fluorescence emission and proton magnetic resonance (MR) spectroscopies via endoscopic access. The in-house developed side-firing 1.9-mm wide dual-sensor integrates a three-fiber optical sensor for fluorescence emission optical spectroscopy and a 1-mm circular radiofrequency (RF) coil for localized MR proton spectroscopy. An MR-compatible manipulator was developed for carrying and mechanically translating the dual-sensor along a linear access channel. The hardware and software control of the system allows reconfigurable synchronization of the manipulator-assisted translation of the sensor, and MR and optical data collection. The manipulator serves as the mechanical link for the three modalities and MR images, MR spectra and optical spectra are inherently co-registered to the MR scanner coordinate system. These spectra were then used to generate spatio-spectral maps of the fluorophores and proton MR-signal sources in three-compartment phantoms with optically- and MR-visible, and distinguishable, materials. These data demonstrate a good spatial match between MR images, MR spectra and optical spectra along the scanned path. In addition to basic research, such a system may have clinical applications for assessing and characterizing cancer in situ, as well as guiding focal therapies.

The validation of complete Fourier direct MR method for diffusion MRI via biological and numerical phantoms

The equations of the Complete Fourier Direct (CFD) MR model are explicitly derived for diffusion weighted NMR experiments. The CFD-MR theory is validated by comparing a biological phantom constructed from nerve bundles and agar gel with its numerical implementation. The displacement integral distribution function estimated from the experimental data is in high agreement with the numerical phantom. CFD-MR's ability to estimate accurately and fully spin diffusion properties demonstrated here, provides the experimental validation of the theoretical CFD-MR model.

Use of ethylene glycol to evaluate gradient performance in gradient-intensive diffusion MR sequences

Imaging a phantom of known dimensions is a widely used and simple method for calibrating MRI gradient strength. However, full-range characterization of gradient response is not achievable using this approach. Measurement of the apparent diffusion coefficient of a liquid with known diffusivity allows for calibration of gradient amplitudes across a wider dynamic range. An important caveat is that the temperature dependence of the liquid's diffusion characteristics must be known, and the temperature of the calibration phantom must be recorded. In this report, we demonstrate that the diffusion coefficient of ethylene glycol is well described by Arrhenius-type behavior across the typical range of ambient MRI magnet temperatures. Because of ethylene glycol's utility as an NMR chemical-shift thermometer, the same (1)H MR spectroscopy measurements that are used for gradient calibration also simultaneously "report" the sample temperature. The high viscosity of ethylene glycol makes it well-suited for assessing gradient performance in demanding diffusion-weighted imaging and spectroscopy sequences.

Quantification and compensation of eddy-current-induced magnetic-field gradients

Two robust techniques for quantification and compensation of eddy-current-induced magnetic-field gradients and static magnetic-field shifts (ΔB0) in MRI systems are described. Purpose-built 1-D or six-point phantoms are employed. Both procedures involve measuring the effects of a prior magnetic-field-gradient test pulse on the phantom's free induction decay (FID). Phantom-specific analysis of the resulting FID data produces estimates of the time-dependent, eddy-current-induced magnetic field gradient(s) and ΔB0 shift. Using Bayesian methods, the time dependencies of the eddy-current-induced decays are modeled as sums of exponentially decaying components, each defined by an amplitude and time constant. These amplitudes and time constants are employed to adjust the scanner's gradient pre-emphasis unit and eliminate undesirable eddy-current effects. Measurement with the six-point sample phantom allows for simultaneous, direct estimation of both on-axis and cross-term eddy-current-induced gradients. The two methods are demonstrated and validated on several MRI systems with actively-shielded gradient coil sets.

Pitx1 haploinsufficiency causes clubfoot in humans and a clubfoot-like phenotype in mice

Clubfoot affects 1 in 1000 live births, although little is known about its genetic or developmental basis. We recently identified a missense mutation in the PITX1 bicoid homeodomain transcription factor in a family with a spectrum of lower extremity abnormalities, including clubfoot. Because the E130K mutation reduced PITX1 activity, we hypothesized that PITX1 haploinsufficiency could also cause clubfoot. Using copy number analysis, we identified a 241 kb chromosome 5q31 microdeletion involving PITX1 in a patient with isolated familial clubfoot. The PITX1 deletion segregated with autosomal dominant clubfoot over three generations. To study the role of PITX1 haploinsufficiency in clubfoot pathogenesis, we began to breed Pitx1 knockout mice. Although Pitx1(+/-) mice were previously reported to be normal, clubfoot was observed in 20 of 225 Pitx1(+/-) mice, resulting in an 8.9% penetrance. Clubfoot was unilateral in 16 of the 20 affected Pitx1(+/-) mice, with the right and left limbs equally affected, in contrast to right-sided predominant hindlimb abnormalities previously noted with complete loss of Pitx1. Peroneal artery hypoplasia occurred in the clubfoot limb and corresponded spatially with small lateral muscle compartments. Tibial and fibular bone volumes were also reduced. Skeletal muscle gene expression was significantly reduced in Pitx1(-/-) E12.5 hindlimb buds compared with the wild-type, suggesting that muscle hypoplasia was due to abnormal early muscle development and not disuse atrophy. Our morphological data suggest that PITX1 haploinsufficiency may cause a developmental field defect preferentially affecting the lateral lower leg, a theory that accounts for similar findings in human clubfoot.

Simulations and experimental demonstration of coupling molecular and macroscopic level modalities with a robotic manipulator

Established and emerging molecular and cellular modalities, such as optical imaging and spectroscopy, offer new opportunities for assessing tissue pathophysiology in situ. A challenge with such applications is their limited tissue penetration and low sensitivity that can be addressed with trans-needle or trans-catheter access. In this work, we describe the use of an actuated manipulator to physically manipulate such sensors to scan an area of interest generating 1-D scans while registering them to a guiding modality. Simulations were performed for a miniature RF coil to determine the voxel size, and experimental studies were conducted using a miniature RF coil manipulated by the MR-compatible device. The experimental results on phantom studies show that potential diagnostic information can be collected by using this methodology. This system was pursued to address a critical limitation of emerging molecular and near-cellular modalities; the limited tissue penetration.

Imaging intratumoral convection: pressure-dependent enhancement in chemotherapeutic delivery to solid tumors

PURPOSE

Low-molecular weight (LMW) chemotherapeutics are believed to reach tumors through diffusion across capillary beds as well as membrane transporters. Unexpectedly, the delivery of these agents seems to be augmented by reductions in tumor interstitial fluid pressure, an effect typically associated with high-molecular weight molecules that reach tumors principally through convection. We investigated the hypothesis that improved intratumoral convection can alter tumor metabolism and enhance the delivery of a LMW chemotherapeutic agent to solid tumors.

EXPERIMENTAL DESIGN

For this purpose, we applied 31P/19F magnetic resonance spectroscopy (MRS) and magnetic resonance spectroscopic imaging (MRSI) to examine the influence of type I collagenase on tumor bioenergetics and the delivery of 5-fluorouracil (5FU) to HT29 human colorectal tumors grown s.c. in mice.

RESULTS

Collagenase effected a 34% reduction in tumor interstitial fluid pressure with an attendant disintegration of intratumoral collagen. Neither mice-administered collagenase nor controls receiving PBS showed changes in (31)phosphorus MRS-measured tumor bioenergetics; however, a time-dependent increase in the content of extracellular inorganic phosphate (Pi(e)) was observed in tumors of collagenase-treated animals. (31)Phosphorus MRSI showed that this increase underscored a more homogeneous distribution of Pi(e) in tumors of experimental mice. (19)Fluorine MRS showed that these changes were associated with a 50% increase in 5FU uptake in tumors of experimental versus control animals; however, this increase resulted in an increase in 5FU catabolites rather than fluoronucleotide intermediates that are required for subsequent cytotoxicity.

CONCLUSIONS

These data indicate that the modulation of convective flow within tumors can improve the delivery of (LMW) chemotherapeutics and show the potential role for noninvasive imaging of this process in vivo.

A novel technology for the imaging of acidic prostate tumors by positron emission tomography

Solid tumors often develop an acidic environment due to the Warburg effect. The effectiveness of diagnosis and therapy may therefore be enhanced by the design and use of pH-sensitive agents that target acidic tumors. Recently, a novel technology was introduced to target acidic tumors using pH low insertion peptide (pHLIP), a peptide that inserts across cell membranes as an alpha-helix when the extracellular pH (pH(e)) is acidic. In this study, we expanded the application of the pHLIP technology to include positron emission tomography imaging of the acidic environment in prostate tumors using (64)Cu conjugated to the pHLIP ((64)Cu-DOTA-pHLIP). Studies showed that this construct avidly accumulated in LNCaP and PC-3 tumors, with higher uptake and retention in the LNCaP tumors. Uptake correlated with differences in the bulk pH(e) of PC-3 and LNCaP tumors measured in magnetic resonance spectroscopy experiments by the (31)P chemical shift of the pH(e) marker 3-aminopropylphosphonate. This article introduces a novel class of noninvasive pH-selective positron emission tomography imaging agents and opens new research directions in the diagnosis of acidic solid tumors.

Imaging transgene activity in vivo

The successful translation of gene therapy for clinical application will require the assessment of transgene activity as a measure of the biological function of a therapeutic transgene. Although current imaging permits the noninvasive detection of transgene expression, the critical need for quantitative imaging of the action of the expressed transgene has not been met. In vivo magnetic resonance spectroscopic imaging (MRSI) was applied to quantitatively delineate both the concentration and activity of a cytosine deaminase-uracil phosphoribosyltransferase (CD-UPRT) fusion enzyme expressed from a transgene. MRSI enabled the generation of anatomically accurate maps of the intratumoral heterogeneity in fusion enzyme activity. We observed an excellent association between the CD-UPRT concentration and activity and the percentage of CD-UPRT(+) cells. Moreover, the regional levels of UPRT activity, as measured by imaging, correlated well with the biological affect of the enzyme. This study presents a translational imaging paradigm for precise, in vivo measurements of transgene activity with potential applications in both preclinical and clinical settings.

Defining the pHi-hyperthermia sensitivity relationship for the RIF-1 tumor in vivo: a 31P MR spectroscopy study

This study quantifies the enhancement of the therapeutic efficacy of hyperthermia resulting from an acutely acidified and accurately monitored intracellular pH (pHi) in a mouse tumor model in vivo. Metabolic manipulation of the physiology of RIF-1 tumor (subcutaneous, on the hind flanks of female C3H/HeJ mice) achieved by i.p. bolus injection of glucose (glycolytic tumor acidification) or 3-O-methylglucose (non-glycolytic tumor acidification) was monitored by 31P magnetic resonance (31P MR) prior to, during and up to 1 h after localized hyperthermia. The pre-hyperthermia 31P MR-observable metabolic parameter that correlates most strongly with thermal sensitivity is pHi. Thermal sensitivity increases linearly with decreasing pHi regardless of the mechanism (glycolytic or non-glycolytic) of metabolic manipulation. The quantitative relationship is described by log10(SF)/EQ43=0.0079 pHi,preHT -0.0606 (R=0.63, P<0.0001), where EQ43 is the thermal heat dose delivered to the tumor (in units of equivalent minutes at 42.5 degrees C), pHi,preHT is the intracellular pH immediately prior to hyperthermia, and SF is the surviving fraction. The therapeutic enhancement is not as dramatic as expected based upon previously reported in vitro studies but is generally consistent with other in vivo studies. The method still represents a viable strategy for enhancing the therapeutic efficacy of hyperthermia, especially when used in combination with other therapeutic modalities.

An 19F Magnetic Resonance–Based In Vivo Assay of Solid Tumor Methotrexate Resistance: Proof of Principle

PURPOSE

Studies in oncology have implicated multiple molecular mechanisms as contributors to intrinsic and acquired tumor resistance to antifolate therapy. Here we show the utility of an (19)F-labeled methotrexate (FMTX) with (19)F magnetic resonance to differentiate between sensitive and resistant tumors in vivo and thus predict therapeutic response.

EXPERIMENTAL DESIGN

Human sarcoma xenografts in nude mice were used in this study. The sarcoma cell lines chosen for this study (HT-1080, HS-16, and M-805) are well characterized in terms of their methotrexate sensitivity and molecular mechanisms of resistance. The pharmacokinetics of tumor uptake/washout of FMTX were monitored via in vivo (19)F magnetic resonance spectroscopy (pulse/acquire with surface coil localization) following an i.v. bolus injection. Response post-therapy, following leucovorin rescue, was monitored via tumor growth.

RESULTS

The three tumor models show differences in both the peak concentrations of tumor FMTX and the dynamics of uptake/retention. These differences are most pronounced for time points late in the magnetic resonance observation period (225-279 minutes post-injection). A statistically significant linear correlation between tumor tissue concentrations of FMTX at these late time points and therapeutic response in the days/weeks post-treatment is shown (R = 0.81, F = 9.27, P < 0.001). Interestingly, a 400 mg/kg i.v. bolus injection of FMTX is a more potent cytotoxic agent in vivo against methotrexate-sensitive tumors than is the parent compound (P = 0.011).

CONCLUSIONS

In principle, the assay method described herein could be implemented in the clinic as a diagnostic tool to make decisions regarding therapeutic protocol for the treatment of osteosarcoma on a case-by-case basis.

In vivo 5-fluorouracil and fluoronucleotideT1 relaxation time measurements using the variable nutation angle method

19Fluorine NMRS has the potential to enable noninvasive predictions of tumor response to 5-fluorouracil (5FU) therapy based on tumor pharmacokinetics. Knowledge of the T1's of 5FU and its fluoronucleotide anabolites (FNuc) is required for quantitative spectral analysis and selection of optimal pulse parameters. We used the variable nutation angle (VNA) method to determine T1's of 5FU and FNuc in subcutaneous Walker 256 rat mammary carcinosarcoma tumors transfected with a cytosine deaminase/uracil phosphoribosyltransferase fusion gene. We calibrated in vivo NAs using methoxydifluoroacetate to ensure the accuracy of these measurements. The T1's were calculated based on signal intensities acquired with NAs of 20 degrees, 35 degrees, 45 degrees, 60 degrees, and 75 degrees. The acquisition order of these NAs was shuffled to reduce the effect of signal variations. The determined T1's for 5FU and FNuc (2.3 +/- 0.1 s and 1.3 +/- 0.1 s, respectively) represent the first reported in vivo measurements for these metabolites in tumor.

A fluorine-labeled methotrexate as a probe for monitoring tumor antifolate pharmacokinetics: synthesis, in vitro cytotoxicity, and pilot in vivo 19F magnetic resonance spectra

The synthesis and characterization of 3'-fluoromethotrexate (FMTX), a novel fluorine-labeled analogue of methotrexate, are presented. Molecular modeling studies indicate that the fluorine atom causes only minimal changes in the structure/binding in the complex of the antifolate with thymidine synthetase and dihydrofolate reductase (DHFR). The in vitro cytotoxicity of this compound is shown to be equivalent to that of the parent antifolate compound. While the focus of this report is the synthetic technique of FMTX, it is also demonstrated that tumor accumulation of the labeled compound in vivo can be observed via 19F magnetic resonance spectroscopy (MRS) in a human tumor xenograft model.

Metabolic response of the CWR22 prostate tumor xenograft after 20 Gy of radiation studied by 1H spectroscopic imaging

PURPOSE

The ability to determine the spatial and metabolic distribution of prostate cancer is essential in assessing initial stage, prognosis, and treatment efficacy. Current markers of tumor progression such as prostate-specific antigen (PSA) do not provide spatial information about tumor extent or regions of high metabolic activity.

EXPERIMENTAL DESIGN

This study used the androgen-dependent CWR22 human prostate tumor xenograft in mice to characterize metabolic, PSA, and tumor volume changes that occurred with untreated growth or radiation therapy (XRT). One cohort of mice was studied as the tumor grew to 400 mm(3), whereas a second cohort was treated with a single 20-Gy fraction of radiation and studied before and 1, 2, and 4 days after XRT. In both cohorts, tumor volume, PSA, and choline:water ratios measured by nuclear magnetic resonance were monitored.

RESULTS

The CWR22 tumor had an untreated tumor-doubling time of 2.6 +/- 0.6 days (n = 7). In untreated mice, PSA strongly correlated with tumor volume (P < 0.01, R(2) = 0.99). The untreated tumor cohort had a PSA-doubling time of 3.2 +/- 0.6 days. Administration of 20 Gy produced a regrowth delay of >15.8 +/- 4.8 days (n = 6). PSA values after XRT were not correlated with post-XRT tumor volume (P < 0.20, R(2) = 0.02). A constant level of the choline:water ratio (0.010 +/- 0.001; n = 22, R(2) = 0.007, P < 0.3) was observed during the course of untreated tumor growth. A statistically significant (P < 0.04, one-tailed t test) 42% decrease in the choline:water ratio at 24 h after administration of XRT preceded observable changes in PSA.

CONCLUSIONS

Nuclear magnetic resonance spectroscopy provided a method with which to monitor metabolic changes of tumor response to XRT that preceded and predicted PSA and tumor volume changes.

Water proton MR properties of human blood at 1.5 Tesla: magnetic susceptibility, T(1), T(2), T*(2), and non-Lorentzian signal behavior

Accurate knowledge of the magnetic properties of human blood is required for the precise modeling of functional and vascular flow-related MRI. Herein are reported determinations of the relaxation parameters of blood, employing in vitro samples that are well representative of human blood in situ. The envelope of the blood (1)H(2)O free-induction decay signal magnitude during the first 100 msec following a spin echo at time TE is well- described empirically by an expression of the form, S(t) = S(o). exp[-R(*)(2). (t - TE) - AR*. (t - TE)(2)]. The relaxation parameters AR* and R(*)(2) increase as a function of the square of the susceptibility difference between red blood cell and plasma and depend on the spin-echo time. The Gaussian component, AR*, should be recognized in accurate modeling of MRI phenomena that depend upon the magnetic state of blood. The magnetic susceptibility difference between fully deoxygenated and fully oxygenated red blood cells at 37 degrees C is 0.27 ppm, as determined independently by MR and superconducting quantum interference device (SQUID) measurements. This value agrees well with the 1936 report of Pauling and Coryell (Proc Natl Acad Sci USA 1936;22:210-216), but is substantially larger than that frequently used in MRI literature. Magn Reson Med 45:533-542, 2001.

The NMR chemical shift pH measurement revisited: analysis of error and modeling of a pH dependent reference

A standard differential calculus-based propagation of error treatment is applied to the traditional chemical-exchange Henderson-Hasselbalch NMR pH model in which the reference shift is pH independent. It is seen naturally from this analysis that (i) the error minimum in derived pH occurs in the region where pH and indicator pKa are equal and that (ii) the dynamic range, or difference between the limiting chemical shifts of acid and base forms of indicator species, determines the insensitivity of the technique to propagation of errors. To extend the useful pH range and utility of NMR pH determination methodology, a more general model is developed in which the internal reference species is also considered as having a pH-dependent chemical shift. Data from standard solution pH titrations are fitted to both models and parameters are estimated for the normally observed family of ionizable phosphorus metabolites (ATP, inorganic phosphate, phosphoethanolamine and phosphocholine) and the xenometabolite 2-deoxyglucose-6-phosphate with either phosphocreatine, the alpha-phosphate of ATP, or H2O taken as the 31P or 1H chemical shift internal reference species as well as with an external reference.