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Resolution of Heterogeneity of Oxygen in Tissues Using EPR Oximetry with Particulates

Benjamin. B. Williams ¹, Oleg Y. Grinberg¹, Eugene Demidenko², Harold M. Swartz<sup>1

1</sup>EPR Center for the Study of Viable Systems, Dartmouth Medical School, Hanover, NH 03755, USA
²Section of Biostatistics and Epidemiology, Dartmouth-Hitchcock Medical Center, Lebanon, NH 03766, USA

INTRODUCTION

The ability to characterize heterogeneity in oxygen concentration is a crucial issue when considering methods to measure pO₂ in tissues because
of the physiological and pathophysiological effects of such heterogeneity. Because of the nature of functioning biological systems,
there MUST be heterogeneity extending into dimensions smaller than cells, as most of the consumption of oxygen occurs in mitochondria.
Therefore, methods to measure oxygen in vivo cannot fully resolve heterogeneity; however, it is essential that their resolution be understood. 
We have developed methods to increase the resolution of EPR oximetry significantly, enabling us to take full advantage of the favorable
characteristics of this method: the ability to make repeated and accurate non-invasive measurements from the same site. 
Two techniques have been developed to measure heterogeneous pO₂ in tissues: 1) regression analysis of multi-component spectra acquired
with no magnetic field gradient, 2) High Spatial Resolution Multi-Site (HSR-MS) EPR oximetry, which uses two spectra acquired in the presence
of field gradients to resolve the heterogeneity.

REGRESSION ANALYSIS METHODS

 To characterize oxygen heterogeneity in tissues we applied methods of linear and nonlinear regression analysis to single EPR spectra
recorded without magnetic field gradients.  Such data may be collected quickly and without the sensitivity reduction that accompanies
an applied gradient.  Initially considering LiPc as the oxygen sensitive probe, the measured spectrum is modeled as a sum
of Lorentzian contributions with varying linewidths.  The linewidth of the n^th component, DB_pp,n , is given by DB_pp,n = DB_pp,0 + d*n , where DB_pp,0  
is the minimum linewidth and d is the uniform separation between the linewidths.  For N components, n=0,1,...,(N-1).  If L_n(B) is the n^th Lorentzian component,
as a function of magnetic field B, the measured EPR spectrum is the linear combination S[a_n*L_n(B)]+noise, where a_n is the frequency coefficient
of the n^th Lorentzian component.  These coefficients are estimated using least‑squares fitting and, after normalizing, can be treated as histogram frequencies.
We apply methods of statistical significance testing to identify the optimal number of components used in the analysis and to test the hypothesis H₀:a_n =0. 

Figure 1   Simulated LiPc spectrum for a sample with heterogeneous pO₂ distribution.

Table 1  True pO₂ distribution used to generate the simulated spectrum of Figure 1 and the distribution estimated using the described technique.

REGRESSION ANALYSIS RESULTS

Numerical simulations have shown that this method allows accurate estimation of the frequency coefficients a_n.  Figure 1 shows a simulated EPR spectrum
of LiPc crystals with an N=5 component pO₂ distribution, as specified in the right upper corner, and with additive random noise.
The true and estimated pO₂ distributions are shown in Table 1, demonstrating the accuracy and precision of this technique.

MULTI-SITE OXIMETRY METHODS

 HSR-MS EPR oximetry is a spectroscopic technique that was developed at the EPR Center to increase the spatial resolution and accuracy of in vivo
oxygen measurements [1]. Through the use of this technique, accurate linewidths can be measured for several individual deposits of oxygen sensitive
particulate spin probes in a heterogeneous environment.  In addition, linewidth measurements can be made at each end of the deposits,
further resolving the pO₂ heterogeneity.  One limitation of the technique is the decrease in the signal‑to‑noise ratio (SNR) of the measured data
as the strength of the applied gradient increases.  Typically, HSR-MS oximetry has been performed with the Zeeman modulation amplitude set to 1/3
of the minimum observed spectral linewidth to avoid distortion of the measured spectra.  We investigated the effect of increasing the Zeeman modulation
amplitude as a means to improve the SNR at high gradient magnitudes and improve the accuracy and precision of pO­₂ measurements. 

Figure 2 Spectra were simulated for a sample with a uniform 0.5 G linewidth and linearly
varying spin intensity for typical gradient strengths and noise level. The multi-site EPR
technique was used to estimate the true linewidth of the sample under (a) conventional,
low modulation conditions and (b) with large modulation amplitude. The precision of the
estimated linewidth improved when large modulation amplitudes were applied due to the
dramatic increase in the SNR.
 

MULTI-SITE OXIMETRY RESULTS

 Through theoretical analysis and simulations, we have found that when the modulation amplitude is increased in proportion to the applied gradients,
accurate pO₂ estimates can be made even with very large modulation amplitudes.  Spectra were simulated for a sample with uniform pO₂
and varying spin probe concentration for two gradient magnitudes and HSR-MS oximetry was performed.  Spectra simulated with typical,
low modulation are shown in Figure 2a along with the fitted spectrum derived using the HSR-MS technique.  With a true linewidth of 0.5 G,
under these conventional conditions the linewidth was estimated to be 0.55 G with a standard error of 0.08 G (n=100).  When the minimum modulation
amplitude was increased to twice the true linewidth and then scaled in proportion to the applied gradient, the accuracy and precision of the linewidth was
observed to improve to 0.50 G ± 0.01 G (n=100).  Spectra simulated with the larger modulation amplitude are shown in Figure 2b.
These spectra demonstrate that overmodulation allows a significant increase in SNR.

DISCUSSION

These studies demonstrate the ability of these two techniques to resolve and measure heterogeneous pO₂ distributions over distances
the size of the deposited crystals. Through these measurements, pO₂ heterogeneity in tissue and its role in normal physiology and disease
can be investigated. This very significantly extends the applicability of EPR oximetry for basic and clinical applications where heterogeneity of pO₂
is a crucial aspect, such as in tumors and peripheral vascular disease. This research has been accepted for presentation
at the International Society for Magnetic Resonance in Medicine Twelfth Scientific Meeting and Conference, May 15-21, 2004.

REFERENCES 

[1] Grinberg OY, Smirnov AI, Swartz HM. High Spatial Resolution Multi-site EPR Oximetry. Journal of Magnetic Resonance 2001;152(2):247-58.

ACKNOWLEDGEMENTS

This work was supported by a NIH (NIBIB) grant PO1 EB002180, “Measurement of pO₂ in Tissues In Vivo and In Vitro,”
and used the facilities of the EPR Center for the Study of Viable Systems supported by NIH (NIBIB) grant P41 EB002032.

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