12

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL.

Nuclear

Magnetic Relaxation in

BME-22,

NO.

1,

JANUARY

1975

Blood

RODNEY A. BROOKS, JOSEPH H. BATTOCLETTI, SENIOR MEMBER, IEEE, ANTHONY SANCES, JR., SANFORD J. LARSON, ROBERT L. BOWMAN, AND VSEVELOD KUDRAVCEV

SENIOR MEMBER, IEEE,

Abstract-The nuclear magnetic relaxation time T, of protons in human blood has been measured as a function of frequency, pH, and hematocrit. For whole blood at 25°C, T1 is approximately 0.1 s at 20 kHz, increasing to approximately 1 s at 50 MHz. T, of whole blood is analyzed in terms of the exchange of water molecules between plasma and erythrocyte cytoplasm. A cellular residence time of 19 ms provides the best fit to the data. The T, values for plasma and cytoplasm are explained in tenns of their protein content, using the well-established theory of nuclear relaxation in macromolecular solutions. The plasma and cytoplasm data are compared with previous T, results for apotransferrin and hemoglobin solutions, respectively, and qualitative agreement is found. The T, values increased with decreasing pH, as is expected from existing data on hemoglobin solutions.

[73 0

Importance of T, to NMR Flowmeter A NUCLEAR magnetic resonance (NMR) flowmeter is usually comprised of three elements: 1) a magnetizer to align the nuclear dipole moments in the liquid, 2) a tagger to change the amplitude of the resulting magnetization, and 3) a detector to sense the change of magnetization. In the design of an NMR flowmeter for the measurement of in vivo blood flow, the generation and maintenance of an adequate change of magnetization of flowing blood at the NMR detector must be insured. This is true whether quasi-steady venous flow is measured using an active tagdetect technique, or pulsatile arterial flow is measured using a self tag-detect method [1]. Two important NMR properties of blood are the static nuclear magnetic susceptibility, w-hich is proportional to the number of hydrogen nuclei, and the relaxation time T,, which determnines the rate of magnetization and demagnetization and hence the duration of the tag.' The susceptibility of blood is adequate, since it contains ap-

I[4

04I )

.5

o

~

g13

r6]X

.2

o

2

5

[8]* I0

.1,

.01

I. INTRODUCTION

r 01 (sec&)

(sec)

.1

I

10

100

Larmor frequency--- MHz

Fig. 1. Existing data on the relaxation time T1 of various types of blood as a function of Larmor frequency. Relaxation rate r = 1/T1. Reference numbers refer to bibliography. *denotes average value.

proximately 83 % water, and each water molecule contains two hydrogen nuclei. However, the T, relaxation time in many cases dictates the size and configuration of the flowmeter. In particular, the maximum spacings between the magnetizer, tagger, and detector are governed by

T7, [3]-ES].

Review of Data Published data on T, of blood as a function of Larmor frequency are shown in Fig. 1. Data on fresh cow blood over the frequency range 2.3 kHz to 1.7 MHz [6] are shown, as well as higher-frequency data taken at the Medical College of Wisconsin [7] and elsewhere [8]-[E1], on a wide variety of blood samples (human, cow, dog, mouse) under a variety of experimental conditions (in vivo, fresh, stored, etc.), using different measuring techniques. The experimental picture is obviously unclear, and a theoretical understanding of the data has been lacking. In order to obtain additional data on T, and a better Manuscript received January 1, 1974. This work was supported in part by the National Institute of General Medical Sciences understanding of its mechanisms, a study of proton Special Research, Fellowship 5F03GM55410, the National Heart and Lung Institute, Contract 70-2216, and the U. S. Army Medical relaxation in blood has been undertaken [4]-[5]. This Research and DJevelopment Command, Contract DADA17-71C- paper is a culmination of the study. 1093. R. A. Brooks is a Special Research Fellow of the National Institute of General Medical Sciences with Biomedical Engineering, Marquette University, Milwaukee, Wis. 53233. J. H. Battocletti and S. J. Larson are with the Department of

Neurosurgery, the Medical College of Wisconsin, Milwaukee, WVis. 53226. A. Sances, Jr., is with the Department of Neurosurgery, the Medical College of Wisconsin, Milwaukee, Wis. 53226, Biomedical Engineering, Marquette University, Milwaukee, Wis. 53233, and the Veterans Administration Center, Wood, Wis. 53193. R. L. Bowman and V. Kudraveev are with the Laboratory of Technical Development, the National Heart and Lung Institute, Bethesda, Md. 20014. 1 These same parameters are also important for NMR flowmeters which measure industrial fluids [2].

II. EXPERIMENTAL DATA

Samnple Preparation Six samples were studied. The first five were fresh human blood, drawn the same day from one person, heparinized, and treated as shown in Table I. Oxygenation and deoxygenation were performed by bubbling moist air and nitrogen, respectively, through the blood for at least 20 min. Separation into plasma and packed cells was

BROOKS

et al.: NUCLEAR MAGNETIC RELAXATION

13

TABLE I ANALYSIS OF BLOOD SAMPLES

TABLE II RELAXATION TIME T1 IN SECONDS AS MEASURED FOR THEJ SIX SAMPLES AT VARIOUS FREQUENCIES

(mn Hg)

pCO2

P02 (mm Hg)

Hct

(5)

Hb (gm 5)

7.26

72

19

45.8

16.3

oxy blood

7.73

6

109

44.2

15.7

oxy plasma

8.01

2

123

00.

Description

1

venous blood

2

3

pH

4

oxy cells

7.88

3

164

5

deoxy plasma

7.84

24

24

6

stored blood

6.54

194

33

Protein (gm %)

rK

6.1* 77.9

26.6 6.6*

39.2

13.5

Note: Electrophoresis on the two plasma samples gave the following protein breakdown. #3 Albumin

66. 7%

i . 1 a)le # \ venous blood

f (MHz)

'I

2 oxy blood

Plasmla

oxy cells

deoxy plasma .280

3 oxy

4c

5

6

blood-bank blood

.02

.106

.085

.269

.045

.1

.113

.102

.331

.055

-

.123 .136

.3

.131

.125

.407

.071

.392

.195

1

.224

.224

.586

.137

.588

.307

6

.599

.559

1.098

.382

1.171

.744

58

.947

;925

-

-

-

-

#5 63. 5-

Alpha-1

.4

2.2

Alpha-2

8.3

7.7

Beta

8.5

9.8

Gamma

16.1

16.8

performed on a small laboratory centrifuge. The sixth sample was outdated blood-bank blood, treated with ACD, 36 days old. After the relaxation experiments were performed, the samples were taken to Automated Biochemical Laboratory, Suffern, N.Y., for an analysis of gas and protein levels. The results are shown in Table I. Relaxation Measurements The relaxation measurements were made with the help of Dr. Ted Lindstrom at IBM Watson Research Laboratory, using apparatus developed by Koenig et al. [12], [13]. The procedure for frequencies below 6 MHz is as follows. The sample tube is placed in a solenoid and magnetized at a field of 1000 G (0.1 T) until equilibrium is reached. The magnetic field is then suddenly changed to the value corresponding to the Larmor frequency at which information is desired and left there for a short time, during which partial relaxation takes place. The resulting magnetization is then measured by stepping the field back to 1000 G (for convenience of measurement) and immediately applying a 90° pulse, which rotates the magnetization vector from the z-direction into the xy plane, where it is detected by the RF coil. The above procedure is repeated with varying time intervals, so that the entire shape of the relaxation curve can be seen. In this manner the relaxation rate is studied at a variety of field strengths, corresponding to different Larmor frequencies, while the pulse measurements are all made at 1000 G. The measurements are programmed automatically by an on-line computer, which fits the data to the best exponential and displays the relaxation rate r= 1/T1. The experimental uncertainty is estimated to be i5%_ Measurements at frequencies above 6 MHz were made using a 180Q-90° pulse series and a Varian electromagnet [13].

"I

I# 5 deoxv (A)

(sec)

PLASMA

#3 oxy()

#6

t.

/

blood bank

WHOLE

.05

PACKED CELLS

#Aoxy

Larmor frequency

--

MHz

Fig. 2. Relaxation time T1 and relaxation rate r versus frequency for six blood samples. Smooth curves are drawn through the experimental points.

while significant differences are observed with regard to other measurements. The main features to notice about the data are 1) the increase in T1 with frequency, 2) the strong difference between blood, plasma, and packed cell samples, and 3) the small but significant difference among the various whole blood samples (#1, 2, and 6). In the next section, the data are discussed in terms of relevant NMR theory, and compared with data on protein solutions. III.

THEORY

Description of Blood Blood consists of a fluid portion (plasma) and a cellular portion. The ratio of cellular volume to total volume, called the hematocrit, is typically 45%. The cellular portion consists predominantly of erythrocytes, or red blood cells, which contain a rich aqueous hemoglobin (Hb) solution (-35 % Hb) within a thin membrane capsule. The plasma contains approximately 91 % water, 7 % proteins, assorted electrolytes, and other biochemicals. The major proteins in plasma are albumin, globulins, and fibrinogen. In the nuclear relaxation experiments, measurements are on protons belonging to water molecules.2 The made Results of the protons is determined by their chemical relaxation The measured nuclear relaxation times are shown in Table II and are plotted in Fig. 2. A comparison of Figs. 1 2 There are other protons in blood, such as those in protein moleand 2 shows that some of the earlier data points [4], [6], cules. However, because of their very short relaxation time, they [7] are consistent with the present data on whole blood, generally do not contribute to the NMR signal.

14

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JANUARY 1975 Erythrocyte membrane

Plasma

alarm.

waler

s Large molecule (.vtnntintrn

aer t

log J (c)

hOai

Smoll molecule

I Il/ro large

Fig. 3. Diagram illustrating the four primary phases of water in blood, and the chemical exchange that takes place among them.

environment, as we shall soon see. There are basically two chemical environments for water in a protein solution: bulk water and water which is bound to protein molecules. The bound water is referred to as water of hydration, or the hydration sphere. The bond is not strong, however, so that there is a continual exchange of water molecules between, the bulk phase and the hydration sphere. In addition, the erythrocyte membrane is highly permeable to water, and water is continually exchanging between plasma and cytoplasm. Thus there are four possible environments for water molecules, with continual exchange among them, as is illustrated in Fig. 3: bulk water and water of hydration, both intracellular and extracellular. To understand the theory of nuclear relaxation in blood, we must first look at relaxation in a homogeneous environment (e.g., bulk water), and then consider the effects of chemical exchange between different phases, or environments. Relaxation in a Homogenous System3 An isolated nucleus precesses about a magnetic field Ho at the angular Larmor frequency (1) yHo where -y is the gyromagnetic ratio of the nucleus. In order for relaxation to take place, there must be a transverse oscillatory field at the Larmor frequency. In a liquid, the oscillatory field is often supplied by the thermal motion, or Brownian motion, of neighboring spins. These spins set up a magnetic field H1 which fluctuates as the molecules bounce and tumble about. The frequency spectrum associated with this fluctuating magnetic field often has the form

coo =

J(c)

-00

Hi (t)H1(t - r) exp (-iwr) dr - 2r'H..

1+ 1.112co2

(2)

where r, is a correlation time characteristic of the thermal motion and the horizontal lines denote average value. This frequency spectrum is illustrated in Fig. 4. In most cases with which we are concerned, the neighboring spins responsible for relaxation are at a fixed distance, i.e., intramolecular, and so rotational motion of the molecule (rather than translational motion) is the dominant mechanism of relaxation. According to diffusion

\,> db/octove slope (I/tolseall

log w

Fig. 4. Frequency spectra of magnetic field energy at a nucletus created by Brownian motion of a neighboring spin. Larger molecules have a longer correlation time (i.e., slower motion) and so produce a different frequency spectrum as illustrated.

theory, the correlation time associated with rotational maotion is Tr = 47rr7a3/3kT (3) where x7 is the fluid viscosity, a the radius of the molecule, k is Boltzmann's constant, and T is the absolute temperature. From (2) and (3), we find that the relaxation rate due to a neighboring spin at a distance b is [20] 4r Trf 1 \ 3y4ji2 (4) 1 T1 lOb6 + W2ar2 1 + 4co2r2/ where Ii is Planck's constant divided by 27r. This expression is valid when both nuclei are protons, as in the case of water.

Frequency Di.ependence of T1 From (4), we see that for W,2 ra, by definition); fafI, fraction of nuclei in each phase. (fa + fb = 1); Ta,Tb residence time in each phase. (Ta/Tb = fa/fb) a = (i/Ta) + (1/Tb) =l/faTb convenient parameter for describing chemical exchange rate; Mi initial magnetization; Mo equilibrium magnetization.

M%)

Fost [excag

0.

0

00 1000 1) Slow exchange limit: If the two populations are static oi (sec-') or slowly changing, then the total magnetic signal contains Fig. 5. Relaxation rates ri and r2 and amplitude A2 for a 2-phase system as a function of chemical exchange rate a between the two separate components, decaying with time constants phases. The parameters used are Tia = .33 s, Tlb = 0.33 S, fb = 45%. Tia and Tlb, respectively. 2) Fast exchange limit: If the exchange rate is rapid compared to the relaxation rates, the total population observable, although ri is still 20% below its fast exchange follows a single exponential decay with an average relaxa- value. tion rate given by Protein Solutions rav = fara + fbrb = ra + fb(rb- ra). (5) The above theory of chemical exchange can be applied 3) Intermediate exchange: In the general case the total to protein solutions, such as the plasma and cytoplasm in magnetization contains two components decaying at two blood. In these cases subscript a refers to bulk water and b different rates, r1 and r2: refers to water of hydration. All experiments on protein solutions indicate that the Mz(t) -Mo = [A1(exp (-r1t) exchange of water between the two phases is very rapid, + A2exp (-r2t)](Mi-Mo) (6) so that (5) is applicable. Bearing in mind the theory of where A1 + A2 = 1. The slower rate r1 is equal to ra in relaxation discussed above, and the large size of protein the slow exchange limit, and increases to ray in the fast molecules (molecular weight 100 000), we see that rb is very large at low frequencies and dominates (5). The exchange limit. The general expression for ri is relaxation time is therefore short, even though the fraction ri= (1/2) (ra + rb + a) of bound water (fb) may be small (e.g., --I%). At high frequencies, however, rb approaches zero and the relaxation ra (1/2)[(rb+ a)2- 4afb(rb ra)]112. (7) is dominated by the bulk phase. Simultaneously, the amplitude associated with r, increases This behavior has been seen in experiments on protein from fa to unity according to the general expression solutions [13], [23], [24], although the situation is usually more complicated since the water of hydration A1 r2-rav (8) itself is multiphasic, involving a distribution of correlation r2 - r times. This simply means that the fb(rb- ra) term in (5) The faster rate r2 is equal to rb in the slow exchange limit must be replaced by a summation over the different and increases without limit as the exchange rate increases, hydration sites, Eifbi(rbi - ra) where each relaxation while the amplitude A2 rapidly drops to zero. The general rbi iS given by (4). The effect of this distribution of rb is expressions are to smooth out the frequency dependence of T1. Equation (5) is sometimes written in the form r2= (1/2) (ra + rb + a) r = ra + kic, + (1/2) [(rb - ra + a) 2- 4afb(rb- ra) ]1/2 (9) -

-

-

=

or

A2

=

ray -

- r

(10)

r2-ri

ki =

(1/c) (r

-

ra)

=

(l/c) (1/T, -l/T1a) (11)

where c is the protein concentration in gm%, i.e., gm protein/100 ml solution. ki has the desirable property of are plotted as a being approximately independent of concentration for low an arbitrary set of parameters. Note how rapidly A2 falls concentration solutions. to zero and how rapidly r2 increases. Thus the r2 decay is often unobservable, even for exchange rates below the fast Membrane Exchange exchange limit. For example, referring to Fig. 5, an of Having seen that the plasma and cytoplasm each exhibit 50 s-1 produces an r2 decay that is experimentally un- a single relaxation rate, we can now apply the preceding The two relaxation rates

and

and the amplitude A2 function of exchange rate in Fig. 5 for r1

r2

a

a

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, JANUARY 1975

16

theory of chemical exchange to the exchange of water molecules through the cell membrane, considering the plasma as phase a and the cytoplasm as phase b. From data on plasma and packed cell samples, we can ascertain ra and rb, and then proceed to analyze data on whole blood samples, using either (5) or (7), as appropriate. This is done in the next section. IV. COMPARISON OF THEORY AND EXPERIMENT Membrane Exchange In all our measurements the relaxation closely approximated a single exponential decay, indicating that the exchange of water across the cell membrane is fairly rapid compared to the relaxation rate. These findings are consistent with other measurements of membrane exchange [25]-E27], which yield a cell residence time of about 10 ms per visit. In contrast, Odeblad et al. [28], found two separable NMR signals in blood at 16 MHz which they attributed to intracellular and extracellular phases with very slow exchange between them. Subsequently, we recorded resonance spectra on blood samples with a Varian 60 MHz spectrometer in an attempt to duplicate Odeblad's findings. The results showed a single resonance peak (see Fig. 6), confirming that the membrane exchange rate is fast, at least at 60 MHz. If the exchange of water across the cell membrane is sufficiently fast, then (5) can be used (fast exchange limit), with the subscripts a and b referring to plasma and red blood cells, respectively. As we have seen, this condition is more stringent than the condition for observing a single exponential decay. Table III shows an analysis of the relaxation rates for whole blood, plasma, and packed cells (samples #2, 3, and 4), using the fast exchange limit. First fb is calculated for the whole blood and packed cell samples, using the rmeasured hematocrits (Table I) and assuming standard values of 94 gm water/100 ml plasma and 72 gm water/ 100nml cells [29]; the results are fb = .378 (#2, whole blood) and fb = .730 (#4, packed cells). Then, at each frequency, the cytoplasm relaxation rate rb is calculated from the plasma and packed cell data, using (5); these results are shown in column 2 of Table III. Finally the relaxation rates for whole blood are calculated from the plasma and cytoplasm rates just given, again using (5), and displayed in column 3. Column 4 shows the ratio of the experimental and calculated relaxation rates for blood. The agreement is within 9 %. The agreement between theory and experiment can be significantly improved by abandoning the fast exchange approximation. The best results (-+t 1 %) are obtained by choosing Tb = 19 ms, which corresponds to a = 188 s-1 for the packed cell sample, and a = 85 s-' for the whole blood sample. These results are shown in the last three columns of Trable III. The calculation is the same as in the preceding paragraph, except that (7) is used instead of (5). While rb = 19 ms is higher than the 10 ms value gen-

Fig. 6. NMR spectra of human blood samples.

TABLE III CALCULATED VALUES FOR THE RELAXATION RATE OF BLOOD USING THE FAST EXCHANGE APPROXIMATION (5) AND THE EXACT EQUATION (7) Exact Calculation (Tb=l9

Fast Exchange Appr. f(MHz)

rb (sec

)

esec)

rblood

rblood

rb

rblood

rblood

(sec-1)

exp/calc

(sec-1)

(sec-i)

exp/calc

11.9

.02

29.6

13.0

.91

30.1

.1

24.1

10.6

.93

24.3

9.88

.99

.3

18.7

.96

18.7

7.92

1.01

8.28

.99

1

9.54

4.51

.99

9.45

4.47

1.00

6

3.31

1.77

1.01

3.28

1-78

1.00

erally quoted, it must be pointed out that we are in a region of the exchange curve (see Fig. 5) where the relaxation rate is not very sensitive to the exchange rate. Besides, there are other uncertainties, such as our knowledge of fb. The significance of this calculation is merely to show that the relaxation data for whole blood can be reasonably explained in terms of membrane exchange between plasma and cytoplasm. Comparison with Protein Solutions The red blood cells contain approximately 35% hemoglobin and very little other protein. Therefore one expects the cellular relaxation rate to be similar to that in a concentrated hemoglobin solution. Such a comparison is shown in Fig. 7, where kl is plotted versus frequency for red blood cells (from column 5 of Table III) and a 38.6% henmoglobin solution [30]. The curves are qualitatively similar; however k1 for cells is significantly greater than k1 for the hemoglobin solution at low frequencies. This may be due to the effect of other proteins or the cell membrane

structure. The blood plasma contains approximately 6.5% protein, of which 2/3 is albumin. Fig. 7 also shows a comparison of k1 for plasma with k, for apotransferrin, a plasma protein

17

BROOKS et al.: NUCLEAR MAGNETIC RELAXATION

red blood cells (Table column 6)

k,

k,

j ( T,I

TI)

(sec-I

Larmor frequency

---

MHz

Fig. 7. Comparison of nuclear relaxation in blood and in protein solutions.

of the globulin class [13]. Again the behavior is qualitatively similar. Quantitative agreement should not be expected in view of the obvious differences in composition. Effect of pH It is well known that pH affects the charge state of a protein molecule, and hence its conformation and its hydration sphere. Therefore pH is expected to affect the relaxation time of water in a protein solution. The three samples of whole blood exhibit a pH variation that may be used to examine this question. Compared with the venous sample (pH = 7.26), the oxygenated sample was slightly alkaline (pH 7.72-7.73) because of CO2 loss during bubbling, while the blood-bank specimen was acid (pH = 6.54) because of the anticoagulant (ACD) and the high CO2 accumulation. As can be seen from Fig. 2, the T1 values for these samples are significantly different. Part of the difference can be explained by the variation in hematocrit. The remainder of the difference is probably due to the pH variation. Relaxation studies on 10% hemoglobin solu-tions [30] showed approximately a 25% decrease in T, per pH unit increase at low frequencies. The variation in T7 of blood is in the same direction and is of the same order of magnitude. A quantitative comparison is not attempted because of the substantial differences in composition between blood and a 10% hemoglobin solution. =

Effect of Temperature All relaxation measurements were made at room temperature (25°C). T1 values at body temperature (37°C) are expected to be significantly greater, based on studies of hemoglobin solutions, which show approximately a 20% increase in T1 at low frequencies when the temperature is raised from 25°C to 36°C [30]. V. CONCLUSIONS The main experimental results on T, of blood have been presented in Fig. 2, and explained in terms of existing theory. The principal features of the results may be summarized as follows. 1) All T7 values increase with frequency, due to the

diminished relaxing power of macromolecules at high Larmor frequencies. 2) The values for whole blood are intermediate between the plasma and packed cell values, in accord with the theory of chemical exchange in a two-phase system. A red cell residence time of 19 ms for water molecules provides the best fit to the experimental data. 3) The plasma data agrees qualitatively with T1 values for an apotransferrin solution, when normalized to unit protein concentration. This supports the premise that the 'prime relaxation mechanism is the diamagnetic protein content. 4) Similarly, the erythrocyte T, data (calculated from plasma and packed cell samples using chemical exchange) agrees with T, data for hemoglobin solutions, except at low frequencies where membrane or other effects may be important. 5) Increasing pH causes T1 to decrease because of its effect on the conformation (shape) of protein molecules. The magnitude of this effect is on the order of 25 % per pH unit at low frequencies. More precise statements on the effect of pH cannot be made on the basis of the present data. 6) An increase of T1 with temperature is expected on the basis of existing hemoglobin data (20 % increase for a temperature change from 25°C to 37°C).

ACKNOWLEDGMENT Grateful acknowledgment is made to Drs. Seymour Koenig and Ted Lindstrom of IBM Watson Research Laboratory. Dr. Koenig provided the equipment for measuring nuclear relaxation and Dr. Lindstrom took the T1 data on the blood samples. We are also grateful to Dr. Lindstrom for making available unpublished data on hemoglobin solutions. We would also like to acknowledge the helpful cooperation of Dr. Harry Saver and Richard Halbach in obtaining and preparing blood samples, and of Dr. Charles Wilkie in running the NMR spectra.

REFERENCES [1] J. H. Battocletti, J. H. Linehan, S. J. Larson, A. Sances, Jr., R. L. Bowman, V. Kudravcev, W. K. Genthe, R. E. Halbach, and S. M. Evans, "Analysis of a nuclear magnetic resonance blood flowmeter for pulsatile flow," IEEE Trans. Bio-Med. Eng., vol. BME-19, pp. 403-407, Nov. 1972. [21 W. K. Genthe, "Process flow measurement experience with the NMR flowmeter," in Flow, Its Measurement Control in Science and Industry, Pittsburg, 1974, Instrument Society of America. [3] R. L. Bowman, V. Kudraveev, J. H. Battocletti, S. J. Larson, S. M. Evans, and A. Sances, Jr., "A non-invasive NMR flowmeter," Proc. of Workshop No. 2 of the 9th International Conference on Medical and Biological Engineering, Melbourne, Australia, Aug. 23-27, 1971, pp. 6-12. [4] J. H. Battocletti, A. Sances, Jr., S. J. Larson, R. E. Halbach, R. L. Bowman, V. Kudravcev, and S. M. Evans, "NMR detection of low magnetization levels in flowing fluids," Paper 22.6 Intermag. Conference, Washington, D. C., April 1973, and IEEE Trans. Magn., vol. MAG-9, pp. 451-454, Sept. 1973. [51 3. H. Battocletti, A. Sances, Jr., S. J. Larson, R. E. Halbach, S. M. Evans, R. L. Bowman, V. Kudraveev, and W. K. Genthe, "NMR T, relaxation times of blood," Proceedings of 26th ACEMB, Minneapolis, p. 302, 1973. [6] T. R. Ligon, "Coil design for low field NMR experiments and NMR measurements on the humani arm," M.S. Thesis, Okla homna State Univ., 1967.

18

IEEE

TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-22, NO. 1, JANUARY 1975

[7] J. H. Battocletti, A. Sances, Jr., S. J. Larson, R. E. Halbach, S. M. Evans, R. L. Bowman, and V. Kudravcev, "A review of NMR techniques applied to biological systems," in Biologic and Clinical Effects of Low-Frequency Magnetic and Electrical Fields, ch. XXII, J. G. Llaurado et al., eds. Springfield, Illinois: C. C. Thomas, 1974. [8] P. Buchman, "NMR blood flowmeter," M.S. thesis, Univ. of Washington, 1959. [9] J. R. Singer, "Biological flow and process tracing using nuclear and electron paramagnetic resonance," IRE Trans. Med. Electron., vol. ME-7, pp. 23-28, Jan. 1960. [10] A. I. Zhernovoi and G. D. Latyshev, NMR in a Flowing Liquid, p. 98, trans. by Consultants Bureau, Plenum Press, 1965. [11] 0. C. Morse, III, "NMR blood flow measurements," Ph.D. thesis, pp. 20-21, Univ. Calif. (Berkeley), 1970. [12] A. G. Anderson and A. G. Redfield, "Nuclear spin-lattice relaxation in metals," Phys. Rev., vol. 116, pp. 583-591, 1959. [13] S. H. Koenig and W. E. Schillinger, "Nuclear magnetic relaxation dispersion in protein solutions-I. Apotransferrin," J. Biol. Chem., vol. 244, pp. 3283-3289, 1969. [14] A. S. Mildvan and M. Cohn, "Aspects of enzyme mechanisms studied by nuclear spin relaxation induced by paramagnetic probes," Advances Enzym., vol. 33, pp. 1-70, 1970. [15] B. Sheard and E. M. Bradbury, "NMR in the study of biopolymers and their interaction with ions and small molecules," Progr. Biophys., vol. 20, pp. 187-246, 1970. [16] J. A. Walter and A. B. Hope, "NMR and the state of water in cells," Progr. Biophys., vol. 23, pp. 1-20, 1971. [17] M. J. Tait and F. Franks, "Water in biological systems," ATature, vol. 230, pp. 91-94, 1971. [18] 0. Jardetzky and N. G. Wade-Jardetzky, "Application of NMR spectroscopy to the study of macromolecules," Ann. Rev. Biochem., vol. 40, pp. 605-634, 1971.-

Pattern Recognition

Applied

[19] B. D. Sykes and M. D. Scott, "NMR studies of the dynamic [20] [21]

[22] [23]

[241 [25]

[26]

[27] [28]

[29] [30]

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to Monitoring

WILFREDO RAMOS VALENZUELA, ALLEN KLINGER, MEMBER,

Waveforms

IEEE, AND JOHN S.

McDONALD

Abstract-This paper demonstrates that fetal heart rate (FHIR) patterns can be classified by algorithmically determined linear discriminants. A nonparametric learning algorithm was applied to 17 samples of five-vectors. The coordinates of each sample vector were visual features derived from the FHR curve and the simultaneous uterine contraction pressure data in accord with medical training-literature. Data were obtained from strip-chart recordings from the Cedars-Sinai Medical Center, Los Angeles, where an FHR monitoring and on-line computer processing system based on an IBM System/7 is being installed. The algorithm converged to linear discriminants that correctly classified all the 17 training samples under four different combinations of initial weights, training sequence, and correction increment. Each of the four linear decisionrules so obtained was applied to 14 new sample vectors. Three classified 11 samples correctly and one classified 13 samples correctly. Medical anomalies (atypical data) were present in all three

misclassified patterns. A perfect success record was found in classifying all seven medically ominous new sample vectors.

ment is authorized to reproduce and distribute reprints for G-overnmental purposes notwithstanding any copyright notation hereon. W. R. Valenzuela and A. Klinger are with the Department of Computer Science, University of California, Los Angeles, Calif. 90024. J. S. McDonald is with the Department of Obstetrics-Anesthesiology, University of Southern California Medical Center, Los Angeles, Calif. 90033.

This paper is concerned with showing that the first technique can be automated. That is, as a loing-range bioengineering objective, our work involves development of. computer programs for the interpretation of FHR changes in relation to UC's. Although we do not use

1.0 INTRODUCTION THE principal role of fetal monitoring is to provide more accurate information on the fetal condition so the obstetrician can determine the best course of action during labor and delivery. Fetal monitoring refers to two techniques: 1) Observation of the fetal heart rate (FHR) and its changes throughout the course of labor with particular attention to the effect of uterine contractions (UC's); 2) Measurement of the acid-base changes which occur Manuscript received October 8, 1973; revised March 15, 1974, during the course of labor through the evaluation and August 11, 1974. This paper was partially sponsored by the Air Force Office of Scientific Research, Air Force Svstems Command, of fetal scalp blood samples [1]. U. S. Air Force, under Grant AFOSR-72-2384. The U. S. Govern-