ph distributions in transplanted neural tumors and...

[CANCER RESEARCH 42, 1498-1504, April 1982]0008-5472/82/0042-OOOOS02.00

pH Distributions in Transplanted Neural Tumors and Normal Tissues ofBDIX Rats as Measured with pH Microelectrodes1

Eckhard JÃ¤hde,Manfred F. Rajewsky,2 and Horst Baumgart!

Institut fÃ¼rZellbiologie (Tumorforschung), UniversitÃ¤t Essen (GH), Hufelandstrasse 55, D-4300 Essen 1. Federal Republic of Germany [E. J., M. F. P.],and Max Planck-Institut fÃ¼rSystemphysiologie, Rheinlanddamm 201, D-4600 Dortmund, Federal Republic of Germany [H. B.]

ABSTRACT

The distribution of pH values was measured in transplantedneuroectodermal TV1A tumors and in brain and kidney of BDIXrats in vivo. Tissue damage during pH measurements could beminimized by the use of Hinke-type pH glass microelectrodeswith maximum diameters of the pH-sensitive tips of S10 jum(sensitivity, 58 to 60 mV/pH unit at 37Â°;response time (95%),

Â¿3sec; drift, so.01 pH unit/hr). The advantages and limitations of this technique are discussed in relation to other methods for the analysis of extracellular pH.

In tumors weighing 1.0 to 2.5 g, pH values ranged from 6.8to 7.1 (mean, 7.0). The pH distribution in tumors weighing 4 to6 g was shifted to slightly lower values, with an average pH of6.9 (range, 6.7 to 7.1). No marked pH differences were foundbetween the tumors and normal tissues. The pH values measured in brain and kidney ranged from 6.6 to 7.3 (mean, 7.0)and 6.7 to 7.3 (mean, 7.1), respectively. Within single tumors,local pH variations in the range of 0.2 to 0.3 pH unit wereobserved. The local pH values measured in certain tumor areasare, however, sufficiently low to partially inhibit proliferationand colony formation in cultured malignant cells.

INTRODUCTION

In animal and human cells, increased rates of hexose transport and aerobic glycolysis are generally, although perhaps notobligatorily (27, 33), associated with malignant phenotypes (forreviews, see Refs. 1, 24, 33, and 49). The relevance of thesealterations for the proliferative properties of malignant cells invivo has not been clearly established. The growth rate in vivoof a series of malignant hepatic tumors has, not unquestioned,been positively correlated to their rate of aerobic glycolysisunder in vitro conditions (6). Due to inefficient clearance ofacidic metabolites from malignant tissues by the poorly developed tumor vasculature and the concomitant decrease in pHe3

(14), an increased rate of aerobic glycolysis may in fact eveninhibit the proliferation of malignant cells in solid neoplasms.Indeed, the proliferation rate of normal and malignant cells inculture has been found sensitive to a reduction of pHe (10, 3).To investigate whether the pH of the cellular microenvironmentcould be a factor controlling the proliferation of malignant cellsin vivo, we have analyzed the distribution of pH values in s.c.-

transplanted neuroectodermal TV1A tumors and in normal tissues of BDIX rats. With the exception of the recent work byBicher ef al. (4, 5) and Vaupel ef al. (42), using Hinke-type

microelectrodes (see Table 1), most earlier pH measurements

1 Research supported by the Deutsche Forschungsgemeinschaft (Ra 119/8).* To whom requests for reprints should be addressed.3 The abbreviations used are: pH,., extracellular pH; pH , intracellular pH;

DMO. 5,5-dimethyl-2,4-oxazolidinedione.Received August 10, 1981; accepted January 7, 1982.

in tumor tissues had been performed with the use of pHelectrodes with tip diameters of 0.1 (46, 47) and ~1 mm (2, 8,

12, 22, 23, 26, 28, 30, 35, 40, 45), respectively. The insertionof such large-size electrodes obviously leads to tissue com

pression and rupture of blood vessels and may give rise toartifacts. Therefore, pH microelectrodes with maximum diameters of the pH-sensitive tips of S10 fim were used for the

present analyses in normoglycemic animals. The corresponding measurements in malignant tumors and normal organs ofhyperglycÃ©mie BDIX rats will be reported in the subsequentpaper (21).

MATERIALS AND METHODS

Animals. Adult male rats of the inbred BDIX strain (9) were used inall experiments. The rats were housed 2/cage and maintained on astandard laboratory diet (Alma, Kempten, Germany) with water adlibitum.

Tumors. The neuroectodermal TV1A transplantation tumor originates from a malignant neurinoma of the trigeminal nerve, induced bya single transplacental pulse of W-ethyl-W-nitrosourea in a fetal (18th

day of gestation) BDIX rat (25). Tumors in the weight range used (1 to6 g) were free of necrotic areas as confirmed by histological examination and separated from the adjacent s.c. tissue by a fibrous capsule.Tumor pieces of ~1 cu mm (transplant passages 21 to 36) were

transplanted s.c. to both flanks of BDIX rats 2 to 3 weeks prior to theexperiments.

pH Measurements. The pH in normal BDIX rat tissues (brain, kidney)and in TV1A tumors was measured using Hinke-type (19) pH glass

microelectrodes (Chart 1; Fig. 1). In view of the automated continuouspH recordings across individual tumors or normal tissues, these micro-

electrodes with their much shorter response times were preferred overThomas-type microelectrodes (see Table 1). The construction of the

microelectrodes used in the present study has been described (36).Briefly, lead glass tubes and pH glass capillaries were drawn by gravityto small tips ~1 /im in diameter in a heating coil. After the tip of thelead glass tube was broken off to produce an opening ~10 urn in

diameter, the pH glass cone was inserted into the lead glass tube sothat it protruded by ~500 /im. The contact zone of both capillaries wasfused over a length of ~100 /im in a micro heating coil, and the pH

glass cone was then drawn to an open tip which was finally closed bya heated platinum wire. The diameter (as measured at the widest upperportion, i.e., at the lead glass boundary; see Chart 1 and Fig. 1) andthe length of the pH-sensitive tips were Â£10 and ~20 jtm, respectively.In modification of the construction reported previously (36), the pH-

insensitive shaft of the microelectrodes was not covered with anadditional radiofrequency sputtered insulation layer. Silver/AgCI electrodes (type 373; Ingold, Frankfurt am Main, Germany) were used asreference electrodes. These were connected either to standard buffersor to the tissues via an interface of an aqueous solution of 2 M KCI and

a glass capillary filled with an aqueous solution of 0.9% NaCI and 1%agar (heated to 100Â°). A Keithley 616 electrometer (Keithley Instruments, Inc., Cleveland, Ohio) with an input resistance of 2 x 1014 ohms

was used as an amplifier. Electrode signals were recorded continuouslyon a Graphirac II pen recorder (Burster, Gernsbach, Germany). For

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pH in Transplanted Tumors and Normal Tissues

Table 1

Diameter of pH- Sensitivity (mV/

Type of pH electrode sensitive tip (firn) pH unit) Response time Drift Application

and termination ofexperiment

Reference

HinketypeHinketypeHinke

type(modified)"Recessedtip"(Thomas

type)"Recessedtip"(Thomas

type)"Glassmembrane"S10(20)6~1

(10-50)Â£20(150)S1

00.5

(e)1.5-1

00 (e)58-60

(37Â°)c49-52(25Â°)55.5

(35Â°)53-56(e)60-62

(37Â°)56-59

(")3

sec(95)"<15sec(e)40

sec(90)1min(95)0.25-35

min(e)30

sec (100)0.01

pHunit/hr<0.01x measuredpHvalue

hr0.001pHunit/hroe0.5

pH unit between startTissue

pHTissuepHTissue

pHpH,pH,Tissue

pH-pH,This

study421813.

413834

See cited references for experimental details.0 Numbers in parentheses, sensing length (Â¿im).c Numbers in parentheses, temperature.d Numbers in parentheses, percentage of theoretical signal difference.e Data not reported.

i t t l t i t t i 4 t l l i -jo

Chart 1. pH glass microelectrode (schematic). A. teflon insulation; B. screen;C, pitch; D, teflon stopper; E, lead glass; F, air; G, polyethylene; H, copper wire;/, soldered contact; J, platinum wire; K, glue; L, platinum wire of internal referenceelectrode fused into lead glass; M, lead glass; N, silver-silver/AgCI layer; O,internal buffer solution; P. lead glass; 0, pH glass.

testing the reference unit, a standard pH electrode (type 275; Ingold)was connected to the electrometer.

Prior to each experiment, the microelectrodes were calibrated 3

5 -100

S

0 S IO IS 20

TimÂ«(min)

Chart 2. Sensing properties of pH glass microelectrodes: sensitivity. Themicroelectrode was calibrated at 37Â° in standard buffers (see "Materials andMethods"). For demonstration, the microelectrode was not rinsed between

measurements in different buffers and the time of contact with a given buffer waslimited to ~1 min. Original registration. Arrows, buffer changes to pH 7.15, 6.83,6.20, 5.80, 7.49, 7.15, 6.83. 6.20, 5.80, 7.49, 7.15, 6.83, 6.20, and 5.80. ThepH values (right ordinate) were calculated from the calibration curve of themicroelectrode (see Chart 4).

times at 37Â°in standard buffers of pH 4.03, 7.39, and 9.09 as well as

pH 5.80, 6.20, 6.83, 7.15, and 7.49. Recalibration was routinelycarried out at intervals of S4 hr. The sensitivity of all well-functioning

microelectrodes was very close to the theoretical value (slope), i.e., 57to 59 mV/pH unit at 22Â°and -60 mV/pH unit at 37Â°(Charts 2 and 4).

Electrodes with a sensitivity of <55 mV/pH unit were not used. Theelectrode response time was measured at 22Â°by quick changes of 2

standard buffers (pH 4.00 and 9.18) without intermittent rinse (Chart3). All electrodes used for pH measurements had a 95% response timeof S3 sec. During consecutive measurements in a standard buffer, theelectrode signals were reproducible within Â±1 mV of the mean. Asdetermined by calibrations at 4- to 8-hr intervals, the drift of the

microelectrodes was Â£0.01 pH unit/hr and did not affect the slope ofthe calibration curve (Chart 4).

All calibrations and pH measurements in tissues were performed inan electrically shielded cage. The microelectrodes and the referencecapillaries were mounted on modified micromanipulators (Leitz, Wet-

zlar, Germany) connected by a flexible shaft to a geared electricaldrive outside the cage. With this device, the microelectrodes could beinserted into tissues either by hand or automatically at a speed of up to500 /Â¿m/min. Immediately prior to the measurements, the rats wereanesthetized with Nembutal (Abbott, Bad Segeberg, Germany; 40 /ig/g body weight) and immobilized on a heated platform within the shieldedcompartment. Core temperature was monitored with a thermocouple(Bailey Instruments Co., Inc., Saddle Brook, N. J.) inserted into thecolon.

APRIL 1982 1499



E. JÃ¤hdeet al.

Prior to pH measurements in TV1 A tumors, the overlying skin wasincised under microscopic control and ~1 0 sq mm of the tumor surface

were freed from overlying s.c. tissue. Care was taken not to damageblood vessels. The fibrous tumor capsule was perforated with a syringeneedle, and the reference capillary was placed on the tumor surfaceavoiding tissue compression. The pH microelectrode was then automatically inserted to a depth of 5 or 10 mm in tumors weighing 1 .0 to2.5 or 4 to 6 g, respectively. As demonstrated by single-point pH

determinations, the pH values recorded immediately after electrodeinsertion, and thereafter for 30 min, remained constant, indicatinginstantaneous stabilization of measuring conditions. Electrode signalswere recorded continuously, and the pH frequency distributions werecalculated from single-point measurements (100-/im steps).

Brain and kidney of BDIX rats were used as control tissues. For pHmeasurements in the brain, the skull overlying the right cerebral hemisphere was opened with a dental drill in a paramedian position, thedura was removed, and the reference capillary was placed on the brainsurface after the meninges had been perforated. The microelectrodewas then inserted to a depth of 4 mm. After incision of the left dorsalskin and musculature over a length of -2.5 cm, the left kidney was

freed from adipose tissue without damaging the supplying blood vessels and fixed in a stable position. The kidney was chosen for technicalreasons since the extremely fragile pH microelectrodes could be more

! Â°

, - 100 -

/--A r 4.0

â€”Iâ€”I 1â€” â€”I 'â€”Iâ€” â€”iâ€”Iâ€”I

0123156

Tim. (mkl)

Chart 3. Sensing properties of pH glass microelectrodes: response time. Themicroelectrode was calibrated at 22" in standard buffers of pH 4.00 and 9.18,

without intermittent rinse. Original registration. Alternating buffer changes (fromleft to righi) to pH 4.00 and pH 9.18, respectively. The pH values (right ordinate)were calculated from the calibration curve of the microelectrode (see Chart 4).

o 50Â®

UI

5.5 65pH

7.0 7.5

Chart 4. Sensing properties of pH glass microelectrodes: drift. The micro-electrode was calibrated (â€¢)and calibrated (O) after an interval of 8 hr. Eachpoint is the mean of 3 single measurements (maximum deviation, Â±1 mV of themean). The drift was calculated from the distance of the 2 calibration curves (0.5mV/hr ~ 0.01 pH unit/hr).

>UC

Â« 40 -

7.0

pH

7.5

Charts. pH frequency distributions in s.c.-transplanted TV1A BDIX rat tumors. pH measurements and calculations of distributions were performed asdescribed in ' 'Materials and Methods." A: tumor weight, 1.Oto 2.5 g; 10 tumors;

number of pH recordings, 500. B: tumor weight, 4 to 6 g; 10 tumors; number ofpH recordings, 1000.

easily inserted into the renal parenchyma than into, e.g., skeletalmuscle. The kidney capsule was incised near the middle of the cortex,the reference capillary was brought into contact with the parenchymalsurface, and the microelectrode was inserted to a depth of 6.5 mm.For both brain and kidney, the pH frequency distributions were determined as outlined for the TV1A tumors.

RESULTS

pH Distributions in TV1A Tumors. The pH frequency distribution in TV1A tumors weighing 1.0 to 2.5 g ranged from pH6.8 to 7.1 (mean, 7.0; Chart 5A). This variation of pH values isdue to (a) pH differences between individual tumors and (to)local intratumoral variations of pH. To analyze the latter parameter, the continuously recorded electrode signals were plotteddirectly as average intratumoral pH profiles (Chart 6). In singletumors, local pH values varied within 0.2 to 0.3 pH unit.However, no relationship between the electrode position (depthfrom the surface) within these tumors and the average local pHwas found (Chart 6/4).

The pH histogram of larger TV1A tumors (4 to 6 g) wasshifted to slightly lower values (Chart 5B). In these tumors, thepH values ranged from 6.7 to 7.1, with a mean of 6.9. The pHprofiles shown in Chart 7 were obtained in 3 different locationsof the same tumor. In 3 different positions at a depth of 1.5 mmbelow the tumor surface, pH values of 6.84, 6.90, and 7.07,respectively, were measured. As reflected by the averageintratumoral pH profile (Chart 66), again no obvious correlationexisted between the insertion depth of the pH microelectrodeand the local pH.

pH Distributions in Normal Tissues (Brain and Kidney). ThepH in BDIX rat brain ranged from 6.6 to 7.3, with a mean of 7.0(Chart 8). The pH values between 6.6 and 6.8, obtained witha frequency of <15%, were all recorded immediately adjacent





7.1 -

7.0-

6.9-

6.8-

7.1 -

7.0-

6.9-

6.8-

2668pH-Electrode Insertion Depth (mm)

10

Chart 6. Average local pH profiles in TV 1A tumors. pH microelectrodes wereautomatically advanced into the tumor tissue at 500-fim steps, and the averagepH values from single-point measurements in individual tumors with standarddeviations (shaded areas) were calculated from the continuously recorded electrode signals. pH values measured in the upper 500-nm section adjacent to thetumor surface are not included, in view of possible damage to the tumor surfaceduring preparation. A: tumor weight, 1.0 to 2.5 g; maximum insertion depth, 5mm; 5 tumors. 8: tumor weight, 4 to 6 g; maximum insertion depth, 10 mm; 6tumors.

o i 2 3 t s t

Insertion Depth (mm)

Chart 7. Local pH profiles in an individual TV1A tumor. The pH microelectrodewas inserted into 3 different areas of a tumor weighing 4.2 g. Original registrationof continuously recorded electrode signals (pH values measured in the upper500-/im section adjacent to the tumor surface not included).

to the brain surface and may be due to local circulatorydisturbances caused by the preparation. The true mean pHvalue for brain may, therefore, be slightly higher than 7.0. Inthe kidney, >95% of the pH values ranged between 6.9 and7.3, with a mean pH of 7.1 (Chart 8).

DISCUSSION

LÃ¡clate production by malignant cells, contrary to normalcells, is closely correlated with the extracellular concentrationof glucose (11, 49). The pH in the interstitial fluid of malignanttumors, therefore, depends on (a) blood flow and interstitialtransport of glucose into the cellular microenvironment and (b)diffusive and convective clearance of acidic metabolites fromthe interstitial space. Any interference with the microcirculation

and the interstitial transport in tumors will thus affect both theavailability of glucose to the tumor cells and the clearance oflactic acid. Consequently, reliable pH determinations in tumortissues require the utmost possible preservation of the capillarynetwork and tissue microarchitecture. However, only in therecent studies by Bicher et al. (4, 5) and Vaupel ef al. (42) ontransplanted mouse tumors and in the present analyses havefor the first time pH microelectrodes with small tip diameters(S10 urn) been applied. All other electrodes thus far used forpH measurements in animal and human tumors had tip diameters of the order of 0.1 (46, 47) and 1 mm (2, 8, 12, 22, 23,26, 28, 30, 35, 40, 45), respectively. The dimensions of theseelectrodes are large as compared to intercapillary distances intransplanted tumors (range, 15 to 150 jum; Ref. 43), and theirinsertion obviously leads to tissue compression and rupture ofblood vessels.

In spite of their small dimensions, the sensing properties ofthe pH microelectrodes used in the present study are comparable to the characteristics of large-size standard pH electrodes

and to the properties of different microelectrodes designedmainly for measurements of pH3 (Table 1). The validity of pH

measurements in tissues with the use of pH glass microelectrodes is also supported by comparison of the present datawith the results of other studies on the pH in malignant andneural tissues in which different analytical techniques havebeen applied (Table 2). On the other hand, even microelectrodes as small as those used here are likely to destroy cellswhen inserted into tissues. The present data must, therefore,be considered as integral values, representing the concentration of I-T ions in the extracellular fluid together with an

unknown contribution from various intracellular compartments.Studies on the relationship betweeh pHe and pH in culturedcells and tissues in vivo have yielded conflicting results. Interpretation of the data is further complicated by the inhomoge-

to-

75

Chart 8. pH frequency distributions of BDIX rat brain and kidney. pH measurements and calculations of pH distributions were performed as described in"Materials and Methods." A: brain; 5 animals: number of pH recordings, 200. 8:

kidney; 5 animals; number of pH recordings, 325.

APRIL 1982 1501



Â£.JÃ¤hdeet al.

Table 2

pH in transplanted tumors and brain of rats: pH determinations without insertionof pH electrodes into tissues

Method used for pHTissuedeterminationWalker

256carcinomaNovikoffhepatomaFibrosarcoma4956Collectionoftumorinterstitialfluidindiffusion

chambers(pHmeasurementoutside

thetumorwithstandardelectrodes)Walker

256 DMOmethodcarcinomaYoshida

DMOmethodsarcomaRat

brain CO2 methodAverage

pH Â±S.D.6.99

Â±0.14(pH.)6.95

Â±0.17(pH.)7.09

Â±0.12(pH.)7.19(pH)7.21

Â±0.18(pH,)7.04

Â±0.01 (pH,)Refer

ence15151537839

neous pH values within different compartments of single cells(29). The "aggregated" pHÂ¡values differ according to both the

type (20, 31, 32) and the concentration (44) of the extracellularbuffer system, the technique used for pH determination (7),and the method of varying the pHe (32). Using the DMO3

method (48), Schloerb era/. (37) observed an increased pH inthe Walker 256 carcinoma after s.c. glucose injection into thetumor-bearing rats, whereas Dickson and Calderwood (8)noted no change in pH but a pronounced reduction of pHe inthe Yoshida rat sarcoma after i.p. administration of glucose. Ata pHe of 7.1, pHi values of 6.6, 7.1, and 7.3, respectively, wereobtained in human peripheral blood lymphocytes in vitro whentrimethylamine, DMO, and trimethylacetic acid were used formeasuring pHÂ¡(7). In a physiological buffer system (NaHCO3),a linear relationship between pH, and pHe was demonstrated incultured murine BP-8 sarcoma cells with the use of a fluores

cence technique (20). Using the DMO method, Poole (31) alsofound a reduced pH in Ehrlich ascites cells when the pHe ofthe bicarbonate-buffered culture medium was lowered to sub-

physiological values. However, consistent with results obtainedin different systems (7, 32), the reduction of pH was not aspronounced as the change in pHe. It may, therefore, be assumed that under conditions where the pH value measured invivo does not exclusively reflect the extracellular value the truepHe is lower than the measured composite value.

From the increased rate of lactate production by malignantcells cultured in media containing high glucose concentrations,one might perhaps expect more pronounced pH differencesbetween tumors and normal tissues, e.g., in the vicinity of aprimary or metastatic tumor. While the latter question might bebest studied in primary animal tumors, we nevertheless did notdetect in the present study marked pH differences betweenbrain and the s.c.-transplanted well-delineated neuroectoder-

mal TV1A tumors in the normoglycemic BDIX rats used here.The lacking difference between the pH distributions of TV1Atumors and normal tissues may be due to the low concentrationof glucose in the interstitial fluid of transplanted tumors (14).Thus, in most of the samples of tumor interstitial fluid analyzedby Gullino ef al. (14), very little or no glucose was detected(mean value, 30 /Â¿M).Physiological conditions in vivo apparentlydo not allow tumor cells to make use of their potential foraerobic glycolysis to a larger extent. The slight shift to lowerpH values seen in larger TV1A tumors (4 to 6 g) may be due toan increased retention of acidic metabolites in the tissue relative to smaller tumors, i.e., a tumor size dependent decline ofvascular drainage (43).

The proliferation rate of both normal and malignant cells inculture is at its optimum only within a restricted range ofmicroenvironmental H+ ion concentrations, and cell replication

can be completely inhibited by reduction of pHe (3, 10). Thus,the pH optima found for the proliferation of cultured malignantrat glioma cells (10) and mouse neuroblastoma cells (3) were7.15 to 7.85 and 7.4 to 7.6, respectively. The proliferation rateof the glioma cells was reduced to half-optimal values at a pHeof 6.8, and the population-doubling time of the neuroblastoma

cells increased from 25 to 60 hr when the pHe was lowered toa range similar to the level measured in TV1A tumors in thepresent study (3, 10). At the average pH of 6.9 found in TV1Atumors weighing 4 to 6 g, colony formation of KB cells andHeLa cells in monolayer culture was reduced to ~15 and~50%, respectively, of the plating efficiency obtained at the

optimal pHe of 7.2 to 7.64 (10). These data seem to indicatethat, at least in certain tumor areas, the pHe could be one ofthe factors affecting the proliferative activity of malignant cellsin vivo. This is supported by observations indicating that afurther reduction of pHe in tumor tissues may be incompatiblewith cell proliferation. Thus, diet-induced acidosis has been

shown to decrease the growth rate of malignant tumors in mice(17), and several authors have stressed the importance of asystemic alkalosis for the growth of solid neoplasms (for review,see Ref. 17). On the other hand, the proliferation rate of severalhuman and murine malignant cell lines in culture was notmarkedly inhibited at a pHe of 6.8 (10), and the cloning efficiency of rat mammary tumor-derived BICR-M1RK-d cells in

semisolid agar medium was only slightly reduced when the pHewas shifted from the optimum range of 7.15 to 7.27 to a rangeof 6.7 to 7.0 (16).

ACKNOWLEDGMENTS

We thank Beate Rickert for skillful technical assistance and Raimund Jaapand Helga Rajewsky for preparation of the charts.

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7. Deutsch. C. J., Holian, A., Holian, S. K., Daniele, R. P., and Wilson, D. F.Transmembrane electrical and pH gradients across human erythrocytes andhuman peripheral lymphocytes. J. Cell. Physiol., 99. 79-93, 1979.

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APRIL 1982 1503



E. JÃ¤hdeet al.

BFig. 1. Construction of pH glass microelectrodes (for details, see "Materials and Methods" and Ref. 36). A, lead glass cone with tip broken off; B, insertion of pH

glass capillary into lead glass tube; C, fusion zone between lead glass and pH glass; D. complete microelectrode after closing of tip.




1982;42:1498-1504. Cancer Res Eckhard Jähde, Manfred F. Rajewsky and Horst Baumgärtl Tissues of BDIX Rats as Measured with pH MicroelectrodespH Distributions in Transplanted Neural Tumors and Normal

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