Dynamic response of breast tumor oxygenation to hyperoxic respiratory challenge monitored with three oxygen-sensitive parameters

Dynamic response of breast tumor oxygenation to
hyperoxic respiratory challenge monitored with
three oxygen-sensitive parameters
Yueqing Gu, Vincent A. Bourke, Jae G. Kim, Anca Constantinescu, Ralph P. Mason,and Hanli Liu The simultaneous measurement of three oxygen-sensitive parameters ͓arterial hemoglobin oxygen sat-uration ͑SaO ͒, tumor vascular-oxygenated hemoglobin concentration ͓͑HbO ͔͒, and tumor oxygen ten- sion ͑pO ͔͒ in response to hyperoxic respiratory challenge is demonstrated in rat breast tumors. The effects of two hyperoxic gases ͓oxygen and carbogen ͑5% CO and 95% O ͔͒ were compared, by use of two groups of Fisher rats with subcutaneous 13762NF breast tumors implanted in pedicles on the foreback.
Two different gas-inhalation sequences were compared, i.e., air– carbogen–air– oxygen–air and air–oxygen–air– carbogen–air.
The results demonstrate that both of the inhaled, hyperoxic gases signifi- cantly improved the tumor oxygen status.
All three parameters displayed similar dynamic response to hyperoxic gas interventions, but with different response times: the fastest for arterial SaO , followed by biphasic changes in tumor vascular ͓HbO ͔, and then delayed responses for pO . Both of the gases induced similar changes in vascular oxygenation and regional tissue pO in the rat tumors, and changes in ͓HbO ͔ and mean pO showed a linear correlation with large standard deviations, which presumably results from global versus local measurements.
Indeed, the pO data revealed heterogeneous regional response to hyperoxic interventions.
Although preliminary near-infrared measurements had been dem- onstrated previously in this model, the addition of the pO optical fiber probes provides a link between the noninvasive relative measurements of vascular phenomena based on endogenous reporter molecules,with the quantitative, albeit, invasive pO determinations.
170.1470, 170.3660, 170.4580, 120.3890, 120.1880, 230.2090.
Introduction
tify those patients who would benefit.
It is widely recognized that hypoxic regions in solid is growing emphasis on tailoring therapy to the indi- tumors may limit the efficacy of nonsurgical therapy, vidual characteristics of each patient’s tumor.
including radiotherapy, photodynamic therapy, and thermore, carbogen ͑5% CO and 95% O ͒ and oxygen have been used on experimental tumors in animals as have been tested, including simple strategies such as well as on clinical trials in patients for many analysis of some 10,000 patients showed only a mod- kinds of respiratory hyperoxic gases are diverse, de- est benefit, and this benefit was restricted to specific pending on the tumor types and individuals.11–13 Accordingly, accurate assessment of tumor oxygen- interventions was largely due to the inability to iden- ation at various stages of tumor growth and in re-sponse to interventions may provide a betterunderstanding of tumor development and may serve Y. Gu, J. G. Kim, and H. Liu ͑Hanli@uta.edu͒ are with the as a prognostic indicator for treatment outcome, po- Biomedical Engineering Program, The University of Texas at Ar- tentially allowing therapy to be tailored to individual nescu, and R. P. Mason are with the Department of Radiology, Various techniques have been developed to mea- University of Texas Southwestern Medical Center, Dallas, Texas sure oxygen tension ͑pO ͒ or vascular oxygenation of Received 8 September 2002; revised manuscript received 15 Jan- requiring biopsy preclude dynamic investigations.
Optical techniques based on light absorption of en- dogenous chromophores, e.g., near-infrared ͑NIR͒ APPLIED OPTICS ͞ Vol. 42, No. 16 ͞ 1 June 2003 spectroscopy of oxygenated and deoxygenated hemo-globin, are entirely noninvasive and allow real-timemonitoring of tumor vascular oxygenation.15–17However, NIR has limited spatial resolution, and itremains to be determined whether vascular oxygen-ation is related to therapeutic outcome.
quantitative pO has been shown to have prognostic value,18–21 but pO represents a balance between ox- explore the interplay of vascular and tissue oxygen-ation.
Electrodes have been used widely to study interventions,22–24 but they are generally limited to a Experimental setup for simultaneous oximetry.
single location and small probes can be fragile.
3-mm-diameter fiber bundles of the NIRS system deliver and de- have ourselves recently shown a correlation between tect the laser light through the tumor in transmittance geometry.
PMT represents a photomultiplier tube.
pO and ⌬HbO in some tumors, but we noted dis- quadrature phase demodulator for retrieving amplitude and phase tinct heterogeneity, and thus, the global NIR mea- The FOXY system comprises three fiber-optic surements were not always related to local pO .25 oxygen-sensing probes that are inserted into different regions of Multiple fiber-optic probes may be inserted into a The pulse oximeter probe is placed on the hind foot of tumor,26–28 and we have now investigated correlation between NIR measurements and multiple ͑three͒ si-multaneous pO measurements.
We now report simultaneous measurements of pression͒ in the middle parts of the tumors, providing three oxygen-related parameters, i.e., arterial hemo- optimal geometry to interrogate deep tumor tissue.
globin oxygen saturation, SaO ; tumor oxygenated Based on modified Beer–Lambert’s law,29 changes hemoglobin concentration, ͓HbO ͔; and tumor oxygen in oxygenated and deoxygenated hemoglobin concen- tension, pO , to assess dynamic responses of rat trations, ⌬͓HbO ͔ and ⌬͓Hb͔, due to respiratory in- vascular ͓HbO ͔ were measured by NIR spectroscopy amplitudes at the two wavelengths and calculated ͑NIRS͒ using a photon-migration, frequency-domain device; changes in regional pO were monitored by a fluorescence-quenched, oxygen-sensing, fiber-optic Ϫ10.63 logͩABͪ758 ϩ 14.97 logͩABͪ785 system ͑FOXY͒; the arterial SaO values were re- corded with a fiber-based, pulse oximeter.
Materials and Methods
Near-Infrared Spectroscopy System for Measurement 8.95 logͩABͪ758 Ϫ 6.73 logͩABͪ785 NIR light ͑700 to 900 nm͒ has considerable tissue penetration depth ͑several centimeters͒ and permitsin vivo sampling of large tissue volumes ͑e.g., human where A and A are the baseline and transient am- breast, brain, skeletal muscle, or tumors͒, since pho- plitudes measured from the NIR system, respective- ton transport in tissue is dominated by scattering ly; d is the source– detector separation; the unit for both ⌬͓HbO ͔ and ⌬͓Hb͔ is millimolar per differential by the oxygenated and the deoxygenated hemoglobin path-length factor ͑DPF͒; and the DPF is for tumor chromophores may be used to determine hemoglobin oxygenation and blood concentration changes.
normalization of ⌬͓HbO ͔ and ⌬͓Hb͔ to their maximal described in detail previously,16,25 a homodyne values can eliminate the effects of d and DPF on the frequency-domain system ͑NIM, Philadelphia, Penn- sylvania͒ was used to monitor the global changes inoxygenated and deoxygenated hemoglobin concentra- Fiber-Optic Oxygen-Sensing System for Measurement tions, ⌬͓HbO ͔ and ⌬͓Hb͔, respectively, in rat breast tumors in response to variations in inhaled gas.
Regional pO in tumors was monitored with a mul- Briefly, the light from two NIR laser diodes ͑758 nm tichannel, fiber-optic, oxygen-sensing system ͑FOXY, and 785 nm͒ was coupled into a bifurcated fiber bun- Ocean Optics, Inc., Dunedin, Florida͒.30 Three dle and illuminated on the tumor, and the transmit- fluorescence-quenched, optical fiber probes ͑AL300, ted light was collected and propagated to a tip diameter 410 ␮m͒ were inserted into different photomultiplier tube ͑Fig. 1͒. The fiber bundles regions of the tumors ͑Fig. 1͒. Probes were posi- were placed on the surface of the tumors in a trans- tioned so that at least one was in a poorly oxygenated mittance mode parallel to the body of the rat.
region ͑low baseline pO ͒ and at least one in a well- fiber tips touched firmly on the skin ͑without com- oxygenated region ͑high baseline pO ͒. If necessary, 1 June 2003 ͞ Vol. 42, No. 16 ͞ APPLIED OPTICS the probes were gently moved through the tumoruntil such diverse regions were located.
cases, the mean pO derived from the three individ- commercial system, few details have been publishedpreviously,31 and no applications to in vivo tumoroximetry have been published to our knowledge.
Light from a pulsed blue LED ͑475 nm͒ was coupledinto one branch of a bifurcated optical fiber bundleand propagated to the probe tip.
the probe is coated with a thin layer of a hydrophobicsolgel material, where an oxygen-sensing rutheniumcomplex is effectively trapped.
ruthenium complex causes fluorescence at ϳ600 nm.
Time profile of the three oxygen-sensitive parameters, i.e., If the excited ruthenium complex encounters an ox- the normalized changes of tumor ⌬͓HbO ͔, the mean changes of ygen molecule, the excess energy is transferred to the tumor ⌬pO , and the arterial SaO with respect to carbogen breathing in a representative 13762NF rat breast tumor ͑No. 1, 3.2 oxygen molecule in a nonradiative transition, de- creasing or quenching the fluorescence signal.
degree of quenching correlates with the oxygen con-centration, and hence, pO .
The fluorescence response of the ruthenium crystal three major orthogonal axes ͑a, b, c͒ were measured complex is highly temperature dependent, so to ac- with calipers and volume estimated with an ellipsoid complish probe calibration it was necessary to stream V ϭ ͑␲͞6͒͑abc͒.
gases of known oxygen concentrations ͑100%, 20.9%, Two groups of rats ͑n ϭ 7 in each group͒ were used 10%, 2%, and 0%͒ through a cylindrical water jacket to compare the effects of carbogen and oxygen on vascular oxygenation of breast tumors.
cally calculated by means of the vendor-supplied soft- ware, with the second-order, polynomial calibration: the reverse sequence of air– oxygen–air– carbogen– 0 ϭ 1 ϩ K ͓O͔ ϩ K ͓O͔2 tion, the FOXY pO probes were applied to five rats from Group 1, and the dynamics of the three oxygen- where, I is the fluorescence intensity at zero oxygen related parameters were measured simultaneously.
concentration ͑nitrogen͒, I is the measured intensityof fluorescence at a pressure of oxygen, ͓O͔ represents the oxygen concentration ͑related to pO ͒, K and K are the first- and the second-order coefficients and are Dynamic Responses of Three Oxygen-Related automatically supplied by the curve-fitting routine Typical time profiles of the normalized ⌬͓HbO ͔, mean ⌬pO , and SaO in response to carbogen inter- Pulse Oximeter for Measurement of Arterial S O vention are shown for a representative 13762NF Arterial SaO of the breast-tumor-bearing rats was breast tumor ͑No. 1, 3.2 cm3͒ in Fig. 2. When the also monitored with a fiber-optic pulse oximeter inspired gas was switched from air to carbogen, the ͑Nonin Medical, Inc., Plymouth, Minnesota͒ placed readings increased rapidly and significantly from the baseline value of 85% to the maximum of two optical fibers used for delivering and receiving 100% within 2.5 minutes ͑ p Ͻ 0.0001͒. The normal- The tips were placed on either side of the ized ⌬͓HbO ͔ showed a sharp initial rise in the first minute ͑ p Ͻ 0.0001͒ followed by a slower, gradual,but further significant increase over the next 19 min ͑p Ͻ 0.001͒. Mean ⌬pO increased rapidly by ap- Mammary adenocarcinomas 13762NF ͑originally ob- proximately 50 Torr within 8 min ͑ p Ͻ 0.0005͒ and tained from the Division of Cancer Therapeutics, also continued a slower and gradual increase over the NIH, Bethesda, Maryland͒ were implanted in skin next 12 min ͑ p Ͻ 0.005͒. Return to breathing air pedicles32 on the foreback of adult female Fisher 344 produced a significant decline for all three signals rats ͑ϳ150 g͒. Once the tumors reached 1–2 cm di- ameter, rats were anesthetized with 150-␮l ketamine SaO and pO displayed a single-phase dynamic hydrochloride ͑100 mg͞ml, i.p.͒ and maintained un- behavior in response to carbogen intervention, der general gaseous anesthesia with 1.3% isoflurane whereas ⌬͓HbO ͔ showed an apparent biphasic re- in air ͑1 dm3͞min͒. Body temperature was main- tained at 37 °C by a warm water blanket.
time constants of a single-exponential response.
were shaved to improve optical contact for transmit- the tumor in Fig. 3, SaO had the fastest response, with a time constant of ␶͑SaO ͒ ϭ 1.1 Ϯ 0.2 min ͑R ϭ APPLIED OPTICS ͞ Vol. 42, No. 16 ͞ 1 June 2003 able ͑ϳ14 Ϯ 11 min͒. No significant correlationswere found between any of the time constants inTable 1.
Time delay, t , between the time when the gas intervention was initiated and the time when thechanges in signals were detected, reveals anotherdifference among the three oxygen-sensitive param-eters.
For tumor 1 ͑Fig. 2͒, the SaO signal was the first to respond to the intervention.
⌬͓HbO ͔ was observed 30 s later with t ϭ 30 s, followed by changes in ⌬pO another 30 s later ͑t ϭ 60 s͒. Similarly, when the gas was returned fromcarbogen to air, the SaO signal decreased immedi- ately, followed by declines in ⌬͓HbO ͔ and in ⌬pO with t of 30 and 120 s later, respectively.
pected, changes in SaO always preceded ⌬HbO , and Dynamic responses of the three oxygen-sensitive param- eters to carbogen intervention in a rat breast tumor ͑No. 1, 3.2cm3͒. Single-exponential Comparison of the Effects of Carbogen and Oxygen 0.204͕1 Ϫ exp͓Ϫ͑t Ϫ 20.02͒͞1.1͔͖ ϩ 0.85 ͑R ϭ 0.93͒, ⌬͓HbO ͔ ϭ 0.655͕1 Ϫ exp͓Ϫ͑t Ϫ 20.36͒͞2.59͔͖ ϩ 0.125 ͑R ϭ 0.89͒, and Switching from air breathing to carbogen or oxygen ⌬pO ϭ 42.68͕1 Ϫ exp͓Ϫ͑t Ϫ 21.01͒͞4.56͔͖ ϩ 16.66 ͑R ϭ 0.98͒; biexponential fitting resulted in ⌬͓HbO ͔ ϭ 0.373͕1 Ϫ exp͓Ϫ͑t Ϫ 20.36͒͞0.61͔͖ ϩ 0.648͕1 Ϫ exp͓Ϫ͑t Ϫ 20.36͒͞21͔͖ ͑R ϭ 0.97͒.
However, the time course was substantially different,requiring a biphasic exponential fit for carbogen, buta single exponential for oxygen ͓Fig. 4͑b͔͒. For the 0.93͒, followed by ͓HbO ͔ with ␶͑⌬͓HbO ͔͒ ϭ 2.59 Ϯ seven tumors in Group 1, there was no significant 0.06 min ͑R ϭ 0.89͒, whereas ⌬pO yielded the slow- difference ͑ p Ͼ 0.3͒ in the maximum magnitude of est response ␶͑⌬pO ͒ ϭ 4.56 Ϯ 0.06 min ͑R ϭ 0.98͒.
⌬͓HbO ͔ caused by carbogen or oxygen interventions Time constants for Group 1 are listed in Table 1.
every case ␶͑SaO ͒ Ͻ ␶͑⌬͓HbO ͔͒ Ͻ ␶͑⌬pO ͒, based on To examine the possible effect of preconditioning required that Group 2 experience a reversed gas in- between the time constant and the tumor volume was tervention, with exposure to oxygen prior to carbogen ͓Fig. 5͑a͔͒. In this case, the time constants of the It is clear that the response of ⌬HbO is not well normalized tumor vascular ⌬͓HbO ͔ were now simi- represented by a single exponential, and thus, a double-exponential expression with two time con- tumors, carbogen no longer induced the biphasic be- stants, ␶ and ␶ , was also used ͑Fig. 3͒. Comparison between the biexponential fitting for ⌬͓HbO ͔ and the single-exponential results for both SaO and ⌬pO in again, the two gases did not produce significantly the first five rat tumors ͑Table 1͒ shows that the time constants of SaO ͑ϳ1.2 Ϯ 0.4 min͒ are similar to sized for both Groups 1 and 2 by a strong linear those of the first phase of ⌬͓HbO ͔ ͑ϳ0.5 Ϯ 0.2 min͒, correlation ͑slope Х 1.16͒ between the ⌬͓HbO ͔ whereas the second phase is longer and highly vari- values observed in response to each of the two con- Time Constants of SaO , ⌬͓HbO ͔, and ⌬pO Response to Carbogen and Oxygen Intervention in the Breast Tumorsa
Single-Exponential Fitting of SaO , ⌬͓HbO ͔ and ⌬pO Double-Exponential Fitting for Single-Exponential aUnder the inhalation sequence of air– carbogen–air– oxygen–air.
bnd, not determined.
1 June 2003 ͞ Vol. 42, No. 16 ͞ APPLIED OPTICS ͑a͒ Dynamic changes in tumor vascular ⌬͓HbO ͔ for a representative 13762NF breast tumor from Group 2 ͑No. 9, 2.6cm3͒ with gas-inhalation sequence reversed compared with Group1.
͑b͒ Average maximum values of normalized ⌬͓HbO ͔ for Group Gas-inhalation sequence reversed compared with Group 1.
͑a͒ Time course of changes in tumor vascular ⌬͓HbO ͔ for ͑c͒ Correlation between maximum ⌬͓HbO ͔ achieved with carbo- a representative 13762NF breast tumor from Group 1 ͑No. 2, 3.0 gen inhalation versus that with oxygen ͑R ϭ 0.97͒: }, carbogen cm3͒ with respect to altering inhaled gas. ͑b͒ Respective curve fits for the carbogen and oxygen interventions.
values of normalized ⌬͓HbO ͔ for the seven breast tumors in Group apparently well-oxygenated regions usually showed alarge and rapid response, whereas those with lower secutive interventions ͓Fig. 5͑c͔͒. In this case, non- baseline pO often showed little change ͓Fig. 6͑a͔͒.
normalized data are shown for specific comparison of The pO responses to the two interventions showed a highly consistent behavior at each individual location ͓Fig. 6͑b͔͒. There was also a distinct correlation be-tween the global NIR measurements and the mean ⌬pO ͑Fig. 7͒. Because of heterogeneity in regional The FOXY pO probes generally indicated distinct pO , the standard deviations of the mean pO values APPLIED OPTICS ͞ Vol. 42, No. 16 ͞ 1 June 2003 dynamic tendency in response to carbogen interven-tion ͑Fig. 2͒.
The simultaneous measurements demonstrate the compatibility of the NIRS system with the FOXYfiber-optic oxygen-sensing system, without interfer-ence.
Both systems are relatively inexpensive and provide real-time measurements, but the multichan-nel FOXY fiber-optic system monitors ⌬pO in spe- cific locations, whereas the NIRS system providesglobal measurements.
with this methodology will be a clinically useful pre-dictor for tumor response to oxygen-dependent inter-ventions and therapies remains to be determined.
However, it is established that measurements of pO2have prognostic value in the clinic18,20 so that corre-lations between pO and NIR measurements would We have previously applied a polarographic oxygen that study provided only a single local pO value, and in some cases correlations with global NIR measure-ments were very poor.
here allows multiple locations to be interrogated si-multaneously.
channels, but our system uses four channels.
fortunately, probes are fragile, and the oxygen-sensitive coating on the tips is readily damaged.
Thus, we only had three probes available for this ͑a͒ Time profiles of tumor ⌬pO , measured with the three Indeed, fiber-optic probe fragility is a well- channels of the FOXY fiber-optic, oxygen-sensing system with re- recognized problem, and our previous experience spect to different gas inhalations for breast tumor No. 3 ͑4.6 cm3͒.
The mean signal for the three channels was calculated and is with the more expensive OxyLite system was also restricted to three channels owing to probe damage.26 individual locations in the tumors in response to carbogen or oxy- The FOXY system ͑ϳ$13k͒ is much less expensive gen for the five tumors in Group 1 ͑R Ͼ 0.8͒.
than the OxyLite ͑ϳ$48k͒, and its mode of action isalso simpler, detecting fluorescent signal intensityrather than fluorescence lifetime.
Discussion
of measuring pO across the whole range of atmo- In this study, we have simultaneously measured the spheric oxygen tensions ͑0 –760 Torr͒, whereas the arterial SaO , the global changes in the ⌬͓HbO ͔ of OxyLite is restricted and becomes very insensitive tumor vasculature, and the regional changes in the ⌬pO of tumor tissue, in response to hyperoxic ͑i.e., rience shows that although the FOXY system pro- carbogen and oxygen͒ gas interventions with a pulse vides precise measurements of ⌬pO , absolute values oximeter, an NIRS system and a multichannel, fiber- three oxygen-sensitive indicators displayed similar system seems to give very accurate pO values.
Our experience shows that the FOXY probes are much easier to use than electrodes, particularly, interms of calibration and stability.
are fragile, we insert them into tumors through a fineneedle ͑25 gauge͒, which readily punctures the sur-rounding skin and penetrates tough fibrous tissues.
The needle is then backed up from the tip to facilitatemeasurements.
utes to settle at a stable baseline value, but then showgood baseline stability and rapid response to inter-ventions ͓Figs. 2 and 6͑a͔͒. They are easily movedwithin the tumor to locate regions, presenting a par-ticular pO of interest, e.g. hypoxic or well oxygen- In the search for appropriate locations, probes are moved forward to interrogate fresh tissues rather Correlation between mean ⌬pO and ⌬͓HbO ͔ for the five breast tumors ͑R Ͼ 0.86͒: }, transition from air to carbogen; ‚, than in reverse, since blood may pool in the tracks 1 June 2003 ͞ Vol. 42, No. 16 ͞ APPLIED OPTICS minimal bleeding on removal of the probes from the rial SaO to increase, as a result of the immediate combination of deoxyhemoglobin with oxygen.
We have found no interference between the NIR highly oxygenated blood circulated in the systemic and FOXY instruments, although any tumor motion vasculature of the rats ͑including the capillary bed of associated with moving the fiber probes can alter the the tumor tissue͒, resulting in a delayed increase in optical contact of the NIR optrodes, and thus, alter ͓HbO ͔ in the tumor vasculature, and led to an un- apparent ⌬HbO . Thus, baseline ⌬HbO is deter- loading of oxygen to the tumor tissue.
mined once the fiber probes are situated.
ponential model of ⌬͓HbO ͔, the fast component has optic probes of the FOXY system have a thick coating a similar time constant to the SaO measured with of fluorescent gel and a black covering, but this wears the pulse oximeter on the hind leg, strongly suggest- with use and gradually allows reception of the NIR ing that it represents arteriolar oxygenation in the Since the LEDs of the two systems operate at very different wavelengths, viz. 475 versus 760 nm, any direct relation with time constants or changes of there is no interference for detection.
amplitude in response to hyperoxic gas interventions.
of local NIR light by the FOXY probe opens the ex- It is increasingly evident that oxygen and hypoxia citing possibility of detecting regional hemoglobin ox- play important roles in tumor development and re- probes could be moved within the tumor to map the invasive means of investigating tumor oxygenation, distribution and path of the transmitted NIR light, particularly in terms of dynamic response to inter- helping to explore and validate the optical character- ventions, but we had previously shown a potential mismatch between global ⌬HbO and local ⌬pO .25 a correlation between local ⌬HbO and ⌬pO .
The data presented here indicate a correlation be- In this study, we have examined a much larger tween the global NIR measurements and mean pO2 values with even as few as three representative loca- shown rigorously that the two hyperoxic gases induce similar changes in vascular oxygenation ͑NIR͒ and important to develop regional NIR measurements regional tissue pO ͑FOXY͒ in this type of rat breast and that even relatively crude mapping could reveal These data are consistent with our previous observations using 19F NMR imaging ͑FREDOM͒33 in studies provide further evidence for the value of this tumor type and also in rat prostate tumors.34,35 If the two gases are indeed equivalent in terms ofmanipulation of tumor oxygenation, it could have This study was supported in part by the Depart- great therapeutic benefit since the popular carbogen, ment of Defense Breast Cancer Research grants which is in use in clinical trials,36 can cause respira- BC000833 ͑YG͒ and BC990287 ͑HL͒, and NIH RO1 CA79515 ͑RPM͒ and RO1 supplement CA79515-S The current data show that ⌬HbO and ⌬pO are ͑VB͒. We are grateful to Mengna Xia and Dawen correlated ͑Fig. 7͒, and thus, such noninvasive obser- Zhao for their assistance with data processing.
vations could have value in the clinic.
gratefully acknowledge Weina Cui for helpful discus- deficiency in our current NIR approach is lack of spatial discrimination, and thus efforts to implementNIR imaging will be of great value.
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1 June 2003 ͞ Vol. 42, No. 16 ͞ APPLIED OPTICS

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