Intrumentation for fast functional optical tomography

REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 73, NUMBER 2 FEBRUARY 2002

Instrumentation for fast functional optical tomographyChristoph H. Schmitz, Mario Locker,a) Joseph M. Lasker,b) Andreas H. Hielscher,b),c)

and Randall L. Barbourc),d)

Department of Pathology, SUNY Downstate Medical Center, Box 25, 450 Clarkson Avenue, Brooklyn,New York 11203

~Received 24 May 2001; accepted for publication 7 October 2001!

In this article, we describe the design rationale and performance features of an integratedmultichannel continuous wave~cw! near-infrared~NIR! optical tomographic imager capable ofcollecting fast tomographic measurements over a large dynamic range. Fast data collection~;70Hz/channel/wavelength! is achieved using time multiplexed source illumination~up to 25illumination sites! combined with frequency encoded wavelength discrimination~up tofour-wavelength capability! and parallel detection~32 detectors!. The described system features acomputerized user interface that allows for automated system operation and is compatible withvarious previously described measuring heads. The results presented show that the system exhibitsa linear response over the full dynamic measuring range~180 dB!, and has excellent noise~;10 pWnoise equivalent power! and stability performance~,1% over 30 min!. Recovered images oflaboratory vessels show that dynamic behavior can be accurately defined and spatially localized.© 2002 American Institute of Physics.@DOI: 10.1063/1.1427768#

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I. INTRODUCTION

In recent years, diffuse optical tomography has becomviable new biomedical imaging modality. The appeal of thmethod lies in the use of nonionizing radiation, the abilityprobe functional states of tissue, and the use of economand compact instrumentation. The technique typically eploys laser diodes that deliver light through optical fibersseveral locations on the tissue surface, and measuremenback-reflected and transmitted light intensities are recorand analyzed. Tomographic reconstruction algorithms pvide the spatial distribution of optical properties or changof these properties for the site under investigation. A numof studies have shown that the resulting parameter mapsbe used to detect breast cancer,1,2 brain activity,3–5 and otherclinically relevant findings.6–8

Several groups have developed instrumentation for ocal tomography over the last eight years. Depending ontemporal characteristics of the illumination source, instmentation can be categorized into systems that use ultraslaser pulses~time-domain measurements!, rf-modulated lightsources ~frequency-domain measurements!, or low-frequency~dc to;kHz! modulated light sources~continuouswave ~cw! measurements!. Examples of time-resolved instrumentation have been described by Ntziachristoset al.9

and Schmidt et al.10 Frequency-domain instrumentatiohas been developed by Pogue,2 Jiang,11 and groups led

a!Also at: Physikalisches Institut der Universita¨t Bonn, Nussallee 12,D-53115 Bonn, Germany.

b!Present address: Depts. of Biomedical Engineering and Radiology, Cobia University, 1010 CEPSR Bldg., MC8904, 530 West 120th St., NYork, NY 10027.

c!Also at: Department of Electric and Computer Engineering, 6 MetrotCenter, Polytechnic University, Brooklyn, New York 11201.

d!Author to whom all correspondence should be addressed; [email protected]

4290034-6748/2002/73(2)/429/11/$19.00

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by Sevick-Muraca12 and Gratton.13 Among others, Siegeet al.,14 Zhao et al.,15 Yamashitaet al.,16 and our group17,18

have focused on the development of high fidelity cw instmentation.

The advantages and disadvantages of these variousproaches have been discussed in detail elsewhere.19 Whiletime-resolved and frequency-domain methods can provdata having richer information content, we neverthelessvor cw measurements in recognition of advantages thatrelated to cost/performance issues. These include the easwhich fast parallel measurements can be accomplished wretaining a large dynamic range. Recently, we have empsized that such capabilities, adapted to imaging studieslow for the investigation of an entirely new class of informtion about tissue function—that associated with the natuspatial and temporal heterogeneity of the vascular respoin large tissue structures.20

In this article, we build on our previous work towarddeveloping instrumentation well suited for dynamic imaginIn particular, we expand on a design concept that emplsilicon photodiodes as optical detectors,18 which overcomesthe limitations of a charge coupled device based imagerscribed earlier.17 Advantages include eliminating sensitivitto ambient light, fast source switching, and simultaneomultiwavelength measurements. Here, we describe theformance features of a fully integrated measuring systempreliminary report of this has recently been given.21

II. INSTRUMENT DESIGN

The system developed is based on a design that provfor fast parallel data capture with a large dynamic rangeemploys dc illumination.18 Guiding our approach has beethe goal of engineering a unit that provides for automa

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430 Rev. Sci. Instrum., Vol. 73, No. 2, February 2002 Schmitz et al.

instrument setup and control as well as to introduce permance features that facilitate the development and evaluaof experimental protocols focused on the measuremenevoked vascular responses.21 This includes the integration osystem software that allows for online viewing of collectdata within various formats as well as the online reconstrtion and display of image parameter maps. Here, we resour focus to presenting the results that define the syshardware performance. Descriptions of our algorithmsimage formation and other features related to system futionality are described elsewhere.22

Figure 1 shows a block diagram of the instrument whodesign rationale was previously described18 but not reducedto practice within an integrated system. The system coulight from two ~or more! laser diodes~1! operating in the 800nm range into one of multiple source fiber bundles~2!. Sev-eral options are available to render the incident beamslinear. For convenience, we simply use a nonpolarized besplitter ~3!. Fast switching between source fiber bundlesmade possible by means of an optical demultiplexer~D-MUX, 4!.

This unit, to be described more fully, employs a brusless dc servomotor to provide for fast, precise source bepositioning. The motor is driven by a controller~5! contain-ing a freely programmable microprocessor. Each source fibundle ~1-mm-diam., 2! forms one branch of a bifurcatefiber bundle~6! and joins the other branch~3-mm-diam., 7!,which is used for light collection on the target surface~8!.These are housed within one of several measuring head~9!that have the property of establishing stable optical contwith tissues of various size and shapes.18 Each of the detec-tor fiber bundles terminates at one silicon photodiode msuring sensor of a multichannel detection unit~10!. The out-put voltages of the detector channels are measured by mof a data acquisition~DAQ! board~11! and stored on a personal computer~PC, 4!. For the purpose of lock-in detectionthe laser diodes are current modulated in the 5–10 kHz raby the laser controller~14!, and digital phase shifters~15! areused to optimize the phase angle between the measuredreference signals.

FIG. 1. Block diagram of the instrument setup. LDD: laser diode driveTECD: thermo-electric cooling drivers,f 1 andf 2: diode current modulationfrequencies, LD1 and LD2: laser diodes, D-MUX: optical demultiplexwith servomotor, DPS1 and DPS2: digital phaseshifters.


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A. Light source

We use high-power laser diodes~LD!, with integratedthermo-electric cooling~TEC!, that are optically coupled tothe D-MUX by means of a pigtailed fiber to which is atached a gradient index lens that serves to produce a subtially collimated beam. The laser diodes~high power devices1110-BUTF-TEC! operate in the 800 nm region and havemaximum optical output power of 400 mW at the distal eof the fiber. These are typically operated at a mean optoutput power of 100 mW; the optical power incident on ttarget is about 30 mW. The lasers are operated by a Newmodel 8000 laser controller mainframe housing up to focombined LD/TEC driver modules~model 8630!, each serv-ing one laser. Each module provides sinusoidal modulaof the LD current with individually selectable frequency anamplitude. The modules also generate reference signatransistor–transistor logic~TTL! level, which are supplied bycoaxial BNC connectors on the real panel of the unit.

Figure 2 shows a detailed view of the D-MUX. The unhouses a brushless dc servomotor that moves a gold-surfmirror, mounted 45° to its shaft, in a start–stop fashion. Iessential that the mirror make a complete stop for a sh

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FIG. 2. Photograph of the optical D-MUX.~a! Complete view of the unit~height;15 in.! with optical fibers attached to it.~b! Detailed view of therotating mirror with the in-coupling optics removed.


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431Rev. Sci. Instrum., Vol. 73, No. 2, February 2002 Fast optical tomography

time ~;10 ms! in order to minimize degradation of the precision of the system due to variations in light intensity durithe detection process. The selected motor~Pacific Scientificmodel R23GENA-RS-NS-01! and accompanying microprocessor control unit~Pacific Scientific model SC902AN-00101! allow for the flexible implementation of the customizemotion control protocols. This unit is capable of performi;75, 14° start–stop motions per second without noticeaovershooting or ringing. The D-MUX unit currently in ushouses up to 25 source fiber bundles that are availabletarget illumination. The software-programmable motor cotroller allows absolute indexing of the motor position aeasy implementation of complex motion protocols. Thislows for user selection of the number, timing, and ordersource fibers used for target illumination. Because the mmum switching speed between two source positions haupper limit, increasing the number of sources will reduceimage-framing rate. For example, with 17 source positioand a 50 Hz switching rate,;3 full tomographic data setper second can be acquired. As described in a recent artic18

we have chosen to implement a time-multiplexing scheinstead of a previously described frequency-multiplexscheme14 in order to maximize the dynamic measurinrange. This serves to enhance the view over which lastructures can be examined.

B. Measuring heads

One of the instrumentation challenges of optical tomoraphy as a medical imaging modality is interfacing the apratus with the tissue under investigation. Because the insity of light exiting the tissue falls exponentially witdistance from the source, a tomographic measurement orequires the detection of faint signals. In order to maximthe signal-to-noise ratio, mostly contact-based measments, usually using optical fibers, are employed. Thismediately presents a challenge of how to accomplishgiven the contradictory demands between the variableand geometry of human anatomy and the need for a flexyet mechanically stable interface. Our approach has beeprovide different interchangeable measuring heads for difent basic geometries. The rationale and design of sevavailable devices—including an iris-like structure, wesuited for imaging structures of circular cross section sucha limb, a flexible pad for planar sites, and a folding hemsphere for breast imaging—have been described in dearlier.18 We have recently added a wristband-like interfafor limb imaging and a helmet device suited for transcraninvestigations. Common to all of these devices is their abito adapt to various target sizes while providing stable optcontact.

Our experience with these has been that by adjustheir fit to provide for modest contact pressure together whaving the fiber ends protrude from the measuring head;1–2 mm, stable and reliable contact throughout the msurement is maintained. This is evidenced by the absencany sudden changes in detector responses as one mighpect would occur should unstable contact be present, anthe depressions in the skin that are seen upon removal o


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device. We recognize consideration of the homogeneityoptical coupling to tissue can having significant implicatiofor how the acquired data should be evaluated. It is for treason that we employ reconstruction methods that evala relative change in detector responses, rather than assuabsolute calibrations can be reliably obtained. In this fasheach channel is referenced to itself, thereby renderingimaging schemes insensitive to possible differences in cpling efficiencies among the fibers.

C. Detection

Figure 3 shows a block diagram of one detector chanWe have selected a silicon photodiode~SiPD! as the photo-sensor because of its excellent linearity~better than 1:1010!,high sensitivity ~noise equivalent power 56.5310215 W Hz21/2!, and ease of operation. The rationale adesign of the detection electronics have been recentlyscribed in detail in a report by Schmitzet al.18 Motivatingour approach was the need to achieve fast detection ovlarge dynamic range, coupled with fast source switchiThis is achieved by synchronizing adjustment of the detecsensitivity for all channels with source movement, thereachieving on-the-fly adaptive gain control.

Briefly, the signal amplification scheme used convethe photocurrent generated by the incident light to a voltaby means of a programmable transimpedance ampl~PGIA! whose transimpedance value~gain!, and hence pho-tosensitivity, can be changed by a factor of 1000. Subquently, a programmable gain amplifier~PGA! can be set toeither a gain of unity or an additional factor of one thousaFollowing appropriate amplification, the signal is fed to oor more lock-in amplifiers@~LIAs!, two are shown# to re-move dc offsets, signals from ambient light, and electronoise. By modulating the lasers at distinct frequencies,ferent wavelengths of light, simultaneously measured, candistinguished.

Sample-and-hold circuits~S/H! are used to permit parallel data capture and to facilitate system timing. A secoPGA located prior to each S/H circuit allows for adjustinthe level of the demodulated~dc! signal, thereby improvingnoise immunity when transmitting analog signals to the dacquisition board. This also serves to effectively increaseusable dynamic range of the analog-to-digital conversion

FIG. 3. Block diagram of detector channel. SiPD: silicon photodiode, PTprogrammable transimpedance amplifier, PGA: programmable gain amfier, Ref. f1, Ref. f2: Reference signals, S/H: sample-and-hold, Outl1 andOut l2: Output signals for different wavelengths; Gain~TTL!, S/H ~TTL!:Digital control signals.


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The amplified signal is then transmitted to a 64-chandata acquisition board~National Instruments model PCI6033E! allowing the simultaneous readout of 32 detecchannels at two wavelengths. This board also provides eprogrammable digital input/output~I/O! ports, which areused for system control and timing~see Sec. I D 2!. Theboard is fully compatible with National InstrumentLABVIEW ™ software, which was used to create an interactgraphical control interface for the instrument.

It is worth noting that the design approach of gaswitching, coupled with use of multiple simultaneous illumnating sources, assumes that the measured signal intenfor any one source-detector pair are largely independwithin an order of magnitude, of the illuminating wavelengths used. We also note that whereas this holds for tisstudies in the near-infrared~NIR! wavelength region, it maynot be suitable in cases where the target optical propeexhibit strong wavelength dependence. In such cases, alected gain setting suitable for one illuminating wavelengmay either saturate or insufficiently amplify a measured snal.

Figure 4 shows a schematic of the multichannel dettion unit. Panel A illustrates a front view, and panel B shoan exploded rear view absent the external chassis. The de

FIG. 4. Panel A. Schematic of the detection unit with detector channPanel B. Rear exploded view of detection unit without external chassis~2!LIM 1, LIM 2: lock-in amplifier modules,~4! supply voltage line,~5! ref-erence signal,~6! read-out lines,~7! gain control lines, DPS1 and DPS2digital phase shifters, DAQ: data acquisition board, and FIFO: first-in-fiout.


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is capable of measuring up to 32 channels in parallel. Edetector channel card~1! can be equipped with either one otwo lock-in amplifier modules~2!, each carrying two LIAs.This allows for the simultaneous measurement of as manfour different light sources. Each detector channel is cnected to a backplane~3!, which provides supply voltage~4!, reference signals~5!, read-out lines~6!, and gain controlsignals ~7!. Depending on the number of modulation frquencies used, up to two phase shifter cards~8! can be in-serted, each containing two digital phase shifters. The detion unit also contains an interface board~9! that serves toconnect analog and digital ports from other hardware usethe instrument~DAQ board, power supply, and motor controller!. The detection unit also contains a system timiboard ~10! that serves to store predetermined gain settiand establishes two-way communication with the motor ctroller unit.

D. System timing

1. Timing scheme

Precise instrument timing is crucial for the applicatiowe seek to pursue, because many different system tasksto be scheduled in a way that allows for maximum imaframing rates without sacrificing measurement precisiFigure 5 shows schematically how the different system taproceed in time as the sources are switched. Tasks thatto be scheduled are: servomotor positioning, parallel muchannel light detection, and data capture.

Optical signal detection is performed for all detectorsparallel, to maximize the achievable frame rate. The detion process for an individual detector channel is compoof three subtasks: setting the detector to the appropriate gallowing the lock-in amplifier to settle, and triggering thS/H circuit. Adjusting the gain setting for each detector wrespect to each source position is crucial because thisvides the dynamic measurement range that is necessaallow for high-quality signals when probing large tissustructures. Switching of these is achieved in a time welllow 1 ms.

A measurement cycle begins by initiating the motmovement to the next stop~source! position and setting thedetectors to the appropriate gain for that source positAfter the mirror has stopped at its new position, the actmeasuring process, i.e., the settling of the LIAs, takes pla

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FIG. 5. System timing diagram.


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The choice of a settling time~or detection bandwidth! for aLIA is always a tradeoff between instrument response~ide-ally immediate, i.e., fast-settling LIA! and the signal-to-noiseratio @~SNR!, which should be large, i.e., slowly settlinLIA #. The consequences of this tradeoff for our applicathave been discussed in detail,18 and have led to a LIA designwith a settling time of 6–7 ms. After this amount of time helapsed, the S/H circuit is triggered, thereby freezing thenal level. This is followed by allowing the motor to proceeto the next position, while the detector channels are simuneously read out by the data acquisition board. Dependinthe number of detector channels/wavelengths used, thisrequire up to;1 ms to complete. The entire cycle is repeataccording to a preselected number of acquisition time poiat a rate on the order of 75 Hz.

2. Hardware implementation

The main timing challenge in our system is the fastmultaneous switching of gain settings for all detector chnels synchronously with the motor movement and dataquisition. We adopted two principal strategies to achieve tFirst, we have chosen to use the motor controller as the cfor the timing of the system tasks. In this manner, we avburdening the host PC, which—as a Microsoft Windowbased system—is not well suited for real-time applicatioThe motor controller contains several freely programmadigital I/O lines that allow synchronized communicationthe motion protocol with the external hardware. Secondwe predetermine the gain settings for all source-detepairs prior to a measurement~see Sec. II D! and store themtemporarily in volatile memory located within the detectiounit. Every detector channel requires four bits to determits gain setting, leading to a total of 128 bits for a 32-chanmodule. Transmitting this information directly from the hoPC to the detection module ‘‘on the fly,’’ i.e., synchronouswith the switching of source positions, would pose a notrivial hardware-timing problem.

Instead, we use a combination of digital shift registeand first-in-first-out~FIFO! memory to transmit the gain setings, as determined from an initial measurement, to thetection hardware and store them temporarily~see Fig. 6!. Theshift registers allow the streaming of information at a moerate speed over a single serial line. This avoids the needa complex handshaking scheme should the suggestedon-the-fly protocol be attempted. The parallel outputs ofshift registers are connected to the data inputs of 8-bit-w

FIG. 6. Use of shift registers and FIFO memory for transmitting and stogain settings for each source-detector pair.


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FIFO buffers, which store groups of eight bits, each encing the gain setting of two detector channels for one souposition. Thus, the bit combinations encoding the gainssuccessive source positions are ‘‘stacked’’ in the order tthey are demanded during the measurement. The uniqueture of a FIFO buffer~as opposed to a random accememory or a last-in-first-out memory! is the ability to re-trieve the stored information in the order it has been stoby applying a digital impulse to the device. The FIFO daoutputs are connected to the detector channels. Aftersource positions have been cycled through, a digital impunotifies the memory chip to restart, repeating the sequeIn this fashion, the FIFO memory acts as a circular buffthereby avoiding the need to store gain settings for each tpoint of the measurement sequence. Because the Fmemory does not require explicit data addressing, the timfor this scheme is very simple and efficient.

The hardware communication layout is shown as a blodiagram in Fig. 7. The program for the motion control prtocol is downloaded from the PC to the motor controllwhich then waits idly until one of its control inputs is addressed by one of the digital I/O lines provided by the mtifunction DAQ board. These I/O lines are also used to tramit the gain settings for each source-detector combinatiothe timing board, where they are stored in FIFO buffers prto measurement.

The measurement is started by initiating a digital inpsignal from the DAQ board to the motor controller, whicthen executes the motion program for as long as the inremains in the activated state. The motor controller startsmirror movement and then sends out a digital pulse that tgers the FIFO buffers, thereby advancing the gain settinAfter the mirror has reached the desired source position,motion control program allows the appropriate time for tLIAs to settle~;7 ms! and then triggers the S/H circuit anthe data acquisition.

E. Instrument control

All instrument control is accomplished through a grapcal user interface created withLABVIEW ™ software. An im-portant and potentially tedious task, should it be impmented using manual methods, is the determination ofappropriate gain settings for all source-detector combi

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tions. Which gain settings are appropriate depends onparticulars of the target. To facilitate this procedure, we himplemented an automated routine that, starting fromlowest gain setting for all detector channels, acquires a msurement, and determines whether the signal level is abopreselected threshold. Typically, we choose a value of 0.to ensure good noise performance. In cases where the slevels fall below this threshold, the gain setting is automacally increased to the next level and the threshold criteriagain tested. This is repeated until all measuring channelall source locations meet the indicated threshold or until treach the maximum gain setting. We have tested the fideof this scheme and found that it can correctly and reprodibly identify the appropriate gain settings, even on relativdense media such as living tissue, and bring the signal lefor each detector to within a desirable measurement ra~typically 0.3–5.0 V!. The interface also allows the choosinof gain settings manually. This functionality can be usedachieve specific gain settings or to check and overwriteresults from the automated setup. Gain settings can be stto a file and reloaded as desired.

The LABVIEW ™ interface furthermore allows the reatime display of the detector data in the form of a coloencoded two-dimensional~2D! map that evolves in time athe measurement proceeds. The screen allows interactivjustment of the chart axes and data scrolling. This featureproven extremely useful in the development and evaluaof investigation protocols.

A variety of versions of the instrument control interfaand the motor program~see Sec. II D 2! are available de-pending on the number of sources and detectors usedparticular application. One special operation mode of thestrument allows one to keep the source at a predetermfixed position while performing the parallel readout of allthe detector channels at a very high rate. This allows stuing fast phenomena near one source position. Currently,Hz acquisition rate is achieved in this mode. The theoretspeed limit of about 150 Hz is determined by the settltime of the detector channels.

F. Calibration

In a recent report,18 we have described a calibration prtocol that provides estimates of the relative efficiency of otical coupling between a target medium and each ofsources and detectors. These estimates are obtained froanalysis of the discrepancy between measured and anpated responses of a homogeneous medium having regeometry. The procedure described determines the mannwhich failure to observe the expected symmetries in thetector readings can be attributed to differences in efficieamong the various measuring channels. The accountinthese differences allows for the comparison of signal intsities among the various measuring channels. Whereasinformation is useful for certain computations, we wishemphasize that such calibration is not always necessarreconstruct dynamic behavior in the optical coefficients.fact, the results shown here, and elsewhere, were achiwithout performing any calibration. This is possible becau


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the data vectors used for image recovery consider onlychange in response relative to a defined state~usually thetemporal mean value!. Thus, each detector is compareditself, thereby avoiding the need to consider interdeteccomparisons.

III. INSTRUMENT PERFORMANCE

A. System specification

Table I summarizes the most important performancharacteristics of the instrument. The detector sensitivitydefined by the noise equivalent power~NEP! as determinedfrom dark noise measurements. The dynamic range ofinstrument is defined by the ratio between the NEP andsignal saturation limit. Precision and long-term stability stuies have been conducted and are discussed in detail nex

Because of the large dynamic range of measuremoptical cross talk between detector channels can be imtant. This can occur because of light leakage withinD-MUX assembly, at the measuring head, and/or withindetection unit itself. To test for leakage within the D-MUXwe compared the measured intensities of light exiting aget vessel when light from the source fiber is and isdirected to the vessel all the while the D-MUX is illuminateby the laser source. Leakage within the D-MUX can resultlight reaching the target through other fiber bundles houin the unit. Should the degree of leakage be significant, tcorresponding appreciable intensities will be recorded ewhen the source fiber is not directed to the target. We hobserved that the cross talk value is,1 part in 104 for anysource-detector configuration.

Cross talk within the detection unit can occur from ligleakages occurring at the fiber–photodetector interfaces.was quantified by comparing signal intensities when ligfrom the target is directed to a detector channel and wheis not, all the while light received from the co-located sourfiber ~the largest signal! is directed to its detector channeComparison of the measured values showed that detechannel cross talk was,1 part in 106 for all source-detectorpairs.

Figure 8 shows the result of a linearity measuremeSystem linearity was determined by adjusting the soulight intensity using calibrated neutral density filters andcording the detector readings over a wide dynamic ranPlotted are the averaged values for the readings fromsource-co-located detectors, versus the nominal optical dsity ~OD! value.

TABLE I. Performance characteristics of the instrument.

Parameter Value

Detector sensitivity 10 pW~NEP!Dynamic range 1:109 ~180 dB!Precision CV,1%, all channelsLong-term stability ,1% over 30 minCross talk~D-MUX ! ,1:1024

Cross talk~detector channels! ,1:1026

DAQ rate 2.7 Hz at 25 sources


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Figure 9 shows the results of system precision measments, as a function of the detector gain. The columns incate the mean value of the coefficient of variation~CV! ofthe signals acquired on a homogeneous, static phantomdata collected over a 2.6 min period~500 continuous measurement points! for different gain settings~15lowest gainand 95highest gain!; the error bars indicate the standard dviation of the CVs. For gain settings 1–6, the fluctuationdetector readings are remarkably low, with CVs well belo1.0%. In this region, the detector noise is very low asource noise contributions~laser noise, in-coupling deficiencies! dominate. At gain 7, the CV value increases to 2.5~corresponding to a SNR of 40!. At still higher gain values,the measurement precision degrades, revealing increasignal variability. This is due to increased detector noisehigher gain settings, which limits overall measurement pcision.

Figure 10 shows the result of a long-term stability stuthat we conducted over a period of nearly 30 min~5000continuous measurement points!. The measurements wertaken on a homogeneous, static phantom having opproperties that required use of only the lowest six gain stings. Therefore, fluctuations in the signal can be attribumainly to changes in in-coupling efficiency, laser power, adrifts in the detection electronics, rather than to detecnoise. Results are presented in a bar graph format with

FIG. 8. Evaluation of linearity performance and dynamic range of thestrument.

FIG. 9. Precision study: Signal variability over 500 time points as a fution of detector gain.


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bars organized into groups according to the different soupositions, with each bar representing the CV of one detechannel. This representation allows for easy identificationdetector channels or source positions having notably goobad performance. For example, the CVs of measured sigassociated with source No. 4 are larger than are thosemost other sources. In addition, we find that detector chnels 11 and 15 tend to have slightly worse noise performathan all other detector channels. This variability reflesubtle differences in the coupling efficiencies amongvarious optical interfaces throughout the system. The maity of source-detector combinations show a long-term staity of better than a 1.0% CV, with most having value,0.5%.

The short-term precision of the instrument is revealedFig. 11, where the results of a 360-data-point phantom msurement are plotted in a bar graph similar to that in Fig.Using the same gain settings as in the long-term study, mCVs are now below 0.5%.

B. Laboratory phantom studies

The purpose of these studies is to experimentally testoverall system performance and sensitivity under controconditions. These depend on both the quality of data coltion and the stability and other characteristics of the recstruction method. One feature of the latter that is relevanour experimental design is the analysis of differential msurements. In practice, the differential measure of mostterest to us is an instantaneous intensity relative to its tporal mean value. Thus, we have sought to collect data

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FIG. 10. Long-term stability study~5000 time points!. Each group of barsrepresents a source position. Individual bars indicate the stability of aticular detector at that source position.

FIG. 11. Short-term stability study~360 time points!.


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provide such information and at the same time allow forexamination of important system properties. Whereas a cprehensive examination of these is beyond the scope ofarticle, measures of interest we have examined includedependence of reconstructed image quality on object locawithin the target vessel, the influence of more complex bagrounds, and the limits on inclusion detectability. Our aproach has been to perform imaging studies on a laboravessel that contains various inclusions that are moved ainside the vessel while the time series image data are bcollected. This simple measurement serves to documenfidelity with which inclusions contrast~i.e., dma5deviationfrom background absorption coefficient anddD5deviationfrom background diffusion coefficient! can be localized andcharacterized as a function of object position in the tarmedium relative to a fixed source-detector geometry. Afurther test, we have repeated these measurements inpresence of a more complex background medium that ctains a 3-mm-thick circular optical void. Our interest in thmeasure stems from a reported finding by Dehghaniet al.23

that diffusion-based imaging solvers, such as the typeemploy, perform poorly under these conditions.

In an effort to a test the limits of image sensitivity, whave performed time-series tomographic measuremwhile stirring a 0.08-mm-diam titanium wire within the tevessel. The latter inclusion produced a maximum relatchange in detector reading on the order of60.5%.

1. Experimental setup

A schematic of the test vessel with the added inclusiin the cross section is shown in Fig. 12. The vessel usedcomposed of white Delrin and measures 7.6 cm in diamehas a height of 15 cm and a wall thickness of 2 mm. Tbackground medium consisted of 1%~v/v! Intralipid and the

FIG. 12. Schematic of dynamic phantom used for demonstrating separ~left: case 1 w/o void, right: case 2 w/ void!.

FIG. 13. The top and bottom rows are the reconstructed profiles of abstion and diffusion coefficients, respectively, from representative imframes for case 1~w/o void!.


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inclusions~three rods! used were 6 mm in diameter and alscomposed of white Delrin. While we did not independenmeasure the optical properties of the inclusions, Fanet al.24 have reported values of a reduced scattering coecient of ms8'12 cm21 and an absorption coefficient ofma

50.02 cm21. These values compare to the reported25,26 op-tical properties of 1% Intralipid ofms8'10 cm21 and ma

50.02 cm21. This indicates that the inclusions are;20%more scattering than the surrounding medium. This is csistent with our detector data showing that, relative tohomogeneous background, introduction of the rods increathe intensity of light received by detectors on the same sof the vessel as the source~i.e., backreflection! and decreasesthe light intensity for detectors positioned on the opposside of the vessel. Data were collected at a rate of;3 Hz,using a 16 source316 detector arrangement positioned inuniform circular array about the vessel, over a period of;25s ~75 image frames!.

Image recovery was achieved using the normalized cstraint method recently described by Peiet al.27 This algo-rithm is an extension of a differential analysis scheme whwe refer to as the normalized difference method.28 As wehave shown, the new scheme is effective in minimizingterparameter crosstalk.27

We wish to emphasize that our image reconstructionforts do not focus on the recovery of the absolute optiproperties. Rather we have strived to define methodsoptimize image contrast and resolution in recovering dnamic features of a target while reducing interparamecross talk and minimizing computing time.

For all reconstruction results shown, solutions were liited to first-order computations terminated after 1000 itetions. The finite element grid used comprised 1296 eleme

2. Results

An example of the image quality recovered from phatom studies is shown in Figs. 13–15. The top row of Fig.

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FIG. 14. The top and bottom rows are the reconstructed profiles of abstion and diffusion coefficients, respectively, from representative imaframes for case 2~w/ void!.

FIG. 15. Spatial maps revealing localized changes inma as a function ofobject location. Shown are representative image frames of the reconstrimage time series of an 80-mm-diameter wire moving about in a 1%—Intralipid background.


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and the bottom row shows the map of recovered changethe diffusion coefficientdD obtained at various times durinthe image time series. Inspection reveals that it is only indD map that we find evidence of the inclusions. Thedma

map is essentially featureless, which is in agreement withactual target properties. For comparison purposes, we hoverlaid ~dotted circles! the actual boundaries and locatioof the inclusions on their recovered positions. Here againsee that these features are accurately recovered, as ialgebraic sign of the inclusions. The quantitative value ofdD contrast however is overestimated~;a factor of 7! andreflects the sensitivity of our current reconstruction scheto errors of this type. Nevertheless, it is evident that majoof the relevant contrast features associated with the timeries ~object position, separation ofma and D, sharpness ofinclusion boundaries, and algebraic sign of perturbation! arecorrectly recovered.

Comparison of these results to those in Fig. 14~measure-ment with optical void! shows that our ability to discriminatthese characteristics is not severely impaired by the presof an intervening nonscattering layer. The location of tinclusions, separation ofma andD, and algebraic sign of theperturbation are all accurately recovered. Some degradain the sharpness of the inclusion boundary is seen whichreflect either the influence of the nonscattering layer,added difficulty of resolving more centrally positioned inclsions or both. As before, we find the quantitative value ofdD contrast is overestimated, in this case by a factor of;3.We also find, in agreement with the phantom properties,notable contrast features in thedma map. Note that the in-tervening layer itself is not seen because it does not conute to the differential measure. This is not a fundamenlimitation, but simply a function of how the particular dawere acquired. Further, results in Fig. 15 reveal that ewhen approaching the limit of detectability, object locatican still be accomplished, regardless of its position invessel. The object moved around in the vessel was a 0mm-diam titanium wire, which produced a maximum vartion in signal levels on the order of60.5%. Here we find,however, that the inclusion size revealed in thedma map issignificantly overestimated. The latter likely reflects both tspatial resolution limits of the method and resolution limimposed by the finite grid size used.

IV. DISCUSSION

A. Comparison of other reported measuring systems

As evidenced by the increasing number of reports inliterature, an interest in developing practical measuring stems for optical tomography remains high. It is instructivemake a specific comparison of this literature. The perfmance characteristics of systems recently reported are lin Table II. Proceeding from the left- to right-hand side, tsystems are organized according to different data collecmodes; cw, frequency domain, and time resolved. Also lisare significant performance characteristics such as photositivity, number of source-detector sites, dynamic range,quisition speed, and tomographic measurement strategie


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The system featuring the highest sensitivity and minformative measurement data is that described by Schmet al.10 These authors developed a single photon counttime-resolved measuring system incorporating 32 bysource-detector sites. Tomographic measurementsachieved by time multiplexing a single illuminating sourtogether with parallel multichannel detection. The dynammeasuring range can be extended by three decades usvariable optical attenuator. While fast data collection wasa specific design objective for this system, the selectedtection scheme nevertheless limits data collection ratesapproximately 1 Hz. In addition, the need to avoid nonlinedetector responses effectively imposes an upper limitsource intensity while also reducing the view angle of msurement. A system employing a similar measurement segy~eight source, two detectors, and two wavelengths! beingused for simultaneous magnetic resonance imaging~MRI!studies has been described by Ntziachristoset al.9,29

Systems based on frequency-domain measurementsdescribed by Franceschiniet al.4 and Pogueet al.2,30 Bothcollect tomographic data by time multiplexing the source ause of a photomultiplier tube~PMT! as a detector. The system by Pogueet al.2,30 is applied to collect full viewmeasurements and, hence, has the need to extend thnamic measurement range. This is achieved using a varifilter wheel. A more recent version of their basic system eploys multiple PMT’s to allow for parallel data collection.31

Image-frame acquisition rates are notably faster with the stem used in Ref. 4~model 96208 Oximeter, available fromISS, Inc., Champaign, IL!. This is achieved using electronitime-multiplexing schemes of the sources and operatingPMT’s parallel at a smaller, fixed dynamic range.

Several reports, including the current one, have adopCW measurement schemes. Typically, these systemsmore economical as they require less sophisticated electics to achieve signal detection. Another feature that sevgroups, including ours, have adopted is the use of frequeencoding methods to allow for simultaneous multiwavlength detection. This option is not available in the casesingle photon counting. As we have recently discussed,18 theuse of this strategy to provide parallel multisite sourillumination—as used in Ref. 14—can significantly limit thachievable dynamic range. We have avoided this by limitthe use of this technique to provide source discriminationonly one measuring site at a time. As noted in the text,achieve a large dynamic range by introducing gain switing. The approach we have adopted is similar to the tenique used by Colaket al.1 Where we differ in functionalitywith the latter system is in the use of a fast optomechansource switch combined with the already noted use ofquency encoding techniques. Colaket al.1 achieve wave-length discrimination by time-multiplexing different laserThus, whereas both systems employ parallel detection,can achieve much faster framing rates and even fasteracquisition rates~540 vs 2100–8600 Hz! even though thesystem by Colaket al.1 employs a much higher sourcedetector density.


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B. Applications for dynamic imaging

Here, we described our efforts to implement a practimeasuring system well suited to characterize the time depdence of optical contrast features in highly scattering meMotivating this work is the hypothesis that optical tomogrphy, adapted to provide a time series of image data,allow for the examination of a large untapped reservoirknowledge regarding tissue function—the spatiotemporalnamics of the vascular response and hemoglostates.6,7,18,20The details of this control—how it is influenceby disease, trauma or pharmacoactive agents—is curreknown by only the grossest of ways. Significantly, wherethe techniques available to characterize these details hbeen lacking, at least as applied to large tissue structuresnevertheless well appreciated that important functionaliof the vasculature are easily discerned in accordance totemporal response. Thus, it is the case that the detectiontime varying signal equal to the rate of ventricular concetration in the periphery can be reliably taken as originatfrom arterial structures. A similar assignment can be maprincipally between the respiratory frequency and the veand the vasomotor frequency and the microvessels. Ashave recently emphasized,6 such well-defined structureresponse features allow for the generation of spatial mthat assign distinct functional responses to anatomical sttures. Supporting this assignment is the simple observathat, in the near infrared region, it is essentially only themoglobin signal that exhibits natural time variability. Alsaiding the practical utility of these measures is the findthat the temporal variations in optical properties can be chacterized with much greater fidelity than can correspondefforts to recover the optical coefficients themselves.20

C. Future developments

One issue emphasized in the literature having particusignificance for practical studies is the need for a robust cbration scheme.32 As we have indicated, depending on thtype of information sought, it is not always necessaryperform a calibration. In instances where it is important,scheme we have implemented makes use of expectedmetries from a homogeneous target. The strategy used isplicable to problems having, for example, approximately clindrical ~e.g., limbs!, hemispherical ~e.g., breast!, orspherical geometries~head model!. While the details of thisare beyond the scope of this discussion, and will be repoelsewhere, we simply point out that the essence of the tenique divides the system of equations corresponding to3D calibration problem into a set of smaller 2D problemeach of which is individually solved in the same mannerdescribed previously.18 The final determination of coeffi-cients, however, requires additional operations that linkresults from the individual subproblems.

Another feature of system functionality, where room fadditional development remains, concerns its real-time cability. As noted in the text, the instrument described can dplay the measured time varying source-detector responsethey are collected. We have found this capability especiauseful in our efforts to develop provocation protocols. A
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even more useful feature would be to reconstruct and dis3D image results in real time. Recently, we have achiethe latter capability using a diffusion-based algebraic recstruction solver28 and are currently developing softwareallow for interactive volume rendering as the image datacomputed on the fly. We note that in optical studies the sof the image data sets is much smaller~typically ,10 000unknowns/frame! than in MRI studies, which significantlylimits the computational needs for image display.

Finally, it is worth emphasizing that the ability to studand characterize dynamic processes in highly scatteringdia is not a capability easily accomplished using other msuring technologies. As noted in the Introduction, our prinpal aim has been to apply the described system for the sof vascular states in living tissue. We recognize, howevthat other application areas may also find the describedpability useful. One such area involves the mixing of poders, which is a process important in the chemical and pmaceutical industries. For instance, it is known that mixfor longer times does not necessarily produce better resand can in fact lead to the resegregation of componentsformation obtained by monitoring the dynamics of the moing solids and voids in a cross sectional view might leadthe devising of protocols that lead to more reproducible phmaceutical formulations.

ACKNOWLEDGMENTS

Two of the authors acknowledge that this research wsupported by National Institutes of Health~NIH! Grant Nos.R01-CA 66184~R.L.B.!, R01 AR46255-01~A.H.H.!, and theNew York City Council Speaker’s Fund for Biomedical Rsearch: Towards the Science and Patient Care~A.H.H.!. Theauthors wish to thank Y. Pei for providing the image recostruction software developed under the support of GrantNIH R01-CA66184.

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Intrumentation for fast functional optical tomography

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