Design of a miniaturized frequency domain near infrared spectrometer with validation in solid phantoms and human tissue

Abstract

Hemoglobin is one of the most important chromophores in the human body, since oxygen is carried to the tissue by binding with the hemoglobin. Therefore measuring the concentrations of oxy-hemoglobin (HbO) and deoxy-hemoglobin (HbR) is very important in both clinical settings and academic fields. Frequency domain near infrared spectroscopy (fdNIR spectroscopy) is a technique that can be used to measure the absolute concentrations of HbO and HbR non-invasively and locally. The fdNIR spectrometer utilizes the attenuation and the phase shift (with respect to the source) that an intensity modulated NIR light experiences in order to calculate the absorption (μ_a) and reduced scattering (μ^′s) coefficient of the tissue. In this work, a miniaturized dual-wavelength fdNIR spectrometry instrument is presented with both tissue-like phantom and in vivo occlusion measurements. Systematic tests were performed on tissue phantoms to quantify the accuracy and stability of the instrument. The absolute errors for μ_a and μ^′s were below 15% respectively. The amplitude and phase uncertainty were below 0.25% and 0.35°. In vivo measurements were also conducted to further validate the system.

Keywords

Frequency domain near infrared spectroscopy CMOS oximetry

Introduction

In vivo biomedical imaging of tissue using NIR spectroscopy can be traced to Frans Jöbsis in 1977,¹ however the field rapidly evolved only recently. In certain wavelengths in the visible and NIR regions (for example 690 nm and 830 nm in this work) the absorption of HbO and HbR are distinct and significantly greater than of water. The basis of NIR spectroscopy in biomedical applications lies here. The absolute concentrations of HbO and HbR can be extracted by sending near infrared light at different wavelengths and collecting the attenuated and scattered light at a single location or multiple locations.

The absolute concentration of HbO and HbR are important biomarker in many applications including pediatric neurology, wound healing, breast tumor detection, and the diagnosis of brain ischemia.^2–5 To this end, several techniques have been developed over the years; continuous-wave NIR spectroscopy (cwNIR spectroscopy), time-domain NIR spectroscopy (tdNIR spectroscopy) and frequency-domain NIR spectroscopy (fdNIR spectroscopy). Even though these techniques differ in how they utilize near infrared light, they all use the same range of wavelengths in the optical window Figure 1.

In fdNIR spectroscopy, the light intensity is modulated with a high frequency sine wave, typically at least tens of MHz. The attenuation and the phase shift information of the light, which traversed the tissue, are used to calculate the absorption (μ_a) and reduced scattering (μ^′s) coefficients.

Several benchtop, commercial fdNIR instruments are readily available with reports of validation performance.^6,7

In this work, the design and validation of a miniaturized fdNIR instrument is presented. The instrument utilizes off-the-shelf laser diodes and a solid-state avalanche photodiode (APD) as the light source and detector. The portable fdNIR system, with ∼30 times smaller footprint in volume compared to commercial fdNIR oximeters, consists of a multi-tier printed circuit board (PCB) stack, a data acquisition card, and a Raspberry Pi controller. The core signal processing circuit is a custom-designed application specific integrated circuit (ASIC), fabricated in a 130 nm (CMOS, complementary metal-oxide-semiconductor) process. The instrument’s accuracy and stability were characterized on calibrated solid tissue phantoms. In vivo measurements were also conducted to further validate the instrument.

Materials and methods

fdNIR theory

The two modalities of fdNIR spectroscopy are a multi-frequency method or a multi-distance method. In multi-frequency measurements, the modulation frequency is swept across a wide range, while the source-to-detector distance is fixed. The phase shift and amplitude at different frequencies can be used to recover the above-mentioned optical parameters of the media. The most significant advantage of multi-frequency method is that the measurement can be accomplished at one single source-to-detector distance. This leads to better immunity to local tissue variations and a more compact probe design. However, the required modulation frequency is beyond 1 GHz for accuracy, which requires high-frequency sources, detectors, and complex circuits.^8,9 In multi-distance measurements, the modulation frequency is fixed, while the measurement is performed at different source-to-detector distances. The absorption (μ_a) and reduced scattering (μ^′s) coefficients of the media can be recovered by feeding the slope of amplitude-distance curve (SAC) and phase-distance curve (S_ϕ) to the following equations

μ_{a} = \frac{ω}{2 v} (\frac{S_{ϕ}}{S_{a c}} - \frac{S_{a c}}{S_{ϕ}})

(1)

μ_{s}^{'} = \frac{S_{a c}^{2} - S_{ϕ}^{2}}{3 μ_{a}}

(2)

where ω is the angular frequency of modulation and ν is the speed of light in the media.¹⁰ To estimate the absolute concentration of HbO and HbR, one only needs the μ_a and μ^′s at two different wavelengths.¹¹ Although accuracy of the multi-distance method is slightly inferior to multi-frequency method, the reduction in hardware complexity is an attractive feature for the multi-distance method to achieve a compact and low-cost design.

Figure 1.

System level block diagram of the fdNIR spectroscopy system.

System architecture

The block diagram of the system is shown in Figure 1. Laser diodes that emit at 690 nm (4 × HL6750 MG) and 830 nm (4 × HL8338 MG) are time division multiplexed each with 120 ms on-time. Two additional time slots are reserved for transmitting the sampled data, which means a single measurement frame takes 1200 ms, which corresponds to 0.83 Hz refresh rate. The laser diodes are coupled to the probe via a fiber bundle. The visible (690 nm) and near infrared (830 nm) energies, modulated at 80.001 MHz travel through the tissue, and are detected by the probe again and converted to electrical signal with an APD (Hamamatsu S9251-15, Hamamatsu City, Japan). The APD was selected for its low junction capacitance (3.6 pF), high photosensitivity (5000 A/W), 3 dB bandwidth (350 MHz) and large photosensitive area (1.5 mm²). The recovered electrical signal is amplified, processed and down-converted in the CMOS ASIC.¹⁶ The entire signal chain is fully differential for optimal common-mode suppression and noise performance. To that end, a reference signal at the same frequency as the laser modulation frequency and differential local oscillator (LO) signals are generated. The down-conversion results in output signals at 100 Hz, which are digitized by the data acquisition system (DAQ, National Instruments Corp., Austin, TX, USA) with sampling rate of 400 kSps and further processed in software to extract the μ_a, μ^′s, and finally the HbO and HbR concentrations.

Probe design

The main requirements for the probe in a multi-distance fdNIR measurement are: (1) flexibility for good coupling with the tissue, (2) several windows that allow NIR light to become incident to the tissue at known distances from the detector window, and (3) large fiber numerical aperture defined previously and diameter to accommodate large area APDs. To that end, a custom probe (ISS, Inc., Champaign, IL) was used. It has a total of five windows; 4 emitter windows, each accommodating two fibers (400 μm in diameter), and one detector window. For the detector window, a 2 mm fiber bundle with 0.55 NA is used. The head of the probe is made of polyurethane so that it can conform to curved surfaces. One end of the each fiber has an SMA connector for sturdy connection with the laser diode or APD mounts. The source-detector distances on the probe are 1.5 cm, 2.0 cm, 2.5 cm and 3.0 cm. The diagram of the probe can be seen in Figure 2. The available optical power at different source-detector distance varies significantly in multi-distance measurements. A high gain can boost the SNR at large source-detector distances but may lead to saturation at small source-detector distances. Although the ASIC has a good dynamic range of 33 dB, tuning the optical power can be a tricky and challenging job in many cases. To solve that problem, a thin film neutral density filter is placed on the surface of the first emitter window as an equalizer. The filter attenuates the optical power at 1.5 cm source-detector distance, which expends the overall dynamic range.

Figure 2.

The probe design.

Electronics

Laser driver

The above-mentioned eight laser diodes are driven by two laser driver circuits, one circuit for each wavelength. These eight laser diodes are mounted onto the PCB via laser driver mounts (Thorlabs S05LM56, Thorlabs Inc., Newton, NJ, USA), and the fibers are coupled to the laser diodes via SMA fiber adapters (Thorlabs PM20-SMA). The mounts and adapters provide sturdy contact and also works as heat sinks. The schematic of the laser driver circuits can be seen in Figure 3.

Figure 3.

Laser driver circuit.

The basic topology of the driver is constant current regulator with a feedback loop that sets the DC voltage at the output of the OP-AMP, using the monitoring current of the integrated photo diodes of laser diodes. This feedback loop adjusts the DC operating point of the RF transistor, so that the monitoring current stays constant, which helps to keep the optical output power of different laser diodes the same. For example, if a laser diode has a lower optical output power than the others with the same forward current, in other words lower monitoring current than expected, the feedback loop increases the forward current which increases the optical power, which in turn increases the monitoring current of that laser diode, and the loop settles.

The DC reference voltage V_ref sets the operating DC voltage at the output of the OP-AMP and the coupling capacitor C_c couples the radio-frequency (RF) modulation signal the DC voltage. The output of the OP-AMP, biases the BJT and results in an emitter current with DC and AC components. The AC component of the current can be adjusted independently from the DC component by adjusting the amplitude of the modulation signal. The OP-AMP was chosen as OPA695 (Texas Instruments) for its very high bandwidth (1.4 GHz for Gain = +2) and unity gain stability. The BJT is chosen as BFP780 (Infenion Technologies) for its linearity (23 dB output 1-dB compression point), maximum current capability (>100 mA). The switching IC is ADG1412 (Analog Devices), picked for its low channel resistance (∼1 Ω) and current capability (>200 mA).

Signal generation

For the multi-distance fdNIR spectroscopy measurement presented here, a total of four RF signals need to be generated; one for laser modulation (80.0001 MHz), one as reference signal (80.0001 MHz) and two as the differential local oscillator (LO) signals (80 MHz) for the down-conversion. Solutions such as crystal oscillators are not suitable because two RF tones that are very near to each other need to be generated. Therefore, a direct digital synthesizer (DDS, AD9959) is implemented for its four differential output channels that are frequency, amplitude and phase independent. The DDS system offers 0.12 Hz frequency resolution, 14-bit phase resolution and exceptional phase noise characteristics. For differential-to-single-ended conversion, baluns are used. The DDS output is filtered by a band-pass filter.

fdNIR ASIC

The fdNIR spectrometer’s ASIC is a custom designed integrated circuit, fabricated in a 130 nm CMOS process.¹² It has two fully differential identical channels that comprise of a low-noise, resistive feedback transimpedance amplifier (TIA), a Gm-C band-pass filter and a double-balanced gilbert mixer. Channel 1 processes the signal from the APD and the parallel channel processes the reference signal generated by the DDS.

The very weak photoelectric current at RF is amplified by ∼120 dB by the front-end TIA. The Gm-C band-pass filter further amplifies the signal and also filters noise signals that may have coupled to the RF signal. The Double-Balanced Gilbert Mixer, down-converts the RF signal to 100 Hz with the help of the local oscillator previously defined signals for the mixer, generated via the DDS (Figure 4).

Figure 4.

FdNIR CMOS ASIC.

Since most APDs that operate in these wavelength ranges with these bandwidths are single-ended products, a dummy capacitor with the same capacitance as that of the APD junction is connected to the input of the Channel 2. Equalizing the capacitances seen by both inputs improves the noise performance and the linearity of the fdNIR ASIC. The two differential output pairs of the fdNIR ASIC are converted to single ended, buffered and further amplified off-chip.

Calibration

The top view of the system can be seen in Figure 5. There are two laser arrays consisting of four laser diodes each, driven by a laser driver circuit. Even though the laser diodes and the laser driver circuits for the two different colors (690 nm and 830 nm) are identical to each other, there is always some mismatch due to manufacturing, layout, aging etc., but most importantly the different coupling efficiencies of each to the tissue.

Figure 5.

Top view of the system.

To compensate for these effects, a simple algorithm for calibrating the system using tissue mimicking solid phantoms with known μ_a and μ^′s was used. Measurements from one phantom, called Calibration Phantom in Table 1, are captured and calibration factors are created for each of the laser diodes as AC_calib = AC_measured/AC_expected and ϕ_calib = ϕ_measured − ϕ_expected, where AC_measured is the recovered AC magnitude, ϕ_measured, is the measured phase shift from a laser diode. The AC_expected is the expected recovered amplitude and ϕ_expected is the expected phase shift for the same laser diode, calculated by the known optical properties of the solid phantom. This approach creates a lookup table that is used to correct for the component and coupling based mismatches.

Table 1.

Solid phantom measurement results using a calibration phantom.

Phantom	Parameters	Expected (mm⁻¹)	Measured (mm⁻¹)	Error
Calibration phantom	μ_a 690 nm	0.0081	—	—
	μ^′s 690 nm	0.761	—	—
	μ_a 830 nm	0.0077	—	—
	μ^′s 830 nm	0.597	—	—
Phantom 1	μ_a 690 nm	0.0015	0.0014	−6.67%
	μ^′s 690 nm	1.023	0.880	−13.9%
	μ_a 830 nm	0.0013	0.00114	−12.3%
	μ^′s 830 nm	0.785	0.764	−2.66%
Phantom 2	μ_a 690 nm	0.0124	0.0142	+14.5%
	μ^′s 690 nm	0.930	0.904	−2.79%
	μ_a 830 nm	0.0106	0.0098	−7.54%
	μ^′s 830 nm	0.763	0.801	+4.98%

Figure 6 shows an example of the calibration algorithm, where the red crosses are the measurement results before the calibration, and the blue stars are after calibration. One important note is that subplots (a) and (c) of Figure 6 show the “linearized amplitudes”. This linearization process enables realization the goal of measuring SAC of the medium, which can be approximated as the slope of ln(ρ²*AC) for reflectance measurements in a semi-infinite media, where ρ is the source-detector separation,¹³ and AC is the amplitude of the measured AC signal. The black dashed lines indicate the SAC and S_ϕ values derived from the known μ_a and μ^′s of the phantom we measure using (equations 1) and (2), and the green dashed lines are the line fit to the calibrated results.

Figure 6.

An example of the calibration algorithm. (a) Linearized and (c) normalized amplitudes for 690 nm and 830 nm lasers. Normalized phases for (b) 690 nm and (c) 830 nm lasers.

It can be seen that after the calibration, the recovered SAC and S_ϕ (green dashed lines) are very close to the known optical values (black dashed lines). Tabulated results for calculated μ_a and μ^′s can be found in Table 1.

Accuracy and stability

The absolute accuracy is affected by both systematic errors and instrumental noise. The systematic errors such as validity of semi-infinite medium assumption, uneven light coupling, and variation in probe fabrication can be minimized by applying more sophisticated calibration and correction methods.¹⁴

Accuracy

To characterize the accuracy of fdNIR instruments, usually measurements on solid and/or liquid phantoms with known optical parameters are conducted. Liquid phantom experiments were reported for previous iteration of the system, which featured the same ASIC, but also comprising mostly of benchtop equipment.¹² In this work, we present the solid phantom experiments where one phantom is used for calibration and two others used for the accuracy and stability measurements.

All three phantoms were fabricated by the Diffuse Optical Imaging of Tissue Lab at Tufts University and their optical properties were characterized by a commercial oximeter system (ISS Model 96208, Fastest Electronics, Walled Lake, MI, USA) using a multi-distance approach. These characterization results were taken as the ground truth and reported under the “Expected (mm⁻¹)” column in Table 1. The calibration phantom provides baseline results. The calibration phantom provides baseline results. Measured data and error results on phantom 1 and 2 are reported in Table 1.

During measurements, the probe was placed on the surface of the solid phantoms. Each laser diode was turned on for 120 ms. Ten readouts from each phantom are averaged and the results are listed in Table 1. The maximum error is less than 15% in all the measurements. The accuracy of our instrument and previously reported fdNIR systems are compared in Table 2.^{8,9,11,14–16}

Table 2.

Accuracy comparison.

Model	Fantini¹¹	Pham⁸	No⁹	Sthalekar¹⁴	Torjesen¹⁵	Stillwell¹⁶	This work
Sensor	PMT	APD module	APD module	APD	APD	APD	APD
Sensing method	Multi-distance	Multi-frequency	Multi-frequency	Multi-distance	Multi-frequency	Multi-frequency	Multi-distance
Frequency (MHz)	120	10–1000	10–1000	100	50–400	1–400	80
Light coupling	3 mm fiber bundle	1 mm fiber	Direct coupling	1 mm fiber and objective lens	6 × 400 μm fiber bundle	6 × 400 μm fiber bundle	2 mm fiber bundle
Maximum error	15%	5%	14.48%	27.13%	5%	10%	15%
Dimensions	N/R	N/R	N/R	N/R	10 × 12 × 16 in	12 × 12 ×3 in	12 × 11.5 × 5 cm
Portable	No	No	No	No	Yes	Yes	Yes

We can see that our design achieved a good level of accuracy among the other reported systems. Especially considering the fact that our system if at least an order of magnitude smaller than systems of accuracy below 15% as well as avoiding the use of expensive (even more so than the complete commercial fdNIR instrument from ISS) and complex equipment such as a vector network analyzers (VNAs), standalone laser controller/drivers or very high speed ADCs that require an field programmable gate array development kit.

Stability

In order to characterize the stability of our measurements, a 15 minute-long solid phantom measurement is performed. The ratios of the measured AC amplitudes of adjacent lasers, and their distribution can be seen in Figure 7, where, (a) shows the measured AC signal ratios of second laser to first and the distribution over 15 min, (b) shows the same quantities for third to second, (c) fourth to third, where first, second, third and fourth lasers refer to increasing source-detector separations.

Figure 7.

(a) The amplitude of second laser normalized to first. (b) The amplitude of third laser normalized to second. (c) The amplitude of fourth laser normalized to third. All are 830 nm lasers.

Similarly, Figure 8 shows the measured phase shifts between adjacent lasers, with (a) showing the phase shifts between second and first, (b) between third and second and (c) between fourth and third lasers.

Figure 8.

(a) The measured phase shift of the second laser with respect to the first. (b) The measured phase shift of the third laser with respect to the second. (c) The measured phase shift of the fourth laser with respect to the third.

Finally, Figure 9 shows the distribution of measured μ_a and μ^′s over 15 min, with (a) and (b) showing the μ_a and μ^′s for 690 nm lasers respectively, and (c) and (d) showing the μ_a and μ^′s for 830 nm lasers respectively.

Figure 9.

The distribution of the measured (a) μ_a and (b) μ^′s respectively for 690 nm. The distribution of the measured (c) μ_a and (d) μ^′s respectively for 830 nm.

It can be seen that there is little to no drift over time, but there are occasional instantaneous spikes for singular data frames. These sudden spikes are due to random errors and they are many standard deviations away from the data, therefore are of no interest to us. The distribution of all the quantities resemble a Gaussian distribution as expected. We also compared the parameters of our instrument with the commercial instrument from ISS in Table 3, where one can see that our design achieved a comparable performance at a much lower size and cost.¹⁷

Table 3.

Comparison between ISS model 96208 and this work.

Parameter	ISS model 96208		This work
Parameter	690 nm	830 nm	690 nm	830 nm
μ_a uncertainty (mm⁻¹)	0.00007	0.00006	0.00025	0.00018
μ^′s uncertainty (mm⁻¹)	0.005	0.004	0.087	0.058
μ_a (mm⁻¹)	0.0015	0.0013	0.0014	0.00114
μ^′s (mm⁻¹)	1.023	0.785	0.880	0.764
Size	36.2×28.9 ×14.6cm		12×11.5×5cm
Cost	>US$20000		US$1200

In vivo occlusion tests

After validating the system on solid phantoms, arterial and venous occlusion tests on the human forearm were done. The probe was placed on the brachioradialis muscle on the right forearm and a regular blood pressure cuff was placed just above the elbow. The optical power from each laser diode is set to meet the ANSI Z136.1 laser safety standards.¹⁹ Different pressures were used for the venous and arterial occlusion tests. The procedures were reviewed and approved by Health Sciences Institutional Review Board (HS IRB) at Tufts University.

Venous occlusion tests

In the venous occlusion test, the subject stayed at rest for 30 s, then 60 mmHg pressure was applied for 60 s, after which the pressure was released, additional measurements were taken for another 60 s. A 60 mmHg pressure can cutoff the venous blood flow but have minimum influence on arterial blood flow. As a result, the arterial blood keeps flowing into the forearm, which will result in an increment in both oxy-hemoglobin and total-hemoglobin. In Figure 10, the chromophore concentrations during a venous occlusion test can be seen. The occlusion was marked with the green shaded region, 30–90 s. During the occlusion test, the HbR cannot leave the forearm but the HbO can enter the forearm since the artery is not occluded. As expected, HbO enters the lower arm, resulting in an increase in concentration. The HbT naturally followed these changes and rises during the occlusion test, as expected.¹⁹ After the pressure is released, the HbO leaves the lower arm and the concentrations returned to baseline levels.

Figure 10.

Venous occlusion test with measured chromophore concentrations.

Arterial occlusion tests

In the arterial occlusion test, the procedure was identical except for the pressure. In this experiment, the applied cuff pressure was 200 mmHg. Under this condition both the artery and the vein are occluded. Therefore, the expected behavior is that while the HbR concentration rises, HbO concentration falls during the occlusion, and HbT stays roughly the same. Figure 11 shows an arterial occlusion test. The occlusion is indicated with the green shaded region again, 30–90 s. As expected, when the occlusion starts the HbR increases and HbO decreases roughly the same amount, hence HbT stays the same. After the cuff is released, there is a rush of oxy-hemoglobin because the artery is reopened, therefore we observe an increase in both HbO and HbT. All results are consistent with previously reported data.

Figure 11.

Arterial occlusion test with measured chromophore concentrations and oxygen saturation.

Conclusion

This work presents the design and validation of a miniaturized, dual-wavelength, multi-distance fdNIR spectrometry instrument. The accuracy and the stability of the system was validated using tissue mimicking solid phantoms. Venous and arterial occlusion experiments were performed on brachioradialis muscle of the right forearm. Although the APD has a much lower gain than PMT, a performance comparable to state-of-the-art commercial instruments is achieved with the help of a custom-designed ASIC implemented in a commercial 130 nm semiconductor process. The miniaturization of fdNIR spectrometry instrument enables the monitoring of absolute hemoglobin concentration on a routine basis. The miniaturized instrument will benefit the use of fdNIR in both research and clinic applications.

Footnotes

Acknowledgements

The authors would like to thank Dr S. Fantini, Dr A. Sassaroli and Dr G. Blaney from Tufts University for guidance and assistance with phantom fabrication and optical characterization.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was in partially funded by a NSF Faculty Early Career Development Award (DBI-0953635), NSF Partnerships for Innovation - Technology Transfer Award (IIP-1919038), and NIH (R01-EB029414).

Ethical approval

This study has been reviewed and approved by Health Sciences Institutional Review Board (HS IRB) at Tufts University.

ORCID iDs

Alper Kılıç

Yun Miao

References

Jöbsis

. Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters. Science 1977; 198: 1264–1267.

Lin

Roche-Labarbe

Dehaes

, et al. Non-invasive optical measurement of cerebral metabolism and hemodynamics in infants. J Vis Exp Epub ahead of print 2013.

Papazoglou

Neidrauer

Zubkov

, et al. Noninvasive assessment of diabetic foot ulcers with diffuse photon density wave methodology: pilot human study. J Biomed Opt 2009; 14: 064032.

Fantini

Heffer

Siebold

, et al. Using near-infrared light to detect breast cancer. Opt Photonics News 2003; 14(11): 24–29.

Calderon-Arnulphi

Alaraj

Amin-Hanjani

, et al. Detection of cerebral ischemia in neurovascular surgery using quantitative frequency-domain near-infrared spectroscopy. J Neurosurgery 2007; 106(2): 283–290.

Buckley

Carp

Lin

, et al. A novel combined frequency-domain near-infrared spectroscopy and diffuse correlation spectroscopy system. In: Biomedical Optics 2014, paper BM3A.17. Washington, DC: The Optical Society, 2014, p. BM3A.17.

Lin

Hagan

Fenoglio

, et al. Reduced cerebral blood flow and oxygen metabolism in extremely preterm neonates with low-grade germinal matrix- intraventricular hemorrhage. Sci Rep 2016; 6: 25903.

Pham

Coquoz

Fishkin

, et al. Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy. Rev Sci Instrum 2000; 71: 2500–2513.

Chou

. Mini-FDPM and heterodyne mini-FDPM: handheld non-invasive breast cancer detectors based on frequency-domain photon migration. IEEE Trans Circuits Syst Regul Pap 2005; 52: 2672–2685.

10.

Fantini

Enrico

Franceschini

, et al. Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique. Appl Opt 1994; 33(22): 5204–5213.

11.

Fantini

. Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry. Opt Eng 1995; 34: 32.

12.

Miao

Koomson

VJ.

A CMOS integrated fdNIRS and tDCS system for simultaneous brain stimulation and monitoring. In: Midwest Symposium on Circuits and Systems, Windsor, ON, 5–8 August 2017, pp.

499–502.

13.

Fantini

Franceschini

Gratton

. Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation. J Opt Soc Am B 1994; 11: 2128.

14.

Sthalekar

Koomson

. A CMOS sensor for measurement of cerebral optical coefficients using non-invasive frequency domain near infrared spectroscopy. IEEE Sens J 2013; 13: 3166–3174.

15.

Torjesen

Istfan

Roblyer

. Ultrafast wavelength multiplexed broad bandwidth digital diffuse optical spectroscopy for in vivo extraction of tissue optical properties. J Biomed Opt 2017; 22(3): 36009.

16.

Stillwell

Kitsmiller

Wei

, et al. A scalable, multi-wavelength, broad bandwidth frequency-domain near-infrared spectroscopy platform for real-time quantitative tissue optical imaging [Internet]. Biomed Opt Express 2021; 12(11): 7261–7279.

17.

Fantini

Franceschini

. Frequency-domain techniques for tissue spectroscopy and imaging. In: Tuchin

(ed). Handbook of optical biomedical diagnostics. Cambridge: Cambridge University Press, 2002.

18.

Bigio

Fantini

. Quantitative biomedical optics: theory, methods, and applications. Cambridge, UK: Cambridge University Press, 2016.

19.

Van Vo

Hammer

Hoimes

, et al. Mathematical model for the hemodynamic response to venous occlusion measured with near-infrared spectroscopy in the human forearm. IEEE Trans Biomed Eng 2007; 5454(4): 573573–584584.