JOIN: Optimized Light Source Activation for Deep Tissue Optical Sensing

Abstract

In wearable optical sensing systems, non-idealities present during measurement affect the quality of acquired signals of interest. The issue is of particular significance in deep tissue sensing applications in which the signal of interest is faint relative to typical noise sources that contaminate the measured data. To mitigate the problem, we investigate the role of optimizing the light source activation pulse, specifically its toggling rate and duty cycle. We identify the potential for the optical source activation signal to mitigate the problem and characterize its design space. Subsequently, we present JOIN, an algorithm that yields the parameters of an optimized activation signal for a given profile of contextual noise profile. Through this algorithm, we strike a balance between avoiding noisy spectral regions associated with environmental disturbances and fitting a judiciously-selected number of signal harmonics into the measurement bandwidth, thereby enhancing the signal-to-noise ratio (SNR) of the acquired data from deep tissue by as much as $6dB$. The proposed method is validated through analytical derivations, as well as test bench and in-vivo measurements on human subjects.

1. INTRODUCTION

Many wearable applications, such as tissue oximetry, utilize lightintensity measurements to sense parameters of interest. This approach involves light emission, typically from light-emitting diodes (LEDs), which are directed into the body toward target tissue layers. As light diffuses into the body, it undergoes absorption and scattering events. A small fraction of the emitted light is diffused outside the body, which can be acquired by non-invasive photo-detectors placed on the body.

The captured light, having traversed various tissue layers, including target deep tissue, may contain information about the concentration of certain molecules in the tissue, enabling non-invasive assessment of specific tissue attributes. The choice of light wavelength depends on the sensing objective, among other factors, and is typically in the visible or near-infrared range of the spectrum in many applications.

Given that human tissue is highly scattered in the visible and near-infrared wavelengths, the light energy detected on the skin’s surface is considerably less than the energy initially emitted into the body. Specifically, the received light signal exponentially attenuates relative to the traveled distance, following Beer-Lambert’s Law [3]. This presents a challenge for designing wearable embedded systems, which are tasked to acquire faint signals indicative of deep tissue properties accurately. Note that the emitted energy has a hard upper bound due to patient safety constraints.

Stated differently, the signals of interest are close to the noise floor of the sensing system, and thus, they tend to have a small signal-to-noise ratio (SNR). It follows that effective noise mitigation strategies, such as coherent averaging of multiple measurements [31], are crucial for the reliable operation of the optical sensing system in such applications.

One application of deep tissue sensing is Trans-abdominal (non-invasive) Fetal Oximetry (TFO), which holds the potential to assist physicians in the timely detection of babies at risk of birth asphyxia [14, 35].

In this application, visualized in fig. 1, a probe containing light emitting diodes (LED) at two near-infrared wavelengths and several photo-detectors is placed on the abdomen of a term pregnant subject. The target tissue of interest is the fetus in-utero, and the objective of the sensing system front end is to acquire dual-wavelength mixed maternal-fetal Photoplethysmogram (PPG) non-invasively signals at the highest possible SNR. Similar to pulse oximetry [9], the acquired PPG signals are processed using downstream signal processing algorithms, which are out of the scope of this paper, to infer fetal blood oxygen saturation, commonly referred to as fS_pO₂.

Figure 1:

Trans-abdominal Fetal Oximetry (TFO), a representative example of non-invasive deep tissue optical sensing [14], involves two nested closed-loop systems. The problem studied in the paper relates to the inner loop.

Intrapartum fetal monitoring using TFO is comprised of two nested closed-loop systems, as seen in fig. 1. The inner loop involves the TFO sensing system, which is attached to the pregnant patient’s abdomen and collects the diffused light intensity signals on the body. The JOIN method proposed in the paper optimizes the sensing loop via tuning the light source parameters based on analysis of the sensed signals and the noise in the system. The outer loop demonstrates a typical labor and delivery scenario in which the improved fetal health assessment enabled by the TFO technology, which encompasses JOIN as a component, assists a care provider-in-the-loop in clinical decision-making and patient management. The focus of this paper is the inner loop of the illustrated cyber-physical system.

Analogous to conventional pulse oximetry, the mixed PPG signals acquired in TFO are expected to demonstrate temporal variations in detected light intensity due to the fetal heart rate (FHR) [21]. Consequently, FHR prominence and its detection accuracy can serve as an intermediate metric for validating and improving the sensing system front-end, decoupled from downstream fS_pO₂ inference algorithms.

This paper investigates a specific approach, namely optimization of the toggling frequency and duty cycle of the light source activation signal, to maximize the quality of signals from deep tissue of interest. We propose JOIN, an algorithm for the joint optimization of the two design parameters of interest, i.e., toggling frequency $(f_0)$ and duty cycle $(d)$ of the LED driving pulse train, which maximizes SNR of the deep tissue signal in the presence of both electronics and environmental noise. In the proposed method, measured tissue signal replicas over the frequency spectrum are averaged, with appropriate weights assigned to them to maximize the signal’s SNR with minimal impact on system complexity. Here, $f_0$ and $d$ are selected so that a judiciously-selected number of signal replicas fit within the data acquisition system’s limited measurement bandwidth.

The contributions of the paper are as follows:

• The impact of noise on the measured PPG signal is analyzed, and mitigation techniques to reduce the impact of present noise, especially at lower frequencies, are explored.

• A novel algorithm, dubbed JOIN, is proposed to judiciously select the LED activation signal’s toggling frequency and duty cycle. JOIN utilizes multiple scaled replicas of the tissue signal, coherently integrating them with appropriate weights to improve the SNR and enhance the performance of the sensing modality.

• Analytical derivations and simulation results are provided to support the effectiveness of JOIN in an illustrative deep tissue sensing application.

• Experimental results from data gathered in controlled environments and human subjects are presented, demonstrating JOIN’s effectiveness.

2. RELATED WORK

Previous studies have explored deep tissue sensing across various applications. Light-based sensing using LEDs is common in low-power wearable applications. The main challenge in light-based sensing of deep tissues is delivering sufficient power into the deep medium. Zhang et al. [34] researched a wearable system that uses microneedles to deliver more light into deeper tissues minimally invasively. In another study, Islam et al. [18] presented an innovative body-worn sensor that enables real-time imaging of deep human tissues, offering a portable and cost-effective solution for monitoring conditions such as cardiovascular disease and tumor growth. In [8], researchers report a method for measuring oxygen saturation in skin tissue that employs LEDs alongside compact and low-power light sensors.

Signal averaging techniques to increase SNR are commonly used in the field, such as the work reported by Böttrich et al. [7]. The proposed method in this paper acquires a longer time-series data stream and segments it into non-overlapping time windows, which are subsequently combined coherently. Other deep tissue sensing modalities have been explored, such as Radio Frequency (RF) alongside coherent averaging techniques to examine deep tissues, aiming to correlate the attributes of reflected signals with specific parameters of interest [32]. However, given its considerably larger wavelength, this approach faces low sensing resolution relative to light-based measurement.

A key aspect of light-based tissue characterization is the understanding of photon propagation in tissue. Jacques et al. have studied light-tissue interaction and have characterized the absorption properties of human tissue [19], based on which models for oxygen diffusion considering tissue absorption have been derived [23]. Mannheimer et al. [25] have researched optimal wavelengths based on the scattering characteristics of tissue. Multiple efforts have concluded that near-infrared (NIR) wavelengths are well-suited for sensing physiological phenomena in deep tissue. Examples of NIR spectroscopy for physiological sensing include work by Niwayama et al. [27] and Liu et al. [24].

A major obstacle in optical sensing is isolating the signal of interest from target deep tissues from other signal and noise sources contributing to the measured data [16]. Therefore, techniques to mitigate the effect of noise are crucial. Some studies have utilized adaptive noise cancellation (ANC) to increase the SNR [1, 4, 12].

Some works have studied the impact of emitted light patterns in an optical sensing system and tuning light source parameters. For example, Vali et al. investigated optimizing LED activation waveform to maximize SNR while considering patient safety [33].

3. BACKGROUND

3.1. Frequency-Modulated Multi-Wavelength Tissue Sensing

When measurements with multiple light wavelengths are required, the system must be able to resolve the wavelength-specific measurements from sampled data. For example in conventional pulse oximetry, at least two different light wavelengths are required to resolve the relative concentration of the two oxy- and deoxy-hemoglobin molecules. The two distinct light sources can be activated in a time or frequency multiplexing schemes, each of which, has its own pros and cons [17].

In this paper, it is assumed that frequency multiplexing is selected to resolve the measurements associated with different light wavelengths. Specifically, each LED, emitting a specific wavelength, is driven with a periodic current waveform $p(t)$ at a known distinct frequency $f_0$. It is demonstrated that the pulse train waveform for activation of the LED is optimal in maximizing SNR while meeting the constraint on the emitted optical power into the body [33]. Consequently, in the remainder of the paper, we assume that $p(t)$ is a pulse train, and use $d$ to denote its duty cycle.

In conventional LEDs, the generated optical energy is a linear function of the LED forward current and some intrinsic properties of the material [2]. As such the average emitted power of the LED $P_E$ depends on the amplitude of the LED pulse $(I)$ and the duty cycle of pulsation $(d)$.

$$P_E\propto \overline{p(t)}=I.d$$

Assuming that the tissue reacts linearly to the emitted optical signal, the received light at the photo-detectors is in the form of

$$y(t)=L.x(t).p(t)+n(t)$$ (1)

where $y(t)$ is the detected photoplethysmogram (PPG) capturing the light reaction to chromophore concentration changes in the deep tissue. $L$ is a scaling constant composed of several factors, such as tissue loss, the LED’s sensitivity to $p(t)$, the detector’s responsivity to the light wavelength, the detector’s area, and the data acquisition system’s gain. Lastly, $x(t)$ is the physiological signal of interest, whose bandwidth is often limited.

3.2. Noise in the Sensing Pipeline

In eq. (1), $n(t)$ is the noise degrading the integrity of acquired signals. Some noise sources have constant power across the spectrum, and thus, their spectral power profile is “white”. An example of a white noise source is the thermal noise of a resistor $R$ for which, the current noise density is constant across the frequency spectrum.

Another source of noise is electromagnetic interference (EMI) from the environment, whose sources are external to the sensing system. Fig. 2 visualizes the a power spectral density (PSD) example of noise observed in optical measurement in which, multiple harmonics of power-line induced EMI are clearly visible. Furthermore, ambient light and most electronics exhibit a higher noise power in frequencies closer to DC. Flicker noise from the electronics is one example of such a noise source [30]. The power spectral density of this “pink” noise is typically inversely proportional to frequency up to some corner frequency.

Figure 2:

PSD of the measured ambient noise. The interference from the 60Hz powerline and its harmonics are visible.

It follows that as the optical measurement moves closer to DC, the noise power increases, potentially degrading the SNR of the acquired tissue PPG signal. As a result, it is desirable to perform the sensing in frequencies that are substantially higher than DC, where the system noise floor is lower. This is accomplished through synchronous detection [5], where the light source is toggled with a known frequency and duty cycle, or equivalently, the chopped optical output is used to illuminate the skin.

3.3. Tissue Signal Copies over spectrum

Since the LED drive signal is a pulse train, its Fourier series can be expressed as:

$$p(t)=Id+\sum _i{a}_i\mathit{\text{cos}}\left(2\pi i{f}_{0}t\right),a_i=2Id\mathit{\text{sinc}}(id)$$ (2)

In eq. (2), $I$ is the pulse amplitude, $d$ is the duty cycle where $d=T_{on}/T$ is the ratio of on-time of the signal over the period, and $f_0=1/T$ is the LED toggling frequency, or equivalently, the measurement frequency. In addition, the $\mathit{\text{sinc}}(x)$ function here appears in the normalized form where $\mathit{\text{sinc}}(x)=sin(\pi x)/\pi x$ with the special case of $\mathit{\text{sinc}}(0)=1$. It follows that the detected PPG signal is composed of weighted tissue signal replicas modulated by harmonic frequencies of the pulse train through the Pulse Amplitude Modulation (PAM) technique [6]. Equivalently, the detected signal spectrum will contain weighted replicas of the tissue PPG signal spectrum at harmonics of the pulse train fundamental frequency [29]. Fig. 3 visualizes the measurement setup, and the spectrum of the received signal, including tissue signal replicas.

Figure 3:

Deep tissue Optical Sensing in the presence of noise.

The sensed data that is modulated to independent frequency channels may be coherently combined to mitigate the effects of attenuation and noise in the medium. Note that in the context of our target applications, tissue signals have a very narrow bandwidth, and the signal replicas are modulated to frequency bands that are far apart enough, and thus, aliasing does not occur. The concept has similarities to the notion of receiver diversity as studied in communication systems [15].

4. ILLUSTRATIVE PROBLEM STATEMENT

In the context of optical tissue sensing applications discussed above, our objective is to determine the optimal configuration for the LED drive pulse train signal, such that the SNR of the acquired tissue signal is maximized. Specifically, given a sensing platform with a known noise profile and measurement bandwidth, our objective is to determine the optimal frequency as well as amplitude and duty cycle of the LED driver signal that would result in the best tissue signal SNR, possibly through averaging of multiple signal replicas, under the hard constraint of a given upper bound on radiated energy into the subject’s body.

We use a real-world scenario with a typical optical sensing system, which utilizes LED light chopped at a select pulse frequency and emitted onto the body. Through this motivating example, we explain how this selection heavily impacts the SNR of the averaged tissue signal. The chopped LED light enters the tissue and modulates the tissue signal to that frequency and all its harmonics. The resulting signal will be captured using optical receivers with intrinsic noise characteristics. Typically, the noise profile is similar to that of pink noise, with a $1/f$ profile in which the noise spectral density decays over higher frequencies.

In the presence of real-world noise in the optical sensing system, one might select a pulse frequency as close as possible to the measurement bandwidth to minimize the impact of optical sensing noise. This approach works well if pulse frequency is the only parameter in our control since less noise is observed in the power spectrum at higher frequencies, boosting the SNR of the detected signal. However, by controlling the pulse’s amplitude and duty cycle alongside its frequency, a more competitive design might be achieved.

Fig. 4 illustrates a motivating example in which the measurement bandwidth is $BW=450Hz$, and the noise profile in the system decreases inversely proportional to the frequency similar to pink noise with the optical sensing system’s noise density at $f=400Hz$ being about $6dB$ lower than at $f=200Hz$.

Figure 4:

PSD of simulated PPG signal received from activating LED with various pulse train configuration

In this example, if the LED signal is pulsated with a pulse train with the duty cycle of $d=50\%$, clearly selecting the pulse frequency at $f_0=400Hz$ outperforms the selection of $f_0=200Hz$, since the received signal is unchanged between these two cases. Still, a lower noise floor is observed at $400Hz$. However, the narrative is different when introducing a different pulse train with a duty cycle of $d=20\%$, and 2.5× the emitted power.

For the sake of this comparison, a simulated pulse train with parameters of $d=50\%,f_0=400Hz$, and $I=1$ is compared against a simulated pulse train with parameters of $d=20\%,f_0=200Hz$, and $I=2.5$, in terms of expected tissue signal SNR, assuming that the higher amplitude does not exceed the maximum power provided by the LED. The two configurations have the same average emitted optical power since the $I.d$ product is constant in both cases and $P_E\propto Id$ as discussed in section 3.1.

The SNR of the fundamental harmonic of the pulse train with $d=50\%$ and $f_0=400Hz$ is $1.62dB$ higher than that of the pulse train with $d=20\%$ and $f_0=200Hz$. However, after combing both the fundamental and the second harmonic of the measurement collected with the latter pulse train, the average SNR improvement is about $6dB$ higher than the SNR of the 50% pulse point captured within the $500Hz$ measurement bandwidth.

A pulse train choice of $d=50\%,f_0=200Hz$, and $I=1$ is omitted in this comparison since it will clearly underperform compared to the aforementioned pulse train with a set selection of $d=20\%,f_0=200Hz$, and $I=2.5$.

This demonstrates why a seemingly inferior choice of selecting a pulse frequency right on the flicker noise slope would outperform selecting a pulse frequency on the tail of flicker noise due to utilizing multiple harmonics captured within the bandwidth of the data acquisition system.

5. TISSUE SIGNAL REPLICAS AND THEIR COMBINATION

The frequency-modulated setup depicted in fig. 3 is adopted in which the tissue signal has scaled replicas at multiple frequencies in the spectrum. By reformatting eq. (1), let $y(t)=s(t)+n(t)$ be the sensed PPG signal, which is the sum of the tissue signal, $s(t)$, and the total noise contribution to the acquired data, $n(t)$. The tissue and noise signals are conceptually composed of constituting signals that make up the scaled replicas in the spectrum, i.e., $y(t)=\sum y_i(t)$ where $y_i(t)=s_i(t)+n_i(t)$. Here $s_i(t)$ is the $i$ ’th PPG signal replica that is modulated to $i{f}_0$ with the power of $\overline{s_i^2(t)}$. Similarly, $n_i(t)$ refers to the noise present around $i{f}_0$ in the spectrum, whose power is given by $E\left[n_i^2(t)\right]$. Thus, the SNR of the $i$ ‘th tissue signal $y_i(t)$ can be formulated as ${\text{SNR}}_i=\overline{s_i^2(t)}/E\left[n_i^2(t)\right]$. Note that $s_i(t)$ and $n_i(t)$ are not correlated. In addition, the noise at each frequency band is also uncorrelated. That is, $E\left[n_i(t)n_j(t)\right]=0\text{if}i\ne j$.

Referring to the Fourier series of a given pulse train with a known amplitude, $I$, frequency, $f_0$, and duty cycle, $d$, from eqs. (1) and (2), the power of each tissue signal replica modulated at the $i$ ‘th harmonic of $f_0$ is given by

$$\overline{s_i^2(t)}=L^2{I}^2{d}^2{\mathit{\text{sinc}}}^2(id)\overline{x^2(t)}$$

The following scenarios about the profile of noise that impacts data acquisition are considered:

• In the first scenario, the noise has a white Gaussian noise (WGN) profile with the distribution of $N\left(0,{\sigma }_N^2\right)$ for which its frequency-independent PSD is defined as $N(f)={\sigma }_N^2=N_0$. In this case, $E\left[n_i^2(t)\right]=N_0$, and SNR of the $i$ ’th tissue signal copy can be formulated as:

  $${\text{SNR}}_i=\frac{L^2{I}^2{d}^2{\mathit{\text{sinc}}}^2(id)}{N_0}\overline{x^2(t)}$$ (3)
• A more realistic scenario, considered next, is that on top of WGN, a pink noise with a given PSD of $N(f)=N_1/f^{\beta }$ impacts the system. Here $N_1$ is noise power at $f=1Hz$, and $\beta$ models the steepness of noise power decline with an increase in frequency, where typically $0<\beta <2$ [26]. Such a noise profile would dominate WGN noise sources at lower frequencies, and at frequencies higher than the corner frequency, $f_c$, the noise PSD would be dominated by the WGN component. As such, the SNR of the tissue signal copy at $i{f}_0$ would depend on the frequency:

  $${\text{SNR}}_i=\left\{\begin{array}{lll}\frac{L^2{A}^2{d}^2{\mathit{\text{sinc}}}^2(id)}{\frac{N_1}{i{f}_0}}\overline{x^2(t)}& \text{if}& i{f}_0<f_c\\ \frac{L^2{A}^2{d}^2{\mathit{\text{sinc}}}^2(id)}{N_0}\overline{x^2(t)}& \text{if}& i{f}_0\ge f_c\end{array}\right.$$ (4)

When the frequency of light source pulsation $\left(f_0\right)$ is within the data acquisition system’s bandwidth, at least one copy of the tissue signal exists in the received signal spectrum. If multiple signal replicas are present in the measurement bandwidth, one can leverage the correlation among replicas to improve the SNR of the target PPG signal. The term spectral averaging is used to refer to the idea, which is particularly promising for deep tissue optical sensing, where tissue signals are faint, and the data acquisition system is likely to have a high bandwidth relative to the LED toggling frequency.

Conceptually, spectral averaging requires extraction of signal replicas from different bands of the spectrum, which can be accomplished through standard steps of band-pass filtering of bands of interest centered around each harmonic of the pulse train $\left(i{f}_0\right)$, followed by demodulation of the filtered output via the synchronous detection technique [10]. This technique relies on demodulating the tissue signal from a superposition of a phase-synced sine (in-phase component) and cosine waves (quadrature component) [28]. After extraction of tissue signal replicas, the correlation of tissue signal present across copies can be leveraged through an information fusion algorithm to improve SNR. It should be noted that there are on-phase discrepancies between the extracted tissue signal replicas.

Frequency division combining is one such fusion algorithm. It averages the extracted tissue signals from each frequency band in the spectrum, where frequency-divided branches from the received signal are coherently combined, using different weights, to enhance the SNR of the signal of interest [15]. This approach assumes that enough copies of the tissue signal over multiple harmonics of $f_0$ exist to yield a measurable improvement compared to the baseline case of signal extraction from $f_0$. Note that the extracted copies of the tissue signal will have no phase difference since the same tissue signal is being modulated using synchronized carrier frequencies.

Specifically, the weight of $w_i$ is assigned to the tissue signal copy extracted from $i.f_0$. Thus, the combined received PPG signal can be formulated as $y_{\Sigma }(t)=s_{\Sigma }(t)+n_{\Sigma }(t)$ where $s_{\Sigma }(t)=\sum w_i{s}_i(t)$ is the combined tissue signal with the power of $\overline{s_{\Sigma }^2(t)}$, and the combined noise being $n_{\Sigma }(t)=\sum w_i{n}_i(t)$ with the power of $E\left[n_{\Sigma }^2(t)\right]$. Since noise over each frequency band is uncorrelated, the total combined noise power can be simplified to $E\left[n_{\Sigma }^2(t)\right]=\sum _i{w}_i^{2}E\left[n_i^2(t)\right]$. As such, the SNR of the weighted averaging method is given by:

$${\text{SNR}}_{\Sigma }=\frac{\overline{s_{\Sigma }^2(t)}}{E\left[n_{\Sigma }^2(t)\right]}=\frac{\overline{{\left(\sum _i{w}_i{s}_i(t)\right)}^2}}{\sum _i{w}_i^{2}E\left[n_i^2(t)\right]}$$ (5)

Assigning appropriate weights to each tissue signal copy is essential for maximizing the SNR of the combined signal. Intuitively, one would expect that signal replicas with higher SNR should play a more significant role in the averaging process. It is proven that Maximal-Ratio Combining is the optimal method of weight assignment, in the sense that it yields the highest SNR [22]. Specifically, the optimal weight for each signal replica is $w_i=\sqrt{{\text{SNR}}_i}$, where ${\text{SNR}}_i$ can be estimated for each signal copy from eq. (3) or eq. (4) depending on the system and ambient noise profile. As such, the improvement in the averaged signal SNR is calculated to be the summation of all extracted tissue signal replicas from $f_0,2f_0,\dots ,i{f}_0$ and the optimal averaged SNR is ${\text{S}\widehat{\text{NR}}}_{\Sigma }=\sum _i{\text{SNR}}_i$ [15,22].

6. IMPROVING SNR IN LIMITED BANDWIDTH

The PPG signal is sampled using a data acquisition system with a $F_s$ sampling rate and limited bandwidth of $BW$. The key point in this work is the assumption of a limited bandwidth, which implies that a limited number of captured harmonics can be employed. A weighted averaging with the maximal-ratio weighting technique is implemented to maximize the system performance. Here, the bandwidth directly affects the system’s performance since it enforces the maximum number of tissue signal copies captured in the system where $M=⌊BW/f_0⌋$ is the total number of copies. The assumptions in this paper are that first of all, $f_0$ is far higher than the frequency of the physical variations of interest in the deep tissue $\left(f_0\gg f_{\mathit{\text{sig}}}\right)$, and also, $BW$ is selected such that at least one tissue signal copy $i{f}_0$ is captured $(M\ge 1)$.

In this section, the optimal averaged tissue signal SNR is outlined, which is a function of the frequency $\left(f_0\right)$ and the duty cycle $(d)$ of the source optical signal and the number of harmonics captured in the bandwidth $(M)$. While tuning the duty cycle of the LED pulse signal, it is crucial to note that the average power of the emitted optical signal will directly relate to $d$. Reducing $d$ will reduce the optical signal’s effectiveness in reaching the deep tissue, resulting in a lower SNR from the deep tissue signal. To compensate for this reduction in the average source-emitted optical power, the LED pulse signal amplitude is increased inversely proportional to the duty cycle, ensuring that the average emitted optical power remains constant throughout this optimization $(Id=\mathit{\text{const}}.)$.

As discussed in section 5, multiple noise behaviors are considered, and the optimal parameter selection is identified in the next section.

6.1. Optimal SNR in the Presence of White Noise

In this case, the noise PSD follows the form of $N(f)=N_0$, and SNR of tissue signal copy on $i{f}_0$ follow eq. (3). By applying the Maximal-Ratio weighted-averaging technique in the case of WGN, the optimal ${\text{SNR}}_{\Sigma }$ will be:

$${\text{S}\widehat{\text{NR}}}_{\Sigma }=\sum _{i=1}^M{\text{SNR}}_i=\frac{L^2\overline{x^2(t)}{I}^2{d}^2}{N_0}\sum _{i=1}^M{\mathit{\text{sinc}}}^2(id)$$ (6)

In eq. (6), there is no dependency on the value of $f_0$ but instead on the number of harmonics $i{f}_0$ captured. Since the average emitted optical power is kept constant, $I^2{d}^2$ term will also be consistent throughout the optimization process. Thus, the optimal ${\text{SNR}}_{\Sigma }$ will only depend on the duty cycle of the LED pulse signal $(d)$ as well as the number of total harmonics $M$ captured within the data acquisition system’s bandwidth.

6.2. Optimal SNR in the Presence of Pink Noise

In observance of “flicker” or “pink noise,” the Noise PSD follows various patterns throughout the frequency spectrum. As pointed out, the noise pattern is consistent until a corner frequency $\left(f_c\right)$ is observed, at this point, the noise PSD is constant. Consequently, the optimal ${\text{SNR}}_{\Sigma }$ improvement is considered in two possible cases depending on the bandwidth of the system and the corner frequency of the noise in the system based on the formulation in eq. (4):

• $BW\le f_c$ : The bandwidth is below the corner frequency, meaning the noise PSD will be $N(f)=N_1/f^{\beta }$. For simplicity, $\beta =1$ is assumed, which means the noise PSD drops linearly in the log scale as frequency increases towards the corner frequency. As such by applying the Maximal-Ratio weighting technique to eq. (5), the optimal ${\text{SNR}}_{\Sigma }$ is:

  $${\text{S}\widehat{\text{NR}}}_{\Sigma }=\frac{L^2\overline{x^2(t)}{I}^2{d}^2{f}_0}{N_1}\sum _{i=1}^{M}i{\mathit{\text{sinc}}}^2(id)$$ (7)

  In eq. (7), the optimal ${\text{SNR}}_{\Sigma }$ directly correlates to the value of the fundamental frequency of the pulse in addition to the number of harmonics captured within the bandwidth and the duty cycle.
• $BW>f_c$: The optimal ${\text{SNR}}_{\Sigma }$ can be derived in this scenario based on the fact that the noise in the system has two patterns depending on the locations of $i{f}_0$ in the frequency spectrum with respect to corner frequency of the pink noise $\left(f_c\right)$. Here $\beta =1$ is also assumed, and as such, the optimal ${\text{SNR}}_{\Sigma }$ will be a combination of eqs. (6) and eq. (7). The objective in this case is:

  $${\text{S}\widehat{\text{NR}}}_{\Sigma }=\frac{L^2\overline{x^2(t)}{I}^2{d}^2{f}_0}{N_1}\sum _{i=1}^{K}i{\mathit{\text{sinc}}}^2(id)+\frac{L^2\overline{x^2(t)}{I}^2{d}^2}{N_0}\sum _{i=K+1}^M{\mathit{\text{sinc}}}^2(id)$$ (8)

  In eq. (8), the objective function has been divided into two portions, one with a total of $K$ harmonics placed before $f_c$ where the noise observed is a pink noise with $1/f$ pattern, and the other with $M-K$ harmonics placed after $f_c$ until the system’s bandwidth where the noise observed is WGN. So, the optimal ${\text{SNR}}_{\Sigma }$ not only depends on the selection of $f_0$ and $d$, same as the other two cases, but also on the actual noise power after the corner frequency $\left(N_0\right)$ and the noise power at $1Hz$ frequency $(N_1)$ which was discussed in section 5. This makes simplifying eq. (8) challenging and varies based on the actual noise observed, and thus, a closed-form solution cannot be devised to tackle this common case. It should be noted that any heuristic solution based on the relative values of observed $N_0$ and $N_1$ could very well be sub-optimal since other factors, such as the system’s bandwidth and location of the corner frequency, also affect the performance.

Hence, we propose JOIN in the next section, which is an algorithm designed to achieve maximum performance in a given noise behavior in real-world data acquisition systems under operating safety limits for the skin as well as the measurement bandwidth constraint of this system.

7. OPTIMIZATION OF PULSE FREQUENCY AND DUTY CYCLE USING JOIN

The previous section formulated the objective function for deep tissue sensing as the optimal received SNR. The proposed JOIN algorithm is adaptive in the sense that it considers the noise in the sensing modality and adjusts the parameters accordingly. The noise profile cannot be statically characterized, as the noise has a strong dependency on the sources that are external to the system, such as the environment in which the system is deployed. To address this issue, the noise in the measurement system is first characterized under no activated light, i.e., dark measurement conditions. The information is then utilized by the JOIN algorithm to tune the light source activation signal for optimized performance in that environment. Stated differently, the method is context-aware in the sense that the generated optimized configurations are influenced, in part, by the environment in which the system operates.

Fig. 5 sketches the high-level idea of this optimization task, leading to a multi-parameter optimization problem with a limitation enforced on the average optical source power and considering a realistically limited bandwidth of the data acquisition system $(BW)$. The objective is maximizing the optimal ${\text{SNR}}_{\Sigma }$ by tuning the duty cycle and fundamental frequency of the pulse signal by observing the noise pattern within the system bandwidth as seen below:

$$\begin{gathered} \text{max}\text{S}{\widehat{\text{NR}}}_{\Sigma } \\ \text{s.t.}{P}_E\le \rho , \\ M{f}_0\le BW, \\ A\le A_{\mathit{\text{max}}} \end{gathered}$$ (9)

Figure 5:

High-level idea of using JOIN for the optimizing the optimal ${\text{SNR}}_{\Sigma }$.

As seen in In eq. (9), this problem has multiple constraints. One such constraint is the maximum number of harmonics observed, which has to be below the system’s bandwidth. The next constraint arises from the safety concerns of any optical sensing application and makes sure the average emitted optical power $P_E$ is limited to $\rho$. As explained in section 3.1, $P_E$ depends on both $I$ and $d\left(P_E\propto I_{FD}d\right)$, which means to keep $P_E$ under control $I$ and $d$ must be adjusted inversely proportional, that is if $I$ is increased, $d$ must decrease. For relaxing this, the first and the third constraints in the following exploration, the product of $I$ and $d$ is kept constant $(Id=\Gamma )$, which means the average emitted optical power is constant $\left(P_E=\rho \right)$. A real wearable system has a limitation on the maximum current supplied to the LED. This caps the LED forward current to $I_{\mathit{\text{max}}}$ and further constrains the optimization task. With the average LED current kept constant, the minimum duty cycle will have a lower bound of $d\ge d_{\mathit{\text{min}}}=\Gamma /I_{\mathit{\text{max}}}$.

For further simplification, the bandwidth limitation $M\le BW/f_0$ is relaxed to $M=⌊BW/f_0⌋$ by selecting a $f_0$ which is an integer divisor of $BW$. This means the last captured harmonic is the $M^{\mathit{\text{th}}}$ harmonic in the measurement bandwidth $M{f}_0<BW$. To make the comparison easier, all ${\text{SNR}}_{\Sigma }$ have been normalized to a baseline case where $d=50\%,M=1$, and $P_E=\rho$. It is pivotal to point out that by changing the duty cycle of the pulse, the amplitude of the pulse is tuned inversely proportional $(I\propto 1/d)$ to keep transferred optical energy into the tissue constant as explained in section 6. The underlying assumption for this optimization problem is that all the optical power from the LED is transmitted to the body, and the tissue’s loss to the input light is constant throughout the frequency spectrum.

Thus, the background noise has different possibilities, and the optimization must be analyzed in multiple settings, as the formulation of the objective function differs for each case.

7.1. JOIN in White Noise

Fig. 6 illustrates the theoretical ${\text{SNR}}_{\Sigma }$ improvement using the JOIN algorithm in the case of WGN. It is inferred that the best performance is achieved if the duty cycle $d$ is decreased while $I$ increases proportionally, so we assume $Id=\Gamma$ is constant. In addition, since in the presence of WGN, noise does not change over frequency, it is more beneficial to select $f_0$ at a smaller fraction of $BW$ so that more harmonics are captured in the data acquisition system’s bandwidth, hence improving the system’s performance. In fig. 6, it is observed that ${\text{S}\widehat{\text{NR}}}_{\Sigma }$ improves with different rates for various duty cycles compared to the baseline of ${\text{S}\widehat{\text{NR}}}_{\Sigma }(d=1/2,I=2\Gamma )$. In the presence of WGN, using JOIN, about $M$ fold improvement is achieved compared to improvements seen in the state-of-the-art deep tissue optical sensing using the BASS algorithm [33] for all duty cycle selections where equal weights were assigned to each tissue signal copy extracted and the combined tissue signal SNR was $\sum {\text{SNR}}_i/M$. The red curve illustrates the theoretical optimal ${\text{S}\widehat{\text{NR}}}_{\Sigma }\left(d,I,f_0\right)$ in the case of WGN $\left({\text{SNR}}_{\Sigma }^{*}\right)$.

Figure 6:

Theoretical ${\text{S}\widehat{\text{NR}}}_{\Sigma }$ improvement compared to ${\text{S}\widehat{\text{NR}}}_{\Sigma }(d=1/2,I=2\Gamma )$ for various duty cycles and pulse frequency selection in case of WGN.

$$\begin{gathered} \text{max}{\text{S}\widehat{\text{NR}}}_{\Sigma }\left(d,I=\Gamma /d,f_0=BW/M\right) \\ =\frac{L^2\overline{x^2(t)}{I}^2{d}^2}{N_0}\sum _{i=1}^M{\mathit{\text{sinc}}}^2(id) \end{gathered}$$ (10)

The maximum performance is achieved if a very small duty cycle is selected while the fundamental frequency is closer to DC. Fig. 6 visualizes an example for the white noise case and $d$ in 5% to 50% range, in which the optimal parameters lie on a vertical line associated with the lowest possible fundamental frequency, as it increases the number of harmonics captured within the system’s bandwidth.

7.2. JOIN in Pink Noise

Here, the optimization problem is analyzed in two cases:

• $BW\le f_c$: In the Pink noise scenario, having a fundamental frequency closer to DC is penalized by the high noise in the DC range of the frequency spectrum. Based on the relaxation of $BW=M{f}_0$, the formulation in eq. (7), which is dependent on the value of $f_0$, is reformulated to eq. (11).

  $$\begin{gathered} \text{max}{\text{S}\widehat{\text{NR}}}_{\Sigma }\left(d,I=\Gamma /d,f_0=BW/M\right) \\ =\frac{L^2\overline{x^2(t)}{I}^2{d}^{2}BW}{M{N}_1}\sum _{i=1}^{M}i{\mathit{\text{sinc}}}^2(id) \end{gathered}$$ (11)

  Equation (11) does not depend on the value of $f_0$ but rather on the selection of $f_0$ with respect to $BW$. As seen in fig. 7, for most of duty cycle selections, there is no reward for choosing a very small $f_0$ to capitalize on combining all tissue signal copies. This is due to the fact that a small selection of the pulse frequency places more harmonics of $i{f}_0$ closer to DC, where the pink noise is expected to be stronger, which ultimately reduces the effectiveness of the weighted averaging scheme. This scenario is studied closer for $d$ in the 5% to 50% range. In this case, i.e., for pink noise, the optimal parameters lie on the red curve shown in fig. 7.
• $BW>f_c$ : In the case of $BW\ge f_c$, the optimization problem can be divided into two optimizations of the terms seen in eq. (8) since both summation terms are non-negative, which means the objective function can be captured as:

  $$\begin{gathered} \text{max}\frac{L^2\overline{x^2(t)}{I}^2{d}^2{f}_0}{N_1}\sum _{i=1}^{K}i{\mathit{\text{sinc}}}^2(id), \\ \text{max}\frac{L^2\overline{x^2(t)}{I}^2{d}^2}{N_0}\sum _{i=K+1}^M{\mathit{\text{sinc}}}^2(id) \end{gathered}$$ (12)

  Since there are dependencies between these two terms, the optimization is not as straightforward as in previous cases, and the design space exploration technique can be utilized to maximize this objective, similar to seen in [11, 13]. For the general case, the JOIN algorithm can be represented using the pseudo-code as seen in Algorithm 1. It’s important to note that the average emitted optical power is set to a constant value, and by adjusting the duty cycle, the amplitude of the pulse signal is increased proportionally. Careful attention needs to be paid to whether the LED pulsation is achievable with higher amplitudes of the pulse signal, knowing the real-world LED drivers have limited power they can generate.

Figure 7:

Theoretical ${\text{S}\widehat{\text{NR}}}_{\Sigma }$ improvement compared ${\text{S}\widehat{\text{NR}}}_{\Sigma }(d=1/2,I=2\Gamma )$ for various duty cycles and pulse frequency selection in case of “Pink noise” and $BW<f_c$.

Algorithm 1.

JOIN

1:	Observe and sample the noise behavior in the measurement system
2:	Set $P_E=\rho$ and hence $Ad=\Gamma$
3:	Initialize ${\text{SNR}}_{\Sigma }^{*}={\text{S}\widehat{\text{NR}}}_{\Sigma }\left(d=1/2,A=2\Gamma ,f_0=BW\right)$
4:	for $d=1/\mathrm{2,1}/\mathrm{3,1}/4,\dots ,d_{\mathit{\text{min}}}$ do
5:	for $f_0=BW,BW/2,BW/3,\dots$ do
6:	Calculate ${\text{S}\widehat{\text{NR}}}_{\Sigma }$ with selected $f_0,d$, with $A=\Gamma /d$
7:	if ${\text{S}\widehat{\text{NR}}}_{\Sigma }>{\text{SNR}}_{\Sigma }^{*}$ then
8:	Set ${\text{SNR}}_{\Sigma }^{*}={\text{S}\widehat{\text{NR}}}_{\Sigma }$
9:	Set $\left(d^{*},A^{*},f_0^{*}\right)=\left(d,A,f_0\right)$
10:	end if
11:	end for
12:	end for
13:	$\left(d^{*},A^{*},f_0^{*}\right)$ are the optimal light source activation selections with optimal achievable combined SNR of ${\text{SNR}}_{\Sigma }^{*}$

8. RESULT

The proposed method in this paper is validated through two sets of empirical methods. Firstly, in a bench-top experiment, a highpower LED is emitted onto an optical tissue phantom that mimics human tissue’s properties. The optical signal is carried via a light guide to a known distance from the photo-detectors on the optical probe (Optode), which is also placed on the tissue phantom. This setup is supposed to simulate a real-world deep tissue system where the PPG signal from the deep tissue is received at the surface. The benefits of this testing modality are the controlled nature of the test and the ability to tune the light source parameters with a desired $f_0,d$, and $I$. Furthermore, the system is employed in-vivo in an actual measurement on a pregnant patient to serve the purpose of deep tissue sensing in non-invasive detection of the fetal heart rate signal. Fig. 9 illustrates the pink noise profile measured in the bench-top test environment. Fig. 11 visualizes the noise profile collected during the patient study, which has a profile similar to that of a WGN. In general, one might observe arbitrary noise characteristics that might not be similar to WGN or pink noise as exemplified in fig. 2. In the example noise PSD, the harmonics of electrical power lines make an appearance in the noise profile, as a classic example of an environmental noise source.

Figure 9:

PSD of noise observed in the test environment up to $BW=20Hz$.

Figure 11:

The Noise measurement in the human study up to 200Hz.

8.1. Demonstration on a Tissue Phantom

A custom-made optical tissue phantom was created with a thickness of 5 cm to replicate the optical properties (including absorption and scattering) of maternal abdominal tissue during term pregnancy. The parameters for these optical properties were obtained from [20].

As illustrated in fig. 8, the optical probe and the light guide are both placed on the tissue phantom, and the measurement ran for about 10 minutes each with a sampling frequency of $F_s=8\mathit{\text{kSps}}$, and the wavelength of $\lambda =740nm$ was selected for the light. A snapshot from the noise in the system up to the bandwidth of $BW=20Hz$ is shown in fig. 9 where the corner frequency of flicker noise is observed to be at $f_c=10Hz$. Here, the observed system noise behavior is a combination of pink and white noise. For these measurements, the two duty cycles of $d=50\%,25\%,20\%,\text{and}10\%$ were selected with peak optical source powers of $120mW,240mW,300mW,\text{and}600mW$, respectively. The measurements were repeated for various pulse frequencies of $f=2.5Hz,5Hz,10Hz,\text{and}20Hz$ and both duty cycles. At these frequencies, the observed noise floor is $-120dB,-122.5dB,-124dB,\text{and}-126dB$, respectively.

Figure 8:

The optical probe placed on a tissue phantom with a light guide placed through.

Assuming a constant loss in the tissue phantom at all selected frequencies and optical powers, the JOIN algorithm is applied to the harmonics of the received PPG signal. Since the tissue phantom has no physiological variations, no tissue signals will be observed; instead, only the peak received signal and each harmonic are considered. Also, it should be noted that the values here are relatively high due to the fact that the signal measured is only the light source carrier signal, and there are no actual pulsations happening in the phantom.

Table 1 shows the ${\text{S}\widehat{\text{NR}}}_{\Sigma }$ results during the bench-top measurements. Here, for a select pulse frequency $\left(f_0\right)$, the results show a consistent improvement if a lower duty cycle (and higher amplitude) is selected. Overall, the selection of $f_0=5Hz$ with $d=10\%$ has the best SNR since within the bandwidth of 20Hz, four harmonics are captured, and the harmonics are relatively away from the Pink noise high noise region. This is the exact reason why the selection of $f_0=2.5Hz$ is inferior to $f_0=5Hz$. Whereas, if the noise observed was WGN, the best strategy would be to select $f_0$ as close as possible to dc. Also, within the same duty cycle, sometimes it is best if a higher pulse frequency is selected to move away from the noise, same as using $d=50\%$ where placing $f_0$ further away from the corner frequency of pink noise $(f_c=10Hz)$ is optimal. The results observed in the bench-top measurement confirm the observations in fig. 7 for the most part, as the measurement environment is controlled. This will not be the case in the real-world measurements, as will be discussed below.

Table 1:

${\text{S}\widehat{\text{NR}}}_{\Sigma }$ measurements for various fundamental frequencies and duty cycle selections during bench-top measurements on a tissue phantom within $BW=20Hz$.

		Pulse frequency
		$f_0=2.5Hz$	$f_0=5Hz$	$f_0=10Hz$	$f_0=20Hz$
Duty Cycle	$d=10\%$	$34.73dB$	35.15dB	$33.37dB$	$31.49dB$
	$d=20\%$	$30.51dB$	$31.88dB$	32.37dB	$31.27dB$
	$d=25\%$	$28.86dB$	$30.21dB$	31.46dB	$30.93dB$
	$d=50\%$	$23.16dB$	$24.94dB$	$25.67dB$	27.67dB

8.2. Demonstration in a Human Subject

This proposed method was applied to detect the Fetal Heart Rate (FHR) during a pregnant patient’s antenatal visit. The protocol for this study was approved by UC Davis Institutional Review Board (IRB), and both the Optical Probe as well as other sensors, such as the fetal ultrasound-based Cardiotocography (CTG) sensor, which is typically used during the patient’s Non-Stress Test (NST). Fig. 10 shows the probe placement and CTG sensor next to each other on the patient’s belly. In this case study, the depth of the closest fetal tissue to the maternal skin is $1.8cm$, and simultaneous data is captured using the CTG sensor alongside the TFO system.

Figure 10:

The optical probe and ultrasound CTG sensor are placed on the abdomen of a pregnant subject. An elastic fabric is used to hold the sensors in place.

LED’s light with a wavelength of $\lambda =690nm$ traverses maternal tissues, and photo-detectors on TFO receive the PPG signal reflected from the deep fetal tissue on the skin surface. Since the allowed measurement time during this study was short, only four sets of design parameters could be validated in the human study. The duty cycles of $d=50\%\text{and}20\%$ were selected for the LED pulse signal with peak optical powers of $326mW$ and $815mW$, respectively.

Also, since the observed noise floor of the system was flat throughout the frequency as illustrated in fig. 11, higher pulse frequencies were selected compared to the bench-top study with selected pulse frequencies of $f_0=190Hz$ and $50Hz$. Since the noise observed is a WGN pattern, it is optimal to move $f_0$ towards DC and use a low-duty cycle with an appropriate amplitude to capture as many harmonics as possible within the bandwidth.

In this experiment, the signal from deep tissue of interest is associated with the fetal heart rate, which can be observed by a trace that lies between $1.8Hz$ and $2.33Hz$ in the spectrogram of captured data in fig. 12a. The highlighted fetal heart rate signal in the optical data spectrogram corresponds to 108 to 140 bpm and matches the ground truth fetal heart rate, collected via ultrasound and illustrated in fig. 12.

Figure 12:

Fetal information extracted during data collection in the human study compared to the ground truth.

The maternal heart rate is at 78 bpm in the study, which can be inferred from the data in fig. 12a. The measurement results for ${\text{S}\widehat{\text{NR}}}_{\Sigma }$ after using the JOIN algorithm are presented in table 2 with optimal parameters of $d=20\%$ and $f_0=50Hz$ with SNR of $9.18dB$ after applying JOIN. In fig. 12a, the spectrogram of weighted-averaged measurement data is presented, which was made using the optimal parameters obtained after applying JOIN on the data captured from the patient using TFO.

Table 2:

${\text{S}\widehat{\text{NR}}}_{\Sigma }$ measurements for various fundamental frequencies and duty cycle selections in the human study.

		Pulse frequency
		$f_0=50Hz$	$f_0=190Hz$
Duty Cycle	$d=20\%$	9.18dB	$3.61dB$
	$d=50\%$	$4.31dB$	5.75dB

An irregularity observed in the data is the drop in SNR when moving from $f_0=190Hz$ and $d=50\%$ to $f_0=190Hz$ and $d=20\%$ where a small improvement is expected based on fig. 6 but most likely, due to the dynamic nature of the environment and movements from the mother or the baby this feat is not achieved. This is a shortcoming of power spectrum-based measurements since disturbances such as motion artifacts will affect the results.

9. DISCUSSION

It should be noted that JOIN works best if there is a high noise floor in the DC range in a low bandwidth setting, the same as the measurements on the test bench. If the data acquisition system can capture multiple harmonics in the PPG signal, selecting the fundamental frequency further into the frequency spectrum would be optimal to deal with only WGN. In addition, the weighted-averaging technique used in JOIN will add to the optical receiver system’s complexity since, for every branch, SNR needs to be calculated first before applying the weighted averaging technique.

In Table 3, multiple SNR improvement methods in deep tissue optical sensing systems are compared. The ANC-based techniques, as seen in [4, 12] rely on a reference noise measurement to tune the noise cancellation parameters, which makes them context-aware. Also, these methods can be considered real-time with a small delay used to tune the parameters. However, these methods work only on captured signals, which means they cannot directly tune the light source activation. The time-domain averaging techniques described in [7] require multiple time-series segments for coherent averaging and noise suppression[31]. This necessitates capturing data over an extended period and segmenting it into smaller time windows, making the process not real-time. In addition, these methods assume the noise to be constant between the multiple measurements; hence, they are not context-aware. Furthermore, similar to ANC-based methods, no adjustments are made to the light source parameters. The method proposed in BASS [33] tunes the light source activation parameters; however, it considers noise to be constant and WGN. As a result, unlike JOIN, it does not address the dynamic and environmentaldependent nature of noise.

Table 3:

High-level comparison of noise suppression methods in deep tissue optical sensing systems.

Method	Real-time	Light Source Control	Context-aware	Ref.
Adaptive Noise Cancellation	Yes	No	Yes	[4, 12]
Time-domain Segment Averaging	No	No	No	[7]
BASS	Yes	Yes	No	[33]
JOIN	Yes	Yes	Yes	This Work

10. CONCLUSION

In this work, we have explored some challenges associated with noise in the system in deep tissue optical sensing using wearables. The various noise patterns in the system were studied, and the benefits of using spectral copies of the tissue signal were analyzed. We discussed the benefits of combining the tissue signal copies with appropriate weights to improve the performance of the deep tissue signal sensing.

Next, the system’s SNR was formulated and optimized using the JOIN scheme. The pulse duty cycle and frequency were tuned to change the number and positions of the signal copies throughout the frequency spectrum with respect to the optical receiver’s bandwidth. The methodology in this paper was validated using controlled bench-top measurements with a known noise pattern. Lastly, this technique was applied to sensing the fetal signal non-invasively in an in-vivo testing on a pregnant patient. The sensing of the fetal signal in the presence of a high noise floor in the human study highlights the advantages of using the proposed method.

CCS CONCEPTS.

• Computer systems organization → Embedded systems; • Applied computing → Life and medical sciences.