Frédéric Bousefsaf

Djamaleddine Djeldjli

Yassine Ouzar

Choubeila Maaoui

Alain Pruski

iPPG 2 cPPG: reconstructing contact from imaging photoplethysmographic signals using U-Net architectures

Keywords: imaging photoplethysmography, U-Net, blood volume pulse

teaching and research institutions in France or abroad, or from public or private research centers.

pulse waveform 1. Introduction In the recent years, research on contactless technologies dedicated to physiological signals measurement have made signicant progress [START_REF] Al-Naji | Monitoring of Cardiorespiratory Signal: Principles of Remote Measurements and Review of Methods[END_REF]. Photoplethysmography (PPG) can be remotely measured by observing the subtle uctuations of skin color. These uctuations reect complex light-tissue interactions, from which their origin is not fully agreed [START_REF] Volkov | Video capillaroscopy claries mechanism of the photoplethysmographic waveform appearance[END_REF]. The simplest cameras (webcams) to the most advanced ones (professional, laboratory or industrial cameras) can be used to reliably measure PPG signals [START_REF] Hassan | Heart rate estimation using facial video: A review[END_REF]. Different regions of interest (ROI) have been studied over time but the face remains the most frequently observed area [START_REF] Zaunseder | Cardiovascular assessment by imaging photoplethysmographya review[END_REF].

The eld is booming and supported by several signicant studies. Computer vision, image processing and articial intelligence (AI) methods have been used or developed specically to reliably transform input video into biomedical parameters [START_REF] Zaunseder | Cardiovascular assessment by imaging photoplethysmographya review[END_REF]. Numerous studies have shown that pulse rate and its variability can be estimated with high robustness. In this context, articial intelligence is playing an increasingly important role [START_REF] Ni | A Review of Deep Learning-Based Contactless Heart Rate Measurement Methods[END_REF] where the most ecient pulse rate measurement methods are now based on deep neural models [START_REF] Yu | AutoHR: A Strong Endto-End Baseline for Remote Heart Rate Measurement With Neural Searching[END_REF]. These architectures are often based on convolutional layers [START_REF] Zhan | Analysis of CNN-based remote-PPG to understand limitations and sensitivities[END_REF] and can be trained with synthetic data [START_REF] Bousefsaf | 3D Convolutional Neural Networks for Remote Pulse Rate Measurement and Mapping from Facial Video[END_REF] reinforced by real data [START_REF] Niu | Synrhythm: Learning a deep heart rate estimator from general to specic[END_REF].

Current research in this eld is now directed towards the measurement of new physiological parameters such as oxygen saturation [START_REF] Moço | Pulse oximetry based on photoplethysmography imaging with red and green light[END_REF] and blood pressure [START_REF] Luo | Smartphone-based blood pressure measurement using transdermal optical imaging technology[END_REF]. They impact the amplitude and waveform of PPG signals over dierent wavelength ranges. Blood pressure estimation based on video analysis is complex and very few works show its feasibility. Two research directions are considered. First, measurement of the pulse transit time (PTT) on single [START_REF] Sugita | Contactless Technique for Measuring Blood-Pressure Variability from One Region in Video Plethysmography[END_REF] or several [START_REF] Fan | Robust blood pressure estimation using an RGB camera[END_REF] ROI. PTT is a parameter considered to be correlated with blood pressure. Secondly, analysis of the PPG signal waveform [START_REF] Luo | Smartphone-based blood pressure measurement using transdermal optical imaging technology[END_REF]. To our knowledge, deep learning techniques based on video analysis have not been considered for the estimation of blood pressure yet.

Training an articial neural network that accurately estimates blood pressure from video is constrained by the amount of available data because few public databases exist. Djeldjli et al. recently showed that temporal, derivative and area features computed from imaging PPG (iPPG) waveform and contact sensor (placed on the nger or the ear) evolve similarly [START_REF] Djeldjli | Remote estimation of pulse wave features related to arterial stiness and blood pressure using a camera[END_REF]. This point is important because it motivates the present study. We envisage estimating BP with a two-stage processing chain. A model dedicated to the conversion of iPPG signals to contact PPG (cPPG) signals using available video dataset corresponds to the rst part of the processing chain. The second stage consists in constituting a deep learning model dedicated to blood pressure estimation from these converted signals by exploiting large existing databases (e.g. MIMIC [START_REF] Goldberger | Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals[END_REF]).

The developments related to the rst stage are presented in this study. To add more details, we propose to train a deep U-shaped neural architecture (U-Net) dedicated to the conversion of contact PPG signals from imaging PPG signals simultaneously measured on the face by conventional video analysis. Continuous wavelet representation of the signals is employed to take advantage of transfer learning through pretrained backbones on large databases. To the best of our knowledge, this is the rst demonstration of a method for accurate reconstruction of cPPG from iPPG signals.

The article includes ve additional sections. Section 2 presents the background and related works. Section 3 introduces the used data and the developed methodologies. The metrics and results of the proposed approach are presented and discussed in section 4. We present the future works and a summary of the contributions in sections 5 and 6, respectively.

Related works

This section reviews the studies that exploit deep learning for iPPG analysis as well as conventional and deep learning approaches for blood pressure assessment from both iPPG and cPPG.

Deep Learning for iPPG signal and pulse rate estimation

Relevant surveys in the imaging PPG eld of research have been proposed the last past years [START_REF] Al-Naji | Monitoring of Cardiorespiratory Signal: Principles of Remote Measurements and Review of Methods[END_REF][START_REF] Hassan | Heart rate estimation using facial video: A review[END_REF][START_REF] Zaunseder | Cardiovascular assessment by imaging photoplethysmographya review[END_REF]. They cover conventional techniques that generally include both image and signal processing approaches to improve PPG signal-to-noise ratio and therefore the estimation of biomedical parameters like pulse and breathing rates. Video and image processing operations like face detection, tracking of region(s) of interest and skin segmentation have been employed [START_REF] Po | Block-based adaptive ROI for remote photoplethysmography[END_REF][START_REF] Bousefsaf | Automatic Selection of Webcam Photoplethysmographic Pixels Based on Lightness Criteria[END_REF][START_REF] Bobbia | Real-Time Temporal Superpixels for Unsupervised Remote Photoplethysmography[END_REF]. Constituting an iPPG signal from a sequence of frames is usually carried out with a spatial averaging operation [START_REF] Verkruysse | Remote plethysmographic imaging using ambient light[END_REF]). Standard signal processing techniques include blind source separation approaches [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF], Fourier and Wavelet transforms [START_REF] Bousefsaf | Peripheral vasomotor activity assessment using a continuous wavelet analysis on webcam photoplethysmographic signals[END_REF]. The impact of color space on pulse rate assessment has also been investigated in previous research [START_REF] Wang | Algorithmic Principles of Remote PPG[END_REF][START_REF] Bousefsaf | Automatic Selection of Webcam Photoplethysmographic Pixels Based on Lightness Criteria[END_REF].

The most recent studies present articial intelligence through deep learning methods to automatically estimate the pulse signal or directly the pulse rate. These approaches currently deliver the best performances and present root mean squared errors between 2.7 and 3.8 beats per minute [START_REF] Ni | A Review of Deep Learning-Based Contactless Heart Rate Measurement Methods[END_REF] on public datasets like UBFC-RPPG [START_REF] Bobbia | Unsupervised skin tissue segmentation for remote photoplethysmography[END_REF], MAHNOB-HCI [START_REF] Soleymani | A multimodal database for aect recognition and implicit tagging[END_REF] and PURE [START_REF] Stricker | Non-contact video-based pulse rate measurement on a mobile service robot[END_REF]. Both hybrid and end-to-end approaches have been investigated. Hybrid strategies take either processed frames or iPPG signals as input and output the biomedical parameters of interest. End-to-end models takes a video (sequence of frames) as input and output the biomedical parameters.

Hybrid strategies combine conventional with deep learning methods. For instance, Qiu et al. developed a three-stage pipeline including face tracking, features extraction and nally pulse rate estimation based on a convolutional neural network (CNN) [START_REF] Qiu | EVM-CNN: Real-time contactless heart rate estimation from facial video[END_REF]. Hsu et al. proposed a deep CNN trained to predict pulse rate based on the timefrequency representation of processed iPPG signals [START_REF] Hsu | Deep learning with timefrequency representation for pulse estimation from facial videos[END_REF]. Chen et al. proposed DeepPhys [START_REF] Chen | Deepphys: Video-based physiological measurement using convolutional attention networks[END_REF] and DeepMag [START_REF] Chen | DeepMag: Source Specic Motion Magnication Using Gradient Ascent[END_REF], deep CNN trained to respectively predict pulse wave and magnify color variations produced by the periodic changes in blood ow. Inputs are transformed using a skin reection model while the convolutional layers are guided using attention masks to ensure the robust estimation of PPG signals under lighting uctuation and motion. They used a modied version of VGG, a model dedicated to object recognition in images [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF].

End-to-end strategies were recently investigated through dierent neural architectures: CNN-based extractor and estimator [START_REF] Petlík | Visual Heart Rate Estimation with Convolutional Neural Network[END_REF], 3D CNN [START_REF] Bousefsaf | 3D Convolutional Neural Networks for Remote Pulse Rate Measurement and Mapping from Facial Video[END_REF][START_REF] Yu | Remote Photoplethysmograph Signal Measurement from Facial Videos Using Spatio-Temporal Networks[END_REF][START_REF] Perepelkina | Heart-Track: Convolutional Neural Network for Remote Video-Based Heart Rate Monitoring[END_REF], combination of CNN and long short-term memory [START_REF] Yu | Remote Photoplethysmograph Signal Measurement from Facial Videos Using Spatio-Temporal Networks[END_REF][START_REF] Lee | Meta-rppg: Remote heart rate estimation using a transductive meta-learner[END_REF], CNN and gated recurrent unit [START_REF] Niu | RhythmNet: End-to-end Heart Rate Estimation from Face via Spatial-temporal Representation[END_REF], Siamese network including two branches with identical structure that analyze two dierent facial regions [START_REF] Tsou | Siamese-rPPG network: remote photoplethysmography signal estimation from face videos[END_REF] and temporal dierence convolution [START_REF] Yu | AutoHR: A Strong Endto-End Baseline for Remote Heart Rate Measurement With Neural Searching[END_REF]. These models have been trained with synthetic data [START_REF] Bousefsaf | 3D Convolutional Neural Networks for Remote Pulse Rate Measurement and Mapping from Facial Video[END_REF] reinforced by real data [START_REF] Niu | Synrhythm: Learning a deep heart rate estimator from general to specic[END_REF][START_REF] Perepelkina | Heart-Track: Convolutional Neural Network for Remote Video-Based Heart Rate Monitoring[END_REF]. They estimate the pulse signal [START_REF] Yu | Remote Photoplethysmograph Signal Measurement from Facial Videos Using Spatio-Temporal Networks[END_REF] or directly the pulse rate from a sequence of images.

Few studies investigated the interpretability and behavior of the models to understand the representations learned by the features. Zhan et al. studied this aspect by analyzing that CNN properly learn PPG during training [START_REF] Zhan | Analysis of CNN-based remote-PPG to understand limitations and sensitivities[END_REF]. They conclude that color variations produced by blood ow uctuations are correctly exploited by the neural networks.

Blood pressure assessment from iPPG

Both systolic and diastolic blood pressures (BP) have been estimated using the propagation time of pulse waves from two dierent skin areas (typically hand and face) in video recordings [START_REF] Sugita | Techniques for estimating blood pressure variation using video images[END_REF][START_REF] Jeong | Introducing contactless blood pressure assessment using a high speed video camera[END_REF]. The positional of the two skin areas must be maintained during the measurement. This approach is therefore very restrictive. The scientic literature covers few studies dedicated to the estimation of BP from a single facial region [START_REF] Jain | Face video based touchless blood pressure and heart rate estimation[END_REF][START_REF] Sugita | Contactless Technique for Measuring Blood-Pressure Variability from One Region in Video Plethysmography[END_REF][START_REF] Viejo | Non-Contact Heart Rate and Blood Pressure Estimations from Video Analysis and Machine Learning Modelling Applied to Food Sensory Responses: A Case Study for Chocolate[END_REF][START_REF] Sugita | Estimation of Absolute Blood Pressure Using Video Images Captured at Dierent Heights from the Heart[END_REF]. To the best of our knowledge, only the seminal work from Luo et al. [START_REF] Luo | Smartphone-based blood pressure measurement using transdermal optical imaging technology[END_REF] presents a pipeline that includes an articial intelligence model. They feed a multilayer perceptron with 155 features (reduced to 30 after principal component analysis) computed from iPPG waves. Their results show that PPG waveform extracted from video exhibits information that relates to BP. All these studies pointed out the feasibility of remote BP monitoring from facial video but showed that there is still room for improvements.

Blood pressure assessment from cPPG

Based on the current literature, there is clear evidence that the uctuations in BP are reected in cPPG signals [START_REF] Elgendi | On the analysis of ngertip photoplethysmogram signals[END_REF][START_REF] Von Wowern | Digital photoplethysmography for assessment of arterial stiness: repeatability and comparison with applanation tonometry[END_REF] even if estimating absolute BP values from cPPG remains a challenging problem. The changes in morphological contours due to interaction of other physiological systems make the extraction of features, and thus the estimation of BP, challenging but achievable [START_REF] Mousavi | Blood pressure estimation from appropriate and inappropriate ppg signals using a whole-based method[END_REF]. Exploration of deep learning techniques is here particularly interesting because it allows overriding of handcrafted features [START_REF] Ibtehaz | PPG2ABP: Translating Photoplethysmogram (PPG) Signals to Arterial Blood Pressure (ABP) Waveforms using Fully Convolutional Neural Networks[END_REF]. These features are somewhat restricted because the cPPG waveform uctuates from subject to subject and also because the ltering procedure can change its morphology [START_REF] Elgendi | The use of photoplethysmography for assessing hypertension[END_REF].

Several recent studies show that deep learning frameworks can eectively be deployed to translate BP from cPPG signals. Tanveer and Hasan proposed to associate articial neural network (ANN) with long short-term memory for BP estimation [START_REF] Tanveer | Cuess blood pressure estimation from electrocardiogram and photoplethysmogram using waveform based ANN-LSTM network[END_REF]. A similar network structure was proposed by Panwar et al. in 2020 [START_REF] Panwar | PP-Net: A Deep Learning Framework for PPG based Blood Pressure and Heart Rate Estimation[END_REF]. 1D CNN replace the ANN part from Tanveer and Hasan architecture. The network concurrently estimates diastolic BP, systolic BP and heart rate from a single cPPG signal. Chowdhury et al. then proposed to employ machine learning algorithms dedicated to BP estimation using cPPG signal and demographic features (e.g. weight and height) [START_REF] Chowdhury | Estimating Blood Pressure from the Photoplethysmogram Signal and Demographic Features Using Machine Learning Techniques[END_REF]. Time, frequency and time-frequency features were extracted from the PPG and their derivative signals. Feature selection techniques were used for reducing the computational complexity and simultaneously decreasing the chance of over-tting the machine learning algorithms. Slapnicar et al. introduced a similar framework but with a deep neural network architecture with residual connections [START_REF] Slapni£ar | Blood pressure estimation from photoplethysmogram using a spectro-temporal deep neural network[END_REF]. A part of the network is dedicated to the analysis of the signal spectral representation using gated recurrent units. Ibtehaz et Raman employed a deep learning based method that manages to predict the continuous BP waveform from cPPG signals. An approximation network learns a rough approximation of the BP waveform while a renement network further enhances the preliminary estimate. The approximation and renement networks are based on U-Net [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF].

Methods

Database and experimental protocol

The data used to learn the neural models (section 3.3) have been presented in a previously published article [START_REF] Djeldjli | Remote estimation of pulse wave features related to arterial stiness and blood pressure using a camera[END_REF]. 12 volunteers aged between 20 and 35 years participated to the study. The experiments were conducted in a dark room where the only source of light was two Neewer LED panels (NL480) set to 2700 lux / m with a color temperature of 3750 K (neutral white light). During the experiments, they were asked to seat at approximately 1 meter from a fast camera (16mm C Series Lens mounted on a EO-2223C Color camera from Edmund Optics). The recorded sequences of RGB images were save without compression at resolution 640 × 480 pixels (24 bits per pixel) and with a frame rate of 125 frames per second. Autoexposure and white balance have been disabled.

The ground truth cPPG signals were recorded using approved contact probes (BVP-Flex / Pro. By Thought Technologies Ltd.) placed on the nger and the ear. Two 60-second videos were recorded for every participant. First video: participants were asked to stay calm and breathe normally. Second video: participants were asked to hold their breath as much as possible, the objective being to cause physiological variations that modify blood pressure and impact the recorded PPG signals. We refer the reader to the original publication for more details concerning the procedure and the material used [START_REF] Djeldjli | Remote estimation of pulse wave features related to arterial stiness and blood pressure using a camera[END_REF]. The database contains 724 signals. Each of them contains 5 PPG waves (more details in section 3.2) dened over 256 values. About 80% of the data (600 signals) were reserved for training and 20% (124 signals) for testing. The sets contain a balanced portfolio of the dierent participants and tasks. We evaluated the models relevance through k-fold cross-validation (k=5). A fold contains 120 signals that are reserved for validation. The 4 remaining folds include 480 signals that are employed for training the neural models.

Image and signal processing

The forehead corresponds to a relevant area of interest in terms of signalto-noise ratio [START_REF] Bousefsaf | Automatic Selection of Webcam Photoplethysmographic Pixels Based on Lightness Criteria[END_REF]. This region has been automatically detected with a model composed of 68 points positioned on the main shapes of the face [START_REF] Kazemi | One millisecond face alignment with an ensemble of regression trees[END_REF]. These dierent points are tracked along the video. Some of them are used to nd the position of the forehead. In practice, algorithms for face and facial landmarks detection included in OpenCV1 and Dlib2 libraries have been employed.

iPPG signals are computed by averaging all the forehead pixels from the green channel. This technique has been used since the very rst publications related to the measurement of contactless PPG signals by camera [START_REF] Verkruysse | Remote plethysmographic imaging using ambient light[END_REF]. The raw iPPG signals are then detrended using a specic low-pass lter [START_REF] Tarvainen | An advanced detrending method with application to HRV analysis[END_REF] based on a smoothness priors that attenuates low frequencies [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF]. We then robustly detect the valleys to extract each PPG signal wave. Each signal is ultimately sampled over 256 points and contains 5 successive iPPG waves. An excerpt is presented in gure 2. The ground truth cPPG signals measured at the nger and the ear are also presented in this gure. All the signals have been standardize (µ = 0 and σ = 1).

In this article, we propose to exploit the wavelet representation of PPG signals to train the dierent neural architectures presented in section 3.3 (gure 1). The continuous wavelet transform (equation 1) of a signal x (t) corresponds to a time-frequency representation computed from a prototype function commonly called mother wavelet. Unlike the Fourier transform, the wavelet transform can detect abrupt changes in frequency using a family of wavelets ψ τ,s (equation 2) computed from the mother wavelet ψ.

CW T

ψ x (τ, s) = ∞ -∞ x (t) ψ τ,s (t)dt (1)
ψ τ,s (t) = 1 |s| ψ t -τ s (2)
ψ τ,s corresponds to the mother wavelet dilated by s and translated by τ . Dilating the wavelet allows the transform to analyze larger portions of signal in the time domain, thus covering lower frequencies. Dierent mother wavelets have been developed and the choice depends mainly on the application and the properties of the signal. The Morlet mother wavelet used in this study was already used in previous work related to the analysis of PPG signals by camera [START_REF] Bousefsaf | Continuous wavelet ltering on webcam photoplethysmographic signals to remotely assess the instantaneous heart rate[END_REF].

The original signal x (t) can be reconstructed by the inverse transform:

x (t) = 1 C ψ ∞ 0 ∞ -∞ 1 s 2 CW T ψ x (τ, s) 1 |s| ψ t -τ s dτ ds (3)
C ψ = ∞ 0 ψ (ζ) 2 |ζ| dζ < ∞ ( 4
)
C ψ is the admissibility condition and ψ is the Fourier transform of ψ.

The continuous wavelet transform was computed on each PPG signal in the frequency range [0.6, 4.5] Hz, which corresponds to the physiological range of the human heart rate [START_REF] Zaunseder | Cardiovascular assessment by imaging photoplethysmographya review[END_REF]. Wavelet representations of dimension 256 × 256 will be used to train the neural architectures presented in section 3.3.

Typical iPPG signal, cPPG signal and their respective wavelet representations (real, imaginary and absolute part) are presented in gure 3. A typical dierence in shape between both signals and in phase between their wavelet representations can be noted: the real part of the iPPG signal starts with a series of low intensity coecients (blue pseudo-ellipse) while the real part of the cPPG signal starts with strong intensity coecients (yellow pseudo- ellipse). The neural network will learn this specicity during the training phase.

Neural architectures

The U-Net neural architecture was initially proposed by Ronneberger et al. [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF]. This network has been used for segmentation of medical images [START_REF] Leclerc | Deep learning for segmentation using an open large-scale dataset in 2d echocardiography[END_REF]. Its architecture consists of a descending (encoder) branch completed by an ascending (decoder) branch, giving a U-shape to the network. The descending branch contains an ensemble of convolution and pooling layers. The ascending branch integrates deconvolution layers connected to the convolutions of the descending branch. Connections help to restore the spatial information. A schematic representation of the network is given in gure 1. In this study, we employ the U-Net1 version proposed by Leclerc et al. recognition tasks in images [START_REF] Too | A comparative study of netuning deep learning models for plant disease identication[END_REF]. Training a U-Net network supported by a backbone consists in optimizing the internal parameters of the decoder part. This approach can be associated to a transfer learning strategy. The various backbones tested and their main characteristics are summarized in table 1. VGG [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF] is a model composed of (3, 3) convolutional layers and pooling layers. The 16-layer version (VGG16) was used in this study. ResNet [START_REF] He | Deep residual learning for image recognition[END_REF] are neural modules nested in a larger network (networkin-network) through residual units composed of convolutional lters. The architecture is about 8 times deeper than VGG. ResNet models at dierent depth levels [START_REF] Bobbia | Real-Time Temporal Superpixels for Unsupervised Remote Photoplethysmography[END_REF][START_REF] Lee | Meta-rppg: Remote heart rate estimation using a transductive meta-learner[END_REF][START_REF] Slapni£ar | Blood pressure estimation from photoplethysmogram using a spectro-temporal deep neural network[END_REF], 101 and 152 layers) were trained on the ImageNet database but only the 101 layers was used in this study. DenseNet networks [START_REF] Huang | Densely connected convolutional networks[END_REF] include Dense blocks that are densely connected together: each layer is directly connected with the following ones. Thus, the input vector of a given layer integrates all the characteristics of those that precede it. The 201-layer version was chosen. Inception networks [START_REF] Szegedy | Inception-v4, inceptionresnet and the impact of residual connections on learning[END_REF] contain modules composed of convolution and pooling layers of dierent sizes. The InceptionV3 and Incep-tionResNetV2 versions (with residual connections) were used in this work.

Conventional regularization techniques (e.g. dropout) have not been introduced while a normalization scheme (i.e. batch normalization) is used in networks having a backbone. These details are summarized in table 1. No output activation function was specied because the targeted task corresponds to a regression in the form of a pixel-to-pixel reconstruction of a two-channel wavelet representation. The number of variables to be trained (weights and biases) is comprised between 2 and 9 million (table 1). The input dimensions of networks with backbones are xed by the data used for their training (256 × 256 pixels RGB images from the ImageNet database). The inputs being in our case two-channels wavelet representations, it is necessary to introduce an adaptation strategy. An additional 2D convolutional layer with a (1, 1) kernel has therefore been placed between the input layer and the encoder part of the network. The neurons of this layer allow conversion of the input from N to 3 channels. The weights of all the networks have randomly been initialized by the method proposed by Glorot and Bengio [START_REF] Glorot | Understanding the diculty of training deep feedforward neural networks[END_REF]. Biases are initialized to zero. The Mean Squared Error (MSE) has been selected as loss for training all the models:

M SE = 1 n i,j CW T i,j -CW T i,j 2 (5)
CW T corresponds to the wavelet transform (see section 3.2) of the ground truth cPPG signal. CW T is the wavelet representation predicted by the neural network starting from the wavelet representation of the iPPG signal.

The architecture implementation was carried out under Python using Keras API and Tensorow library. The Segmentation Models library [START_REF] Yakubovskiy | Segmentation Models[END_REF] proposed by P. Yakubovskiy was used to develop the neural networks presented in table 1. The training sessions were launched over 5000 epochs through batches of 16 images. We used, in this study, the Adam optimization algorithm [START_REF] Kingma | A method for stochastic optimization[END_REF] with a learning rate of 0.0001. A dedicated computer equipped with a dual Intel Xeon Silver 4114 and two Nvidia Quadro P6000s was used to carry out network learning.

Waveform estimators

Dierent features have been proposed to characterize the waveform of a PPG signal [START_REF] Elgendi | On the analysis of ngertip photoplethysmogram signals[END_REF]. In order to validate the predictions of the neural architectures presented in the previous section, we propose to compare the estimates of the most commonly observed waveform features [42] [43] between the reconstructed PPG signal (computed using the inverse transform of the predicted wavelet representation) and the ground truth cPPG signal. It has recently been shown that some of these features can properly be estimated on iPPG signals [START_REF] Djeldjli | Remote estimation of pulse wave features related to arterial stiness and blood pressure using a camera[END_REF], the contact and contactless waveform features evolving in a same way. Pulse Area (PA) and area computed between the start of the wave and the inection point (A1) and between the inection point and the end of the wave (A2). Amplitude: Systolic Amplitude (SA) and Diastolic Amplitude (DA).

Waveform features can be categorized into 4 families: temporal, amplitudebased, area-based, and (rst and second) derivative-based. All features are presented in gure 5. We refer the reader to the article of Elgendi et al. [START_REF] Elgendi | On the analysis of ngertip photoplethysmogram signals[END_REF] which details the PPG waveform features and their physiological interpretation.

Temporal features

The Pulse Interval (PI) corresponds to the total time of the wave, which is measured between two successive valleys. This feature is used to estimate the pulse rate. The Crest Time (CT) corresponds to the time between the start (rst valley) and the main peak of the wave. The Diastolic Time (DT) corresponds to the time between the main peak and the end of the wave. ∆T corresponds to the time between the main peak and the secondary peak. Dicrotic Notch Time (Tn) is the time between the start of the wave and the dicrotic notch. A2T corresponds to the time between the dicrotic notch and the end of the wave. Pulse Width at Half Height (PWHH) is the time equal to the width of the wave at half height. The First Derivative Peak Time (D1PT) parameter corresponds to the time between the start of the wave and its rst derivative peak.

Features based on rst and second derivatives

The points a, b, c, d and e (gure 5a) are detected on the second derivative of the PPG signal. These points reect the wave inections. They are used to compute all the ratios presented in gures 9, 10 and 11. These ratios change with age and reect arterial stiness [START_REF] Von Wowern | Digital photoplethysmography for assessment of arterial stiness: repeatability and comparison with applanation tonometry[END_REF].

Area-based features

The area-based features are shown in gure 5b. The Pulse Area (PA) parameter corresponds to the total area of the PPG wave. Area 1 (A1) is computed between the start of the wave and the inection point (systolic phase). Area 2 (A2) is computed between the inection point and the end of the wave (diastolic phase). The Inection Point Area ratio (IPA) corresponds to the ratio between A2 and A1.

Amplitude-based features

The systolic (SA) and diastolic (DA) amplitudes are calculated from the main and the secondary peaks (gure 5c). The Reection Index (RI) is the ratio between DA and SA while the Augmentation Index (AI) is the dierence between SA and DA divided by SA.

Metrics

In this section, we detail the dierent metrics employed for evaluating the performances of the models. The Root Mean Squared Error (RM SE, equation 6) has been computed between the PPG traces obtained after inverse wavelet transform (equation 3). Because the amplitudes are arbitrary and normalized, we also propose the Mean Absolute Percentage Error (M AP E, see equation 7). Both metrics along with scatter plots and Pearson correlation coecients have been used to quantify the level of agreement between the predicted ( P P G) and the ground truth signals (P P G).

RM SE =

1

n i P P G i -P P G i 2 (6)
M AP E = Independently of the measurement site, the network supported by ResNeXt101 presents the lowest M SE, thus indicating the best performance in terms of wavelet transform reconstruction (real and imaginary parts). We note that performances of architectures supported by VGG16 and DenseNet101 are close from ResNeXt101. Backbones based on ResNet and ResNeXt structure with squeeze and excitation are less ecient. U-Net1 presents higher M SE values than the other models. This observation probably reects the fact that the network contains between 4 to 5 times less trainable parameters. Models supported by a backbone performed generally better. This translates a real impact of pre-trained convolutional layers on very large databases. As a reminder, the backbone layers are blocked during the training phase. Inception-based backbones also present degraded performances.

Regarding the two sites, ear measurements deliver better general performances (lower M SE) than nger measurements. We assume that this gap reects the dierences between signal waveform: a PPG signal measured at the forehead surface is generally closer to a PPG signal measured at the ear than measured at the nger [START_REF] Hartmann | Quantitative Comparison of Photoplethysmographic Waveform Characteristics: Eect of Measurement Site[END_REF].

Point-to-point validation of reconstructed PPG signals

This section is dedicated to the evaluation of PPG signals produced by the neural architectures presented in table 1.

The trained neural models deliver a two-channel wavelet representation (a real part and an imaginary part). The temporal PPG signal is then reconstructed from the inverse transform (equation 3). An example is presented in gure 6, where we can appreciate the prediction quality of the real and imaginary parts of the wavelet transform produced by the U-Net ResNeXt101 network. The phase has been properly recovered. We can also observe that the dicrotic notch is well reproduced whereas it was almost absent on the raw iPPG signal. The reconstructed PPG signal is smooth and its width is smaller. This shows that the network properly corrects the high frequency coecients, which transcribe the noise, as well as the central frequency coecients, which determine the pulse signal.

In order to better appreciate the quality of the reconstruction, we present, in gure 7, a superposition of a reference nger cPPG signal and the PPG signal predicted by the U-Net network supported by ResNeXt101 (after computation of the inverse wavelet transform). The RM SE and M AP E have been computed between the two signals (equations 6 and 7). The results after cross-validation on k-fold are presented in table 3. The predictions delivered by the neural models present good overall performance.

The error on the U-Net network supported by ResNeXt101 is slightly lower, which is consistent with the results presented in section 4.1 and table 2. This particular network was therefore selected for further analysis. Figure 8 presents scatter plots coupled with Pearson correlation coecients. These representations aim to assess and compare the amplitudes of iPPG, ground truth cPPG and reconstructed cPPG signals over the test set. The graph representing cPPG ear against iPPG signals is not presented in this gure because of its close similarity with the graph presented in gure 8a. The concentric shape of the points distribution reects the natural waveform dierence between raw iPPG signals and cPPG signals. This specicity is mainly due to the dicrotic notch which is generally prominent on cPPG signals and, in contrast, not perceptible on iPPG signals (see gure 2 for a typical example). The inherent pulse width dierence between cPPG and iPPG signals also impacts the scatter plot representation presented in gure 8a. Figure 8b depicts nger and ear cPPG measurements and is provided for information.

Figures 8c and8d illustrate the quality of cPPG signal reconstruction by the U-Net ResNeXt101 network on the test set. The Pearson correlations coupled with the statistical results presented in table 4 (in particular the low M AP E) show that the PPG waveform is suitably reconstructed through its wavelet representation. This conclusion is valid for both nger (gure 8c) and ear (gure 8d) cPPG signals.

We propose, in the next subsection, an in-depth analysis of these results by studding pulse waveform features, whose values are originally very dierent between iPPG and cPPG signals.

Waveform features

The point-to-point evaluation presented in the previous subsection provides an overall vision of the predictions quality made by the neural architecture presented in table 1. Here, we propose an evaluation of the reconstructed PPG waves through specic waveform features across the test set. The studied features have briey been presented in section 3.4. They are divided into 4 categories: temporal, area-based, amplitude-based and based on rst and second derivatives.

Scatter plots along with their correlation coecients are presented for each feature in gures 9 and 10. We focus this specic evaluation on the U-Net ResNeXt101 network. A good general performance on each feature can be observed on each subgure, showing that the neural network (that take as input CWT of iPPG waves) reliably recovered the shape of nger and ear cPPG waves. As a reminder, iPPG signals computed from video on the forehead region are quite noisy, include artifacts and present a signature that is very dierent from cPPG signals measured on other sites [START_REF] Hartmann | Quantitative Comparison of Photoplethysmographic Waveform Characteristics: Eect of Measurement Site[END_REF] (see gure 2).

Several temporal features like PI (total width of the pulse wave) show high correlations. PI directly reects the pulse rate, a parameter estimated from iPPG signals with reliability and precision. Crest time (CT) presents better correlation than DT (diastole time), which seems to be in accordance with studies focusing on arterial pressure estimation based on PPG waveform analysis [START_REF] Ibtehaz | PPG2ABP: Translating Photoplethysmogram (PPG) Signals to Arterial Blood Pressure (ABP) Waveforms using Fully Convolutional Neural Networks[END_REF]. In contrast, the temporal parameter ∆T exhibits low correlation. We assume that the specic points associated with the detection of ∆T, in particular the secondary peak, are less accurately recovered. Its estimation is therefore potentially less reliable. It is however interesting to note that this weak correlation is also observed in gure 11 that presents a scatter plot computed between nger cPPG and ear cPPG signals for each waveform feature.

The parameters related to the amplitudes (SA, DA, RI and AI) present more or less high scores. The arbitrary nature of the PPG signals amplitudes makes their estimation very complex. The amplitude of cPPG signals is mainly modulated by the pressure applied between the sensor and the measurement site, by the light absorption of the tissues as well as by the optical properties of the skin. The iPPG signal amplitude also depends on the emitted and reected quantity of light, the distance as well as internal camera parameters. In general, the predictions produced from nger cPPG signals (gure 9) exhibit higher correlations for the amplitude features than for the predictions computed from ear cPPG signals (gure 10).

Waveform features related to areas and derivatives are relatively well transcribed by the neural model. The correlations presented in gures 9 and 10 are close to the correlations between nger cPPG and ear cPPG signals presented in gure 11.

Overall, the reconstructions of cPPG signals measured on the ear (gure 10) exhibit features that are slightly better correlated with the corresponding ground truth than those measured on the nger (gure 9). This conclusion The principal limitation of this study corresponds to the small number of volunteers that participated to the experiments. First validation of the concept on well-formed signals validated this choice. Thus, the videos we employed present a high frame rate which, after processing, results in highly sampled iPPG signals. These signals do not completely reect those constituted from frames delivered by conventional cameras or webcams. In addition, participants were asked to remain still even during the breath holding experiment.

Several ways of improvement for this work are therefore considered. We rst propose expanding the currently limited database by increasing the number of recordings and participants. We also envisage studying the impact of skin color, which directly aects the quality of PPG signals, on performances by assessing the evolution of waveform features against skin phototype.

Continuous wavelet transform using Morlet's wavelet has been employed in this work. We propose evaluating the impact on performances with dierent mother wavelets as well as investigating dierent time-frequency representations like short-time Fourier and constant-Q transforms. Modication of the internal parameters of the U-Net architectures (e.g. the number of layers and number of neurons by layer) will also be assessed. Moreover, we propose to study the impact of convolutional attention networks [START_REF] Chen | Deepphys: Video-based physiological measurement using convolutional attention networks[END_REF] and temporal dierence convolution [START_REF] Yu | AutoHR: A Strong Endto-End Baseline for Remote Heart Rate Measurement With Neural Searching[END_REF] on performances. Currently, the wavelet transform of 5 consecutive waves sampled over 256 values are inputted to the neural network. We envisage varying the number of consecutive waves but with particular consideration for small values (e.g. a single wave) that can produce inconsistencies in the time-frequency representations.

As stated at the beginning of this section, the videos used in this research were acquired by a fast (125 fps) camera. We plan to study in future work iPPG signals computed from recordings delivered by conventional (30 fps) cameras. The waves present, in this context, less details and are therefore more complex to analyze. Training models with larger volume of data can however be envisaged because many databases dedicated to the study of PPG signals measured by conventional cameras are now publicly available.

Inputting video in an U-Net architecture rather than time-frequency representation will be the subject of long-term research. We propose to test 3D U-Net architectures coupled with custom loss function that will constrain reconstruction of cPPG signals through their waveform features. This specic loss function will be directly integrated into the training phase. The neural network will thus try to minimize an overall error regarding the shape of the pulse waves. Compliance with these criteria could thus allow high quality reconstruction of cPPG from iPPG waves.

Summary of contributions

We proposed, in this article, neural architectures that allow accurate recovering of cPPG signals from iPPG signals estimated in video recordings. The reconstruction is carried out using the time-frequency representation of the signals via the continuous wavelet transform. The proposed neural networks correspond to U-Net architectures supported by specic backbones. The recovered signals present waveform features close to those computed on ground truth nger and ear cPPG signals. To the best of our knowledge, this is the rst demonstration of a method for accurate reconstruction of cPPG from iPPG signals.

The main motivation behind this work corresponds to the possibility of proposing an estimation of arterial blood pressure from video by analyzing iPPG signals. The next step towards this direction is therefore the integration of the recovered cPPG signals into AI models dedicated to the estimation of blood pressure using contact signals collected from large public databases [START_REF] Slapni£ar | Blood pressure estimation from photoplethysmogram using a spectro-temporal deep neural network[END_REF][START_REF] Panwar | PP-Net: A Deep Learning Framework for PPG based Blood Pressure and Heart Rate Estimation[END_REF][START_REF] Ibtehaz | PPG2ABP: Translating Photoplethysmogram (PPG) Signals to Arterial Blood Pressure (ABP) Waveforms using Fully Convolutional Neural Networks[END_REF]

Figure 2 :

 2 Figure 2: Excerpts of participant #1 (collected during breath holding experiment). Top gure: raw iPPG signals computed with a spatial averaging operation over the forehead region [19]. Video recordings have been collected using a fast camera (125 frames per second). Reference cPPG signals have been recorded with contact probes placed on the nger (middle gure) and the ear (bottom gure).

Figure 3 :

 3 Figure 3: The continuous wavelet transform of the iPPG signal (top gure) and cPPG signal (ear or nger, see bottom gure for a nger cPPG signal) is computed in the frequency range [0.6, 4.5] Hz. The wavelet representation of the iPPG signal (a complex image with a real and imaginary part) serves as input for training the neural networks presented in section 3.3. The absolute of the continuous wavelet transform is depicted for information and is not learned by the model.

  [START_REF] Leclerc | Deep learning for segmentation using an open large-scale dataset in 2d echocardiography[END_REF]. The model hyperparameters vary slightly compared to the original version proposed by Ronneberger et al. Details are presented in table 1. The number of lters is given for the rst and for the last convolutional block as well as at the center of the network, where the spatial information is most compressed. Each convolutional layer integrates a core (3, 3) coupled to a Rectied Linear Unit (ReLU) activation function.A Backbone (e.g. VGG16) can be integrated into the encoder part of the U-Net network (gure 4). Its internal parameter are blocked during training (the weights of the network remain xed). In practice, a backbone correspond to a model subpart pre-trained on ImageNet, a database deployed for object

Figure 4 :

 4 Figure 4: A backbone corresponds to a pre-trained network included in the encoder part of U-Net.

Figure 5 :

 5 Figure5: Presentation of the features computed from a PPG wave. These parameters have been categorized in four groups. Temporal: Pulse Interval (PI), Crest Time (CT), Diastolic Time (DT), time between the main peak and the secondary peak (∆T), Dicrotic Notch Time (Tn), Pulse Width at Half Height (PWHH), time between the dicrotic notch and the end of the wave (A2T) and First Derivative Peak Time (D1PT). Derivatives: a, b, c, d and e correspond to specic points that are detected on the second derivative. Area: Pulse Area (PA) and area computed between the start of the wave and the inection point (A1) and between the inection point and the end of the wave (A2). Amplitude: Systolic Amplitude (SA) and Diastolic Amplitude (DA).

Figure 6 :

 6 Figure 6: The real and imaginary parts of the reconstructed wavelet transform by the U-Net network supported by ResNeXt101 (middle gures) are similar to those computed from the nger ground truth signal (bottom gures). We can notice a small phase dierence in the wavelet representations of the raw iPPG signal (top gures) and the ground truth cPPG signal (bottom gures). The neural network learned this specicity, the reconstructed wavelet transform being in phase with the ground truth one. The absolute representations are depicted for information.

Figure 7 :

 7 Figure 7: PPG signal prediction (bottom gure) from an iPPG signal (top gure). U-Net supported by ResNeXt101 and trained on nger cPPG signals produced wavelet coecients that gave, after inverse transform, the reconstructed PPG signal. Ground truth and reconstructed signals are quite similar even if small discrepancies can be noticed.

Figure 8 :

 8 Figure 8: Scatter plots along with their respective Pearson correlation (ρ). All the pvalues are lower than 0.001. The concentric shape observed in gure (a) reects the natural waveform dierence between raw iPPG signals and cPPG signals. Figure (b) depicts nger and ear cPPG measurements. Bottom row gures present the cPPG signals reconstructed by the U-Net ResNeXt101 network for both nger (c) and ear (d) measurement sites.

Figure 9 :Figure 10 :

 910 Figure 9: Scatter plots showing the dierent waveform features computed from ground truth nger cPPG signals (cPPG finger , x-axis) against the waveform features computed from signals reconstructed by U-Net ResNeXt101 network ( cPPG finger , y-axis). Associated Pearson correlation coecients are presented for each feature (on each sub-gure). p-values are all lower than 0.001.

Figure 12 : 5 .

 125 Figure 12: Predictions of lesser quality include approximate dicrotic notch reconstruction (top gure) or phase discrepancies (bottom gure). The signals presented in the two subgures correspond to nger PPG signals.

  .

  work has been partly funded by the Contrat Plan État Région (CPER) Innovations Technologiques, Modélisation et Médecine Personnalisée (IT2MP) and Fonds Européen de Développement Régional (FEDER).

Table 1 :

 1 Main properties of the U-Net networks used in this study.

	Network	Number of conv. lters	Lowest resolution Normalization Number of parameters
	U-Net1 [55]	32 ↓ 128 ↑ 16 8 × 8	∅	2M
	U-Net VGG16 [30]	64 ↓ 512 ↑ 16 8 × 8	BatchNorm	9M
	U-Net VGG19 [30]	64 ↓ 512 ↑ 16 8 × 8	BatchNorm	9M
	U-Net ResNet101 [56]	64 ↓ 2048 ↑ 16 8 × 8	BatchNorm	9M
	U-Net ResNeXt101 [57] 64 ↓ 2048 ↑ 16 8 × 8	BatchNorm	9M
	U-Net SE-ResNet101 [58] 64 ↓ 2048 ↑ 16 8 × 8	BatchNorm	9M
	U-Net SE-ResNeXt101 [58] 64 ↓ 2048 ↑ 16 8 × 8	BatchNorm	9M
	U-Net InceptionResNetV2 [59] 32 ↓ 2080 ↑ 16 8 × 8	BatchNorm	7.5M
	U-Net InceptionV3 [59] 32 ↓ 448 ↑ 16 8 × 8	BatchNorm	8M
	U-Net DenseNet201 [60] 64 ↓ 128 ↑ 16 8 × 8	BatchNorm	8.5M

  The M SE correspond to the minimum validation loss (equation 5) observed during training. Each value presented in the table corresponds to the average and standard deviation computed for a specic U-Net network from the lowest M SE of each fold.

	1 n	i	P P G i -P P G i P P G i	(7)
	4. Results and discussion
	4.1. Learning performance
	Network	M SE f inger	M SE ear
	U-Net1	0.382 ± 0.054	0.266 ± 0.024
	U-Net VGG16	0.319 ± 0.029	0.224 ± 0.032
	U-Net VGG19	0.322 ± 0.033	0.232 ± 0.031
	U-Net ResNet101	0.341 ± 0.037	0.244 ± 0.022
	U-Net ResNeXt101	0.316 ± 0.036 0.222 ± 0.022
	U-Net SE-ResNet101	0.367 ± 0.031	0.249 ± 0.021
	U-Net SE-ResNeXt101	0.368 ± 0.042	0.259 ± 0.024
	U-Net InceptionResNetV2 0.385 ± 0.041	0.268 ± 0.030
	U-Net InceptionV3	0.386 ± 0.036	0.271 ± 0.026
	U-Net DenseNet201	0.317 ± 0.036	0.234 ± 0.027
	Table 2: k-fold cross-validation results for each model presented in table 2. The M SE
	(see equation 5) is computed between predicted and ground truth CWT transforms (real
	and imaginary parts). U-Net1 corresponds to the neural network proposed by Leclerc et
	al. [55], which does not include a pre-trained backbone. All the other neural networks are
	U-shaped architectures supported by a backbone.

k-fold cross-validation results for each model are presented in table 2.

Table 4

 4 presents the same results but across the test set. Additional comparisons, in particular raw iPPG against ground truth cPPG signals, are presented for information. The errors are here much more important, the M AP E being higher than 50%. The last row of the table is given for comparison and indicates the error between the cPPG signals recorded on the two measurement sites.

	Network	cPPG finger vs cPPG finger	cPPG ear vs cPPG ear
		RM SE	M AP E	RM SE	M AP E
	U-Net1	0.260 ± 0.018	0.064 ± 0.010	0.210 ± 0.010	0.033 ± 0.007
	U-Net VGG16	0.245 ± 0.013	0.053 ± 0.014	0.196 ± 0.014	0.031 ± 0.010
	U-Net VGG19	0.248 ± 0.011	0.055 ± 0.012	0.197 ± 0.014	0.034 ± 0.006
	U-Net ResNet101	0.251 ± 0.013	0.058 ± 0.009	0.205 ± 0.010	0.032 ± 0.008
	U-Net ResNeXt101	0.244 ± 0.014 0.045 ± 0.008 0.196 ± 0.009 0.032 ± 0.009
	U-Net SE-ResNet101	0.260 ± 0.010	0.058 ± 0.008	0.207 ± 0.012	0.032 ± 0.005
	U-Net SE-ResNeXt101	0.261 ± 0.014	0.060 ± 0.003	0.211 ± 0.012	0.037 ± 0.009
	U-Net InceptionResNetV2 0.265 ± 0.012	0.063 ± 0.008	0.213 ± 0.013	0.038 ± 0.007
	U-Net InceptionV3	0.266 ± 0.011	0.061 ± 0.010	0.213 ± 0.011	0.032 ± 0.004
	U-Net DenseNet101	0.245 ± 0.012	0.052 ± 0.007	0.201 ± 0.012	0.033 ± 0.004

Table 3 :

 3 k-fold cross-validation for RM SE and M AP E (see equations 6 and 7) computed between reconstructed PPG signals and ground truth cPPG signals. cPPG finger and cPPG ear correspond to ground truth cPPG signals measured at nger and ear respectively (see signal depicted in blue in gure 7 for a typical example). cPPG finger and cPPG ear correspond to reconstructed PPG signals computed by inverse transform on the CWT predicted by the dierent neural architectures (see signal depicted in orange in gure 7 for a typical example).

	Comparison	RM SE M AP E	ρ
	cPPG finger vs cPPG finger	0.219	0.045	0.97
	cPPG ear vs cPPG ear	0.185	0.0187 0.98
	cPPG finger vs iPPG	0.985	0.534	0.47
	cPPG ear vs iPPG	0.994	0.543	0.46
	cPPG finger vs cPPG ear	0.198	0.020	0.98

Table 4 :

 4 RM SE, M AP E and Pearson correlation (ρ) computed across samples included in the test set for ground truth cPPG signals, predicted cPPG signals and raw iPPG signals. An illustration of an iPPG signal is presented in black in gure 7. Predicted signals ( cPPG) are produced by the selected U-Net ResNeXt101 model (see signal depicted in orange in gure 7 for a typical example). All correlations presented p-values lower than 0.001.

  Figure 11: Scatter plots showing the dierent waveform features computed from ground truth nger cPPG signals (cPPG finger , x-axis) against the waveform features computed from ground truth ear cPPG signals (cPPG ear , y-axis). Associated Pearson correlation coecients are presented for each feature (on each sub-gure). p-values are all lower than 0.001.is in accordance with what we presented in sections 4.1 and 4.2, in particular in tables 2 and 3. We assume that this dierence in performance is due to the recovering of the dicrotic notch and the secondary peak that characterize PPG signals. The notch is much more prominent on nger cPPG signals than on ear cPPG signals. It directly impacts the prole of the wave by considerably modifying the inections and therefore the features linked to the second derivatives. The neural models trained on the wavelet representations computed from nger cPPG signals must therefore recover the coecients describing the dicrotic notch with more diculty because this trait is rarely apparent on raw iPPG signals. The top illustration presented in gure 12 shows a prediction of lesser quality where the successive dicrotic notches are approximately reconstructed by the model. The bottom illustration exhibits phase discrepancies. These dierences do not systematically impact the shape of the waves but can create unwanted uctuations in several temporal features, the number one factor being the pulse interval.

https://opencv.org/

http://dlib.net/


Nathan A Seifert

Dr Daniel P Zaleski

Cristobal Perez

Prof. B Justin L H Neill

Brooks H Pate
email: brookspate@virginia.edu

Montserrat Vallejo-López

Alberto Lesarri
email: lesarri@qf.uva.es

Dr Emilio J Cocinero

Fernando Castaño

Isabelle Kleiner

Dr Cristóbal Pérez

Montserrat Vallejo-López

Dr Mr N A Seifert

Pate

Prof Mrs M A Vallejo-López

Lesarri

Prof. F Castaño

Prof. I Kleiner

Probing the C-H•••π Weak Hydrogen Bond in Anesthetic Binding: The Sevoflurane-Benzene Cluster

published or not. The documents may come

Weak hydrogen bonds are characterized by very low interaction energies (< 20 kJ mol - 1 ), making these forces especially sensitive to modulation and cooperativity. Model molecular clusters formed by haloalkanes and small organics reveal how C-H•••O, [1] C-H•••S, [2] C-H•••N [3] , or C-H•••F-C [4] interactions tend to associate to maximize the number and strength of non-bonding forces, as illustrated by the nine simultaneous C-H•••F contacts in the cage structure of the difluoromethane trimer. [5] Much less structural information is available on the weaker (dispersion-dominated) C-H••• interaction, despite its influence in organic, organometallic and biological chemistry.

Reviews by Nishio, [6] Desiraju and Steiner [7] based most of their conclusions on crystallographic or ab initio studies. Alternatively, rotational spectroscopy recently analyzed several clusters involving phenyl  acceptors, [8,9,10,11] in absence of perturbing crystal or matrix effects. In particular, F 3 CH•••benzene [8] represents a prototypical C-H•••(Ph) interaction, with the C-H bond pointing to the center of the aromatic ring.

However, the short hydrogen bond distance r (H•••Benzene) = 2.366(2) Å suggests a stronger interaction than with other  acceptors, prompting our interest for systems with a less acidic H, larger size and the possibility of competing interactions. The cluster of sevoflurane-benzene is interesting from a chemical and biological point of view.

Sevoflurane is a common volatile anesthetic and the benzene cluster might model the local interaction with aromatic side-chains at the protein receptors. [12] Chemically, sevoflurane combines different donor and acceptor groups, including oxygen lone-pairs, several C-F "organic fluorine" bonds (recognized as weak acceptors), and two kinds of activated isopropyl and fluoromethyl C-H bonds. Recently, van der Veken et al. studied the vibrational spectra, reporting the observation of two different species. [13] However, the interpretation of the experimental data was largely based in quantum chemical calculations. In comparison, our rotational study has identified forty-six separate high-resolution spectra from distinct isotopologues, accurately resolving the molecular structure and the internal dynamics of the benzene ring.

The results of the conformational screening of sevoflurane-benzene can be found in Figure 1 intensities of the vibrational bands. [13] The analysis of the rotational spectrum was possible thanks to recent advances in broadband (chirped-pulse) Fourier-transform microwave (CP-FTMW)

spectroscopy. [14,15] An overview of the 2-8 GHz MW spectrum is shown in Figures 2 andS1 (Supporting Information). The strongest transitions arise from the sevoflurane monomer (signal-to-noise ratio SNR  20000:1). The sevoflurane-benzene parent species was ca. 50 times weaker, more than sufficient to detect all independent spectra from each heavy-atom monosubstituted isotopologues ( 13 C, 18 O) in natural abundance (0.2-1%). Hyperfine splittings were immediately noticeable in the transitions of the complex, and eventually attributed to the internal rotation of the benzene monomer about the sevoflurane frame. The symmetry point group of the internal rotor is C 6 , which contains four irreducible representations (A, B, E 1 and E 2 ). Therefore, each rotational transition is split into four separate symmetry components. We collect in Table 2 the experimental rotational constants derived for the parent species, for which the six-fold internal rotation barrier was determined as V 6 = 32.8687( 27) cm -1 . The details of the barrier calculation will be reported separately. Isotopic substitutions in sevoflurane are similarly complicated by the internal rotation. However, substitutions on benzene break its C 6 symmetry, resulting in simpler asymmetric-top spectra. For this reason, our strategy was based on the use of a sample of monodeuterated benzene, allowing a manageable assignment of all the sevoflurane isotopologues in the cluster.

The sensitivity of the experiment was so high as to detect the doubly-substituted D/ 13 C isotopologues in natural abundance with good intensity (e.g. SNR ≥ 3:1). Finally, and despite the extremely high spectral density, 33 of the 60 possible D/ 13 C isotopologues were assigned and every carbon had at least one associated isotopologue assignment.

The spectral assignment was aided by automatic routines developed in Virginia. [START_REF]Program Autofit[END_REF] The rotational parameters and experimental transitions for all 46 measured species are presented in Tables 2 andS1-S47. No other conformations of sevoflurane-benzene were detected. Two sevoflurane homodimers will be reported separately.

The analysis of the multi-isotopic rotational spectra led to an accurate experimental structure for the cluster, including all heavy atoms and the six benzene hydrogens. Application of the Kraitchman's equations [17] confirmed that the sevoflurane monomer [18] is not distorted upon complexation, as usually assumed for weak and moderately strong hydrogen bonds. Later, a least squares fitting resulted in the groundstate effective (r 0 ) structure. [START_REF] Rudolph | Advances in Molecular Structure Research[END_REF][START_REF] Kisiel | Program STRFIT[END_REF] The dimer has 3N-6 = 75 independent degrees of freedom for a total of 138 experimental observations (three moments of inertia per species). Therefore, sevoflurane-benzene offers the possibility to determine a nearly full effective structure for a molecular complex, which is very rare. On assumption of ab initio constrains (M06-2X) only for the positions of the three sevoflurane hydrogens and F-C-F bond angles, the molecular structure of Table S49 was obtained. A comparison with the theoretical geometries can be found in Figures 3 andS3, and Table S50.

Interactive 3D-PDFs can be found in Figures S4-S6.

Consequently, we have addressed the structure, internal dynamics and origin of the weak unions between sevoflurane and a benzene molecule through multi-isotopic rotational spectra. A single conformation was observed in the cold (T rot  2 K) supersonic jet, corresponding to the predicted global minimum primarily bound through the isopropyl C-H bond of sevoflurane. There is no indication of the second species with fluoromethyl bonding suggested from a weak band in the low-resolution IR spectra, [13] either because of thermal depopulation, or because of conformational hydrogen bonding distances, but not unreasonable for bifurcated or secondary weak hydrogen bonds, as bond distances up to 2.876-3.246 Å were identified in the difluoromethane trimer [5] and related clusters. [1,4] It is thus likely that the multiple weak fluorine hydrogen bonds are a contributor to the relative staggered orientation of the benzene ring and sevoflurane. An additional argument originates from the barrier hindering the internal rotation of the benzene moiety, which strikingly compares with the free-torsion between the two subunits of F 3 CH•••benzene. The theoretical data outline the difficulty to treat dispersion forces. The B3LYP method fails to reproduce the cluster geometry, as first observed by a poor agreement with the rotational constants. The B3LYP C-H••• hydrogen bond is ca. 0.5 Å longer than the experimental value and it predicts the ring slightly tilted with respect to the C-H bond (98º).

Conversely, the MP2 and M06-2X values (92.3º and 91.9º, respectively) agree fairly well with the r 0 determination (92.65(43)º). Significantly, in B3LYP the benzene ring is actually rotated ca. 25º from the eclipsing orientation of the global minimum. Thus, this optimal staggering is actually dependent on the proper treatment of the dispersion contribution to the C-H••• weak hydrogen bond. These results suggest that both electrostatics and dispersion play important roles in determining the complexation geometry of sevoflurane-benzene. Similar discrepancies of B3LYP were observed for (phenol) 2 . [10] In comparison, the MP2 or M06-2X methods with a modest Pople triple- basis set acceptably accounts for the spectral results. MP2 and M06-2X mostly differ by a slight rotation in the benzene orientation, which could be attributed to the low-lying benzene torsional mode (14 cm -1 ).

In conclusion, the new developments in broadband rotational spectroscopy lead to unparalleled levels of sensitivity for molecules and molecular clusters of increasing size (>10-20 heavy atoms). A theoretical methodology with a balance between accuracy, computational cost and portability is crucial for further experiments. As a result, rotational studies are essential in benchmarking the theoretical procedures for efficient description of weak non-bonding forces.

Keywords: Anesthetics, Noncovalent Interactions, Rotational Spectroscopy, Weak Hydrogen Bonding

Entry for the Table of Contents

Table 2:

Experimental rotational constants for the parent species and the benzene 13 C and 2 D isotopologues of sevoflurane-benzene (full listing in Supporting Information).

Species A /MHz [a] B /MHz C /MHz Δ J /kHz [b] Δ JK /kHz Δ K /kHz N [c] RMS /kHz Parent (A) 508.42070(40) [d] 358.82931 (13) 338.32685(13) [

  contain a variety of weak hydrogen bonding effects, mostly based on a C-H••• interaction originated in the isopropyl or fluoromethyl groups, or in combinations of C-H•••F and C-H••• weak contacts. The predicted global minimum (conformer 1) shows an intriguing topology for benzene not seen in other conformers, where eclipsing one hydrogen with the fluoromethyl group allows for the other 5 hydrogens to be optimally staggered between the sevoflurane substituents. This arrangement makes conceivable some contribution from the two bifurcated and one single C-H•••F interactions, which could enhance the attractive character of the primary C-H••• link. The simplicity of this optimally staggered C-H⋯π interaction is energetically favored by ca. 10.3-13.5 kJ mol -1 . Conformers 1 and 2 correspond to the observations of van der Veken et al., who found a population ratio of conf 1: conf 2  15:1 in Xe cryosolution based on the

  relaxation in the jet. The C-H•••(Ph) weak hydrogen bond r (H•••Benzene) = 2.401(16) Å is slightly longer than in the complex with trifluoromethane (r (H•••Benzene) = 2.366(2) Å), but still reflects the important activation role of the electronegative F and O atoms. The electrostatic contribution due to the interaction of the acidic hydrogen and the Lewis basic  benzene cloud likely enhances the C-H••• interaction with respect to aliphatic systems. [21] The geometry of the complex suggests that the main C-H••• interaction is modulated by secondary C-H•••F weak contacts between three aromatic hydrogens and the fluorine atoms in sevoflurane. The calculated distances for the secondary interactions range from 3.095(14) Å in OCH 2 F⋯H 1 to 3.293(12)-3.531(15) Å in CF 3 ⋯H interactions. These values are 0.5-1 Å longer than the conventional fluorine

Figure 1 .

 1 Figure 1. The predicted lowest-energy conformers of sevoflurane-benzene (MP2/6-

Figure 2 .

 2 Figure 2. A section of the CP-FTMW spectrum of sevoflurane-benzene-D 1 (6.8 million acqusitions, positive traces). The six symbols correspond to a unique 2 D-isotopologue (negative traces for predictions). The bottom panel shows a selection of 13 C/ 2 D double

Figure 3 .

 3 Figure 3. Views of the sevoflurane-benzene structure. The ball-and-stick frameworks

  and Table 1 (five lowest-energy conformers). The most stable conformations

The authors from the University of Virginia acknowledge funding support from the NSF Major Research Instrumentation program (CHE-0960074). M.V.-L., A.L., E.J.C. and F. C thank the MICINN and MINECO (CTQ-2011-22923, CTQ-2012-39132), the Basque government (IT520-10) and the UPV/EHU (UFI11/23) for funds. M.V.-L. and E.J.C. acknowledge a Ph.D. grant and a "Ramón y Cajal" contract, respectively. Computational resources of the UPV-EHU were used in this work.

4 / -20.6 / -4.4 [a] Rotational constants (A, B, C), electric dipole moment components (  ,  = a, b, c), Watson's S-reduced centrifugal distortion constants (D J , D JK , D K , d 1 , d 2 ), Gibbs free energies at 298 K and 1 atm (G), Electronic energies with zero-point corrections ((E+ZPE)) and dissociation energies (E d ).