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1.
Bioinformatics ; 2024 Jun 03.
Artículo en Inglés | MEDLINE | ID: mdl-38830086

RESUMEN

MOTIVATION: Imaging Mueller polarimetry has already proved its potential for biomedicine, remote sensing and metrology. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms. First, one must check the physical realizability of the experimental Mueller matrices in order to filter out non-physical data, ie to test the positive semi-definiteness of the 4 × 4 Hermitian coherency matrix calculated from the elements of corresponding Mueller matrix pixel-wise. For this purpose, we compared the execution time for the calculations of i) eigenvalues, ii) Cholesky decomposition, iii) Sylvester's criterion, and iv) coefficients of the characteristic polynomial (two different approaches) of the Hermitian coherency matrix, all calculated for the experimental Mueller matrix images (600 pixels × 700 pixels) of mouse uterine cervix. The calculations were performed using C ++ and Julia programming languages. RESULTS: Our results showed the superiority of the algorithm iv) based on the simplification via Pauli matrices over other algorithms for our dataset. The sequential implementation of latter algorithm on a single core already satisfies the requirements of real-time polarimetric imaging. This can be further amplified by the proposed parallelization (e.g., we achieve a 5-fold speed up on 6 cores). AVAILABILITY AND IMPLEMENTATION: The source codes of the algorithms and experimental data are available at https://github.com/pogudingleb/mueller_matrices.

2.
Opt Lett ; 47(21): 5549-5552, 2022 Nov 01.
Artículo en Inglés | MEDLINE | ID: mdl-37219266

RESUMEN

The advent of imagers with integrated linear polarization selectivity opens new opportunities for researchers interested in the polarization properties of biological tissues. In this Letter, we explore the mathematical framework necessary to obtain common parameters of interest: azimuth; retardance; and depolarization with reduced Mueller matrices that can be measured with the new instrumentation. We show that in the case of acquisition close to the tissue normal, simple algebraic analysis of the reduced form of the Mueller matrix yields results very close to those obtained with more complex decomposition algorithms applied to a complete Mueller matrix.

3.
Opt Lett ; 45(8): 2168-2171, 2020 Apr 15.
Artículo en Inglés | MEDLINE | ID: mdl-32287183

RESUMEN

Reflectance Mueller matrix (MM) polarimetry is being used to characterize biological media in multiple clinical applications. The origin of the reflectance polarimetric data is often unclear due to the impact of multiple scattering and tissue heterogeneity. We have developed a new, to the best of our knowledge, multimodal imaging technique combining MM reflectance, MM digital confocal imaging, and co-registered nonlinear microscopy techniques. The instrument unveils the origin of reflectance polarimetric signature in terms of confocal reflectance data. The reconstructed reflected MM demonstrates the capability of our method to provide depth-resolved 3D polarization response from complex biological media in terms of depolarization, retardance, and orientation parameters.


Asunto(s)
Microscopía/instrumentación , Fantasmas de Imagen , Reproducibilidad de los Resultados
4.
Wound Repair Regen ; 23(2): 149-62, 2015.
Artículo en Inglés | MEDLINE | ID: mdl-25832563

RESUMEN

The ability to phenotype wounds for the purposes of assessing severity, healing potential and treatment is an important function of evidence-based medicine. A variety of optical technologies are currently in development for noninvasive wound assessment. To varying extents, these optical technologies have the potential to supplement traditional clinical wound evaluation and research, by providing detailed information regarding skin components imperceptible to visual inspection. These assessments are achieved through quantitative optical analysis of tissue characteristics including blood flow, collagen remodeling, hemoglobin content, inflammation, temperature, vascular structure, and water content. Technologies that have, to this date, been applied to wound assessment include: near infrared imaging, thermal imaging, optical coherence tomography, orthogonal polarization spectral imaging, fluorescence imaging, laser Doppler imaging, microscopy, spatial frequency domain imaging, photoacoustic detection, and spectral/hyperspectral imaging. We present a review of the technologies in use or development for these purposes with three aims: (1) providing basic explanations of imaging technology concepts, (2) reviewing the wound imaging literature, and (3) providing insight into areas for further application and exploration. Noninvasive imaging is a promising advancement in wound assessment and all technologies require further validation.


Asunto(s)
Diagnóstico por Imagen , Piel/patología , Cicatrización de Heridas , Heridas y Lesiones/diagnóstico , Enfermedad Crónica , Diagnóstico por Imagen/instrumentación , Diagnóstico por Imagen/métodos , Medicina Basada en la Evidencia , Humanos , Puntaje de Gravedad del Traumatismo , Microcirculación , Guías de Práctica Clínica como Asunto , Piel/irrigación sanguínea , Piel/lesiones , Heridas y Lesiones/patología
5.
Opt Lett ; 39(10): 3010-3, 2014 May 15.
Artículo en Inglés | MEDLINE | ID: mdl-24978260

RESUMEN

We have investigated the potential of tissue phantoms fabricated with thermosoftening- and photopolymerization-based three-dimensional (3D) printers for use in evaluation of biophotonic imaging systems. The optical properties of printed polymer samples were measured and compared to biological tissues. Phantoms with subsurface channels as small as 0.2 mm in diameter were fabricated and imaged with microscopy, x-ray microtomography, and optical coherence tomography to characterize morphology. These phantoms were then implemented to evaluate the penetration depth of a hyperspectral reflectance imaging system used in conjunction with a near-infrared contrast agent. Results indicated that 3D printing may provide a suitable platform for performance testing in biophotonics, although subsurface imaging is critical to mitigate printer-to-printer variability in matrix homogeneity and feature microstructure.


Asunto(s)
Materiales Biomiméticos/síntesis química , Fantasmas de Imagen , Polímeros/química , Impresión Tridimensional/instrumentación , Tomografía/instrumentación , Diseño de Equipo , Análisis de Falla de Equipo
6.
Appl Opt ; 53(18): 4061-71, 2014 Jun 20.
Artículo en Inglés | MEDLINE | ID: mdl-24979441

RESUMEN

Narrow-band imaging (NBI) is a spectrally selective reflectance imaging technique that is used clinically for enhancing visualization of superficial vasculature and has shown promise for applications such as early endoscopic detection of gastrointestinal neoplasia. We have studied the effect of vessel geometry and illumination wavelength on vascular contrast using idealized geometries in order to more quantitatively understand NBI and broadband or white light imaging of mucosal tissue. Simulations were performed using a three-dimensional, voxel-based Monte Carlo model incorporating discrete vessels. In all cases, either 415 or 540 nm illumination produced higher contrast than white light, yet white light did not always produce the lowest contrast. White light produced the lowest contrast for small vessels and intermediate contrast for large vessels (diameter≥100 µm) at deep regions (vessel depth≥200 µm). The results show that 415 nm illuminations provided superior contrast for smaller vessels at shallow depths while 540 nm provided superior contrast for larger vessels in deep regions. Besides 540 nm, our studies also indicate the potential of other wavelengths to achieve high contrast of large vessels at deep regions. Simulation results indicate the importance of three key mechanisms in determining spectral variations in contrast: intravascular hemoglobin (Hb) absorption in the vessel of interest, diffuse Hb absorption from collateral vasculature, and bulk tissue scattering. Measurements of NBI contrast in turbid phantoms incorporating 0.1-mm-diameter hemoglobin-filled capillary tubes indicated good agreement with modeling results. These results provide quantitative insights into light-tissue interactions and the effect of device and tissue properties on NBI performance.


Asunto(s)
Vasos Sanguíneos/anatomía & histología , Vasos Sanguíneos/metabolismo , Hemoglobinas/metabolismo , Modelos Cardiovasculares , Modelos Estadísticos , Análisis Espectral/métodos , Animales , Simulación por Computador , Diseño Asistido por Computadora , Diseño de Equipo , Análisis de Falla de Equipo , Humanos , Luz , Iluminación , Imagen Molecular/instrumentación , Método de Montecarlo , Fantasmas de Imagen , Dispersión de Radiación
7.
Sensors (Basel) ; 14(7): 12127-48, 2014 Jul 08.
Artículo en Inglés | MEDLINE | ID: mdl-25006996

RESUMEN

Rapid, accurate, and minimally-invasive glucose biosensors based on Förster Resonance Energy Transfer (FRET) for glucose measurement have the potential to enhance diabetes control. However, a standard set of in vitro approaches for evaluating optical glucose biosensor response under controlled conditions would facilitate technological innovation and clinical translation. Towards this end, we have identified key characteristics and response test methods, fabricated FRET-based glucose biosensors, and characterized biosensor performance using these test methods. The biosensors were based on competitive binding between dextran and glucose to concanavalin A and incorporated long-wavelength fluorescence dye pairs. Testing characteristics included spectral response, linearity, sensitivity, limit of detection, kinetic response, reversibility, stability, precision, and accuracy. The biosensor demonstrated a fluorescence change of 45% in the presence of 400 mg/dL glucose, a mean absolute relative difference of less than 11%, a limit of detection of 25 mg/dL, a response time of 15 min, and a decay in fluorescence intensity of 72% over 30 days. The battery of tests presented here for objective, quantitative in vitro evaluation of FRET glucose biosensors performance have the potential to form the basis of future consensus standards. By implementing these test methods for a long-visible-wavelength biosensor, we were able to demonstrate strengths and weaknesses with a new level of thoroughness and rigor.


Asunto(s)
Técnicas Biosensibles/instrumentación , Concanavalina A/química , Transferencia Resonante de Energía de Fluorescencia/instrumentación , Glucosa/análisis , Diseño de Equipo , Análisis de Falla de Equipo , Glucosa/química , Técnicas In Vitro , Reproducibilidad de los Resultados , Sensibilidad y Especificidad
8.
J Biomed Opt ; 29(5): 052901, 2024 May.
Artículo en Inglés | MEDLINE | ID: mdl-38817337

RESUMEN

The editorial introduces the two-issue JBO Special Section on Polarimetry in Biomedical Optics and provides resources for further exploration.


Asunto(s)
Óptica y Fotónica , Humanos
9.
J Biomed Opt ; 29(5): 052918, 2024 May.
Artículo en Inglés | MEDLINE | ID: mdl-38282917

RESUMEN

Significance: Preterm birth is defined as a birth before 37 weeks of gestation and is one of the leading contributors to infant mortality rates globally. Premature birth can lead to life-long developmental impairment for the child. Unfortunately, there is a significant lack of tools to diagnose preterm birth risk, which limits patient care and the development of new therapies. Aim: To develop a speculum-free, portable preterm imaging system (PPRIM) for cervical imaging; testing of the PPRIM system to resolve polarization properties of birefringent samples; and testing of the PPRIM under an IRB on healthy, non-pregnant volunteers for visualization and polarization analysis of cervical images. Approach: The PPRIM can perform 4×3 Mueller-matrix imaging to characterize the remodeling of the uterine cervix during pregnancy. The PPRIM is built with a polarized imaging probe and a flexible insertable sheath made with a compatible flexible rubber-like material to maximize comfort and ease of use. Results: The PPRIM device is developed to meet specific design specifications as a speculum-free, portable, and comfortable imaging system with polarized imaging capabilities. This system comprises a main imaging component and a flexible silicone inserter. The inserter is designed to maximize comfort and usability for the patient. The PPRIM shows high-resolution imaging capabilities at the 20 mm working distance and 25 mm circular field of view. The PPRIM demonstrates the ability to resolve birefringent sample orientation and full field capture of a healthy, non-pregnant cervix. Conclusion: The development of the PPRIM aims to improve access to the standard of care for women's reproductive health using polarized Mueller-matrix imaging of the cervix and reduce infant and maternal mortality rates and better quality of life.


Asunto(s)
Nacimiento Prematuro , Embarazo , Lactante , Niño , Recién Nacido , Femenino , Humanos , Calidad de Vida , Cuello del Útero/diagnóstico por imagen
10.
Opt Lett ; 38(5): 805-7, 2013 Mar 01.
Artículo en Inglés | MEDLINE | ID: mdl-23455305

RESUMEN

We propose an inter-Ascan speckle decorrelation based method that can quantitatively assess blood flow normal to the direction of the optical coherence tomography imaging beam. To validate this method, we performed a systematic study using both phantom and in vivo animal models. Results show that our speckle analysis method can accurately extract transverse flow speed with high spatial and temporal resolution.


Asunto(s)
Procesamiento de Imagen Asistido por Computador/métodos , Tomografía de Coherencia Óptica/métodos , Animales , Fantasmas de Imagen
11.
J Opt Soc Am A Opt Image Sci Vis ; 30(1): 51-9, 2013 Jan 01.
Artículo en Inglés | MEDLINE | ID: mdl-23456001

RESUMEN

In this study, we propose a generic speckle simulation for optical coherence tomography (OCT) signal, by convolving the point-spread function (PSF) of the OCT system with the numerically synthesized random sample field. We validate our model and use the simulation method to study the statistical properties of cross-correlation coefficients between A-scans, which have been recently applied in transverse motion analysis by our group. The results of simulation show that oversampling is essential for accurate motion tracking; exponential decay of OCT signal leads to an underestimate of motion that can be corrected; lateral heterogeneity of sample leads to an overestimate of motion for a few pixels corresponding to the structural boundary.


Asunto(s)
Modelos Teóricos , Tomografía de Coherencia Óptica/métodos , Estadística como Asunto
12.
Physiol Meas ; 44(11)2023 Nov 29.
Artículo en Inglés | MEDLINE | ID: mdl-37494945

RESUMEN

Photoplethysmography is a key sensing technology which is used in wearable devices such as smartwatches and fitness trackers. Currently, photoplethysmography sensors are used to monitor physiological parameters including heart rate and heart rhythm, and to track activities like sleep and exercise. Yet, wearable photoplethysmography has potential to provide much more information on health and wellbeing, which could inform clinical decision making. This Roadmap outlines directions for research and development to realise the full potential of wearable photoplethysmography. Experts discuss key topics within the areas of sensor design, signal processing, clinical applications, and research directions. Their perspectives provide valuable guidance to researchers developing wearable photoplethysmography technology.


Asunto(s)
Fotopletismografía , Dispositivos Electrónicos Vestibles , Monitores de Ejercicio , Procesamiento de Señales Asistido por Computador , Frecuencia Cardíaca/fisiología
13.
J Biomed Opt ; 27(8)2022 05.
Artículo en Inglés | MEDLINE | ID: mdl-35534924

RESUMEN

SIGNIFICANCE: Monte Carlo (MC) methods have been applied for studying interactions between polarized light and biological tissues, but most existing MC codes supporting polarization modeling can only simulate homogeneous or multi-layered domains, resulting in approximations when handling realistic tissue structures. AIM: Over the past decade, the speed of MC simulations has seen dramatic improvement with massively parallel computing techniques. Developing hardware-accelerated MC simulation algorithms that can accurately model polarized light inside three-dimensional (3D) heterogeneous tissues can greatly expand the utility of polarization in biophotonics applications. APPROACH: Here, we report a highly efficient polarized MC algorithm capable of modeling arbitrarily complex media defined over a voxelated domain. Each voxel of the domain can be associated with spherical scatters of various radii and densities. The Stokes vector of each simulated photon packet is updated through photon propagation, creating spatially resolved polarization measurements over the detectors or domain surface. RESULTS: We have implemented this algorithm in our widely disseminated MC simulator, Monte Carlo eXtreme (MCX). It is validated by comparing with a reference central-processing-unit-based simulator in both homogeneous and layered domains, showing excellent agreement and a 931-fold speedup. CONCLUSION: The polarization-enabled MCX offers biophotonics community an efficient tool to explore polarized light in bio-tissues, and is freely available at http://mcx.space/.


Asunto(s)
Fotones , Programas Informáticos , Algoritmos , Simulación por Computador , Luz , Método de Montecarlo
14.
Biosensors (Basel) ; 12(10)2022 Sep 24.
Artículo en Inglés | MEDLINE | ID: mdl-36290924

RESUMEN

Cervical cancer is one of the most significant global health inequities of our time and is the fourth most common cancer in women worldwide, disproportionally affecting developing countries where the disease burden is 84%. Sometimes referred to as preventable cancer, it progresses slowly, providing a window of time for routine screening in which pre-cancerous lesions can be identified and treated. The high mortality rate can be attributed to many reasons, including the high cost of cytology-based screening, lack of human resources to conduct screening, and inadequate preventive medicine services and systems. Due to its slow progression, early intervention is feasible with appropriate screening. However, the standard screening procedures require access to lab-based tests and physician expertise. Several imaging devices have been introduced in the literature to aid cervical screening in low-resource settings. This review details the instrumentation and clinical testing of devices currently deployed in low-resource locations worldwide. The devices' imaging, portability, illumination, and power requirements (among other metrics) are documented with specifics of human pilot studies conducted with these tools.


Asunto(s)
Neoplasias del Cuello Uterino , Femenino , Humanos , Neoplasias del Cuello Uterino/diagnóstico por imagen , Neoplasias del Cuello Uterino/prevención & control , Detección Precoz del Cáncer/métodos , Tamizaje Masivo/métodos
15.
Biomed Opt Express ; 13(2): 571-589, 2022 Feb 01.
Artículo en Inglés | MEDLINE | ID: mdl-35284190

RESUMEN

A polarization enhanced laparoscopy (PEL) imaging system was developed to examine the feasibility of utilizing PEL to augment conventional white light laparoscopy (WLL) in the visualization of peritoneal cancer metastases. The system includes a modified tip to illuminate tissue with linearly polarized light and elements in the detection path enabling recording of corresponding images linearly co- and cross-polarized relative to the incident light. WLL and PEL images from optical tissue phantoms with features of distinct scattering cross-section confirm the enhanced sensitivity of PEL to such characteristics. Additional comparisons based on images acquired from collagen gels with different levels of fiber alignment highlight another source of PEL contrast. Finally, PEL and WLL images of ex vivo human tissue illustrate the potential of PEL to improve visualization of cancerous tissue surrounded by healthy peritoneum. Given the simplicity of the approach and its potential for seamless integration with current clinical practice, our results provide motivation for clinical translation.

16.
J Biomed Opt ; 27(3)2022 03.
Artículo en Inglés | MEDLINE | ID: mdl-35352513

RESUMEN

SIGNIFICANCE: Obesity is a worldwide epidemic contributing directly to several cardiovascular risk factors including hypertension and type 2 diabetes. Wearable devices are becoming better at quantifying biomarkers relevant for the management of health and fitness. Unfortunately, both anecdotal evidence and recent studies indicate that some wearables have higher levels of error when utilized by populations with darker skin tones and high body mass index (BMI). There is an urgent need for a better evaluation of the limits of wearable health technologies when used by obese individuals. AIMS: (1) To review the current know-how on changes due to obesity in the skin epidermis, dermis, and subcutis that could affect the skin optical properties; (2) for the green wavelength range, to evaluate the difference in absorption and scattering coefficients from the abdominal skin between individuals with and without elevated BMI. The changes include alterations in layer thickness and cell size, as well as significant differences in chromophores and scatterer content, e.g., water, hemoglobin, collagen, and lipids. APPROACH: We have summarized literature pertaining to changes in skin and its components in obesity and report the results of our search using articles published between years 1971 and 2020. A linear model was used to demonstrate the absorption and reduced scattering coefficient of the abdominal skin of individuals with and without elevated BMI in the green wavelength range (530 to 550 nm) that is typically found in most wearables. RESULTS: The general trends indicate a decrease in absorption for both dermis and subcutis and an increase in reduced scattering for both epidermis and dermis. At 544-nm wavelength, a typical wavelength used for photoplethysmography (PPG), the absorption coefficient's relative percentage difference between high and low BMI skin, was 49% in the subcutis, 19% in the dermis, and negligible in the epidermis, whereas the reduced scattering coefficient relative difference was 21%, 29%, and 165% respectively. CONCLUSIONS: These findings suggest that there could be significant errors in the output of optical devices used for monitoring health and fitness if changes due to obesity are not accounted for in their design.


Asunto(s)
Diabetes Mellitus Tipo 2 , Índice de Masa Corporal , Epidermis , Humanos , Obesidad/diagnóstico por imagen , Piel/irrigación sanguínea , Piel/diagnóstico por imagen
17.
Biomed Opt Express ; 12(12): 7445-7457, 2021 Dec 01.
Artículo en Inglés | MEDLINE | ID: mdl-35003845

RESUMEN

Commercially available wearable devices have been used for fitness and health management and their demand has increased over the last ten years. These "general wellness" and heart-rate monitoring devices have been cleared by the Food and Drug Administration for over-the-counter use, yet anecdotal and more systematic reports seem to indicate that their error is higher when used by individuals with elevated skin tone and high body mass index (BMI). In this work, we used Monte Carlo modeling of a photoplethysmography (PPG) signal to study the theoretical limits of three different wearable devices (Apple Watch series 5, Fitbit Versa 2 and Polar M600) when used by individuals with a BMI range of 20 to 45 and a Fitzpatrick skin scale 1 to 6. Our work shows that increased BMI and skin tone can induce a relative loss of signal of up to 61.2% in Fitbit versa 2, 32% in Apple S5 and 32.9% in Polar M600 when considering the closest source-detector pair configuration in these devices.

18.
Biomed Opt Express ; 12(4): 2236-2249, 2021 Apr 01.
Artículo en Inglés | MEDLINE | ID: mdl-33996226

RESUMEN

We propose an approach for discriminating fibrillar collagen fibers from elastic fibers in the mouse cervix in Mueller matrix microscopy using convolutional neural networks (CNN) and K-nearest neighbor (K-NN) for classification. Second harmonic generation (SHG), two-photon excitation fluorescence (TPEF), and Mueller matrix polarimetry images of the mice cervix were collected with a self-validating Mueller matrix micro-mesoscope (SAMMM) system. The components and decompositions of each Mueller matrix were arranged as individual channels of information, forming one 3-D voxel per cervical slice. The classification algorithms analyzed each voxel and determined the amount of collagen and elastin, pixel by pixel, on each slice. SHG and TPEF were used as ground truths. To assess the accuracy of the results, mean-square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) were used. Although the training and testing is limited to 11 and 5 cervical slices, respectively, MSE accuracy was above 85%, SNR was greater than 40 dB, and SSIM was larger than 90%.

19.
Biosensors (Basel) ; 11(4)2021 Apr 16.
Artículo en Inglés | MEDLINE | ID: mdl-33923469

RESUMEN

Photoplethysmography (PPG) is a low-cost, noninvasive optical technique that uses change in light transmission with changes in blood volume within tissue to provide information for cardiovascular health and fitness. As remote health and wearable medical devices become more prevalent, PPG devices are being developed as part of wearable systems to monitor parameters such as heart rate (HR) that do not require complex analysis of the PPG waveform. However, complex analyses of the PPG waveform yield valuable clinical information, such as: blood pressure, respiratory information, sympathetic nervous system activity, and heart rate variability. Systems aiming to derive such complex parameters do not always account for realistic sources of noise, as testing is performed within controlled parameter spaces. A wearable monitoring tool to be used beyond fitness and heart rate must account for noise sources originating from individual patient variations (e.g., skin tone, obesity, age, and gender), physiology (e.g., respiration, venous pulsation, body site of measurement, and body temperature), and external perturbations of the device itself (e.g., motion artifact, ambient light, and applied pressure to the skin). Here, we present a comprehensive review of the literature that aims to summarize these noise sources for future PPG device development for use in health monitoring.


Asunto(s)
Frecuencia Cardíaca/fisiología , Monitoreo Fisiológico , Fotopletismografía , Artefactos , Presión Sanguínea , Humanos , Respiración , Procesamiento de Señales Asistido por Computador , Dispositivos Electrónicos Vestibles
20.
Sci Rep ; 11(1): 2570, 2021 01 28.
Artículo en Inglés | MEDLINE | ID: mdl-33510428

RESUMEN

Cardiovascular disease is one of the leading causes of death in the United States and obesity significantly increases the risk of cardiovascular disease. The measurement of blood pressure (BP) is critical in monitoring and managing cardiovascular disease hence new wearable devices are being developed to make BP more accessible to physicians and patients. Several wearables utilize photoplethysmography from the wrist vasculature to derive BP assessment although many of these devices are still at the experimental stage. With the ultimate goal of supporting instrument development, we have developed a model of the photoplethysmographic waveform derived from the radial artery at the volar surface of the wrist. To do so we have utilized the relation between vessel biomechanics through Finite Element Method and Monte Carlo light transport model. The model shows similar features to that seen in PPG waveform captured using an off the shelf device. We observe the influence of body mass index on the PPG signal. A degradation the PPG signal of up to 40% in AC to DC signal ratio was thus observed.


Asunto(s)
Fotopletismografía/métodos , Arteria Radial/fisiología , Animales , Fenómenos Biomecánicos , Presión Sanguínea/fisiología , Índice de Masa Corporal , Análisis de Elementos Finitos , Humanos , Método de Montecarlo
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