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1.
IEEE Sens J ; 24(11): 18359-18371, 2024 Jun.
Artículo en Inglés | MEDLINE | ID: mdl-39301509

RESUMEN

Needle insertion using flexible bevel tip needles are a common minimally-invasive surgical technique for prostate cancer interventions. Flexible, asymmetric bevel tip needles enable physicians for complex needle steering techniques to avoid sensitive anatomical structures during needle insertion. For accurate placement of the needle, predicting the trajectory of these needles intra-operatively would greatly reduce the need for frequently needle reinsertions thus improving patient comfort and positive outcomes. However, predicting the trajectory of the needle during insertion is a complex task that has yet to be solved due to random needle-tissue interactions. In this paper, we present and validate for the first time a hybrid deep learning and model-based approach to handle the intra-operative needle shape prediction problem through, leveraging a validated Lie-group theoretic model for needle shape representation. Furthermore, we present a novel self-supervised learning and method in conjunction with the Lie-group shape model for training these networks in the absence of data, enabling further refinement of these networks with transfer learning. Needle shape prediction was performed in single-layer and double-layer homogeneous phantom tissue for C- and S-shape needle insertions. Our method demonstrates an average root-mean-square prediction error of 1.03 mm over a dataset containing approximately 3,000 prediction samples with maximum prediction steps of 110 mm.

2.
J Med Robot Res ; 9(1-2)2024.
Artículo en Inglés | MEDLINE | ID: mdl-38948444

RESUMEN

Flexible needle insertion procedures are common in minimally-invasive surgeries for diagnosing and treating prostate cancer. Bevel-tip needles provide physicians the capability to steer the needle during long insertions to avoid vital anatomical structures in the patient and reduce post-operative patient discomfort. To provide needle placement feedback to the physician, sensors are embedded into needles for determining the real-time 3D shape of the needle during operation without needing to visualize the needle intra-operatively. Through expansive research in fiber optics, a plethora of bio-compatible, MRI-compatible, optical shape-sensors have been developed to provide real-time shape feedback, such as single-core and multicore fiber Bragg gratings. In this paper, we directly compare single-core fiber-based and multicore fiber-based needle shape-sensing through similarly constructed, four-active area sensorized bevel-tip needles inserted into phantom and ex-vivo tissue on the same experimental platform. In this work, we found that for shape-sensing in phantom tissue, the two needles performed identically with a p-value of 0.164 > 0.05, but in ex-vivo real tissue, the single-core fiber sensorized needle significantly outperformed the multicore fiber configuration with a p-value of 0.0005 < 0.05. This paper also presents the experimental platform and method for directly comparing these optical shape sensors for the needle shape-sensing task, as well as provides direction, insight and required considerations for future work in constructively optimizing sensorized needles.

3.
Medicine (Baltimore) ; 102(46): e36098, 2023 Nov 17.
Artículo en Inglés | MEDLINE | ID: mdl-37986329

RESUMEN

There is a lack of studies comparing the risk of cardio-cerebrovascular disease between angiotensin receptor blockers (ARBs) of different half-lives. We aimed to compare the risks of myocardial infarction (MI), heart failure (HF), and cerebrovascular disease with the use of valsartan, losartan, irbesartan, and telmisartan with different half-lives in a national claim-based retrospective cohort of patients aged ≥ 40 years with hypertension. To establish a cohort exposed to valsartan, losartan, irbesartan, or telmisartan, we performed propensity score (PS) matching and used an as-treated approach to evaluate exposure. The Cox regression model was employed to calculate hazard ratios, which were based on the incidence rate for each newly occurring event of MI, heart failure, or cerebrovascular disease. These hazard ratios were calculated to compare the risk of MI, heart failure, and cerebrovascular disease associated with valsartan, losartan, and irbesartan in comparison to telmisartan. A PS-matched cohort of 148,229 patients was established for each of valsartan, losartan, irbesartan, or telmisartan. The matched cohort analysis showed that the adjusted hazard ratio (aHRs, 95% confidence interval) for MI was higher for valsartan use (1.39, 1.33-1.45) and losartan use (1.10, 1.05-1.15) but lower for irbesartan use (0.90, 0.86-0.94) compared with the reference (telmisartan). The aHRs for HF were not different among these ARBs (angiotensin receptor blockers). The aHR for cerebrovascular disease was lower for valsartan use (0.85, 0.83-0.87) and losartan use (0.80, 0.78-0.82) but higher for irbesartan use (1.11, 1.09-1.13) compared with the reference. We found differences in the risk of MI and cerebrovascular disease with the use of different ARBs compared to telmisartan use. Valsartan, and losartan with a short half-life, which showed a higher risk of MI, had a lower risk of cerebrovascular disease. Conversely, irbesartan with a long half-life, which showed a lower risk of MI, had a higher risk of cerebrovascular disease.


Asunto(s)
Trastornos Cerebrovasculares , Insuficiencia Cardíaca , Infarto del Miocardio , Humanos , Losartán/efectos adversos , Irbesartán/efectos adversos , Telmisartán/uso terapéutico , Valsartán/uso terapéutico , Antagonistas de Receptores de Angiotensina , Estudios Retrospectivos , Tetrazoles/efectos adversos , Compuestos de Bifenilo , Bencimidazoles/efectos adversos , Inhibidores de la Enzima Convertidora de Angiotensina , Insuficiencia Cardíaca/epidemiología , Infarto del Miocardio/inducido químicamente , Infarto del Miocardio/epidemiología , Trastornos Cerebrovasculares/epidemiología
4.
ArXiv ; 2023 Sep 08.
Artículo en Inglés | MEDLINE | ID: mdl-37731661

RESUMEN

Flexible needle insertion procedures are common for minimally-invasive surgeries for diagnosing and treating prostate cancer. Bevel-tip needles provide physicians the capability to steer the needle during long insertions to avoid vital anatomical structures in the patient and reduce post-operative patient discomfort. To provide needle placement feedback to the physician, sensors are embedded into needles for determining the real-time 3D shape of the needle during operation without needing to visualize the needle intra-operatively. Through expansive research in fiber optics, a plethora of bio-compatible, MRI-compatible, optical shape-sensors have been developed to provide real-time shape feedback, such as single-core and multicore fiber Bragg gratings. In this paper, we directly compare single-core fiber-based and multicore fiber-based needle shape-sensing through identically constructed, four-active area sensorized bevel-tip needles inserted into phantom and ex-vivo tissue on the same experimental platform. In this work, we found that for shape-sensing in phantom tissue, the two needles performed identically with a p-value of 0.164 > 0.05, but in ex-vivo real tissue, the single-core fiber sensorized needle significantly outperformed the multicore fiber configuration with a p-value of 0.0005 < 0.05. This paper also presents the experimental platform and method for directly comparing these optical shape sensors for the needle shape-sensing task, as well as provides direction, insight and required considerations for future work in constructively optimizing sensorized needles.

5.
Int Symp Med Robot ; 20232023 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-37292169

RESUMEN

Bevel-tip needles are commonly utilized in percutaneous medical interventions where a curved insertion trajectory is required. To avoid deviation from the intended trajectory, needle shape sensing and tip localization is crucial in providing the operator with feedback. There is an abundance of previous work that investigate the medical application of fiber Bragg grating (FBG) sensors, but most works select only one specific type of fiber among the many available sensor options to integrate into their hardware designs. In this work, we compare two different types of FBG sensors under identical conditions and application, namely, acting as the sensor for needle insertion shape reconstruction. We built a three-channel single core needle and a seven-channel multicore fiber (MCF) needle and discuss the pros and cons of both constructions for shape sensing experiments into constant curvature jigs. The overall needle tip error is 1.23 mm for the single core needle and 2.08 mm for the multicore needle.

6.
Annu Int Conf IEEE Eng Med Biol Soc ; 2022: 4397-4401, 2022 07.
Artículo en Inglés | MEDLINE | ID: mdl-36086006

RESUMEN

The determination of flexible needle shape during insertion is critical for planning and validation in minimally invasive surgical percutaneous procedures. In this paper, we validate a needle shape-sensing method using fiber Bragg grating (FBG) sensors over sequential needle insertion lengths in gel phantom and real tissue. Experiments on a four-active area, FBG-sensorized needle were performed in both isotropic simulated tissue and inhomogeneous animal tissue with computed tomography (CT) as the ground truth of the needle shape. The results show that the needle shape obtained from the FBG sensors has an overall consistent accuracy in real tissue in comparison to the phantom gel. The results validate a viable 3D needle shape-sensing model and reconstruction method over various insertion depths in comparison to the needle shapes determined from CT in both gel phantom and real tissue.


Asunto(s)
Agujas , Tomografía Computarizada por Rayos X , Animales , Procedimientos Quirúrgicos Mínimamente Invasivos , Fantasmas de Imagen
7.
IEEE Sens J ; 22(22): 22232-22243, 2022 Nov 15.
Artículo en Inglés | MEDLINE | ID: mdl-37216067

RESUMEN

Flexible bevel-tipped needles are often used for needle insertion in minimally-invasive surgical techniques due to their ability to be steered in cluttered environments. Shapesensing enables physicians to determine the location of needles intra-operatively without requiring radiation of the patient, enabling accurate needle placement. In this paper, we validate a theoretical method for flexible needle shape-sensing that allows for complex curvatures, extending upon a previous sensor-based model. This model combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod to determine and predict the 3D needle shape during insertion. We evaluate the model's shape sensing capabilities in C- and S-shape insertions in single-layer isotropic tissue, and C-shape insertions in two-layer isotropic tissue. Experiments on a four-active area, FBG-sensorized needle were performed in varying tissue stiffnesses and insertion scenarios under stereo vision to provide the 3D ground truth needle shape. The results validate a viable 3D needle shape-sensing model accounting for complex curvatures in flexible needles with mean needle shape sensing root-mean-square errors of 0.160 ± 0.055 mm over 650 needle insertions.

8.
Rep U S ; 2022: 3505-3511, 2022 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-36636257

RESUMEN

Complex needle shape prediction remains an issue for planning of surgical interventions of flexible needles. In this paper, we validate a theoretical method for flexible needle shape prediction allowing for non-uniform curvatures, extending upon a previous sensor-based model which combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod to determine and predict the 3D needle shape during insertion. We evaluate the model's effectiveness in single-layer isotropic tissue for shape sensing and shape prediction capabilities. Experiments on a four-active area, FBG-sensorized needle were performed in varying single-layer isotropic tissues under stereo vision to provide 3D ground truth of the needle shape. The results validate a viable 3D needle shape prediction model accounting for non-uniform curvatures in flexible needles with mean needle shape sensing and prediction root-mean-square errors of 0.479 mm and 0.892 mm, respectively.

9.
J Exp Biol ; 224(Pt 6)2021 03 12.
Artículo en Inglés | MEDLINE | ID: mdl-33536306

RESUMEN

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.


Asunto(s)
Lagartos , Locomoción , Animales , Fenómenos Biomecánicos , Movimiento (Física) , Serpientes
10.
Int Symp Med Robot ; 20212021 Nov.
Artículo en Inglés | MEDLINE | ID: mdl-35187545

RESUMEN

There has been much research exploring the use of fiber Bragg grating (FBG)-sensorized needles in the prostate biopsy procedure, but all FBG needles used in the research need to be calibrated, which is time consuming and prone to human errors. In this work, a semi-automatic robotic system was developed to perform FBG needle calibration. Compared to manual calibration results, the robotic system is able to calibrate FBG needles with the similar level of accuracy as achieved by an experienced manual operator, thus reducing the time cost during the needle calibration process.

11.
Integr Comp Biol ; 60(1): 171-179, 2020 07 01.
Artículo en Inglés | MEDLINE | ID: mdl-32215569

RESUMEN

Snakes can move through almost any terrain. Similarly, snake robots hold the promise as a versatile platform to traverse complex environments such as earthquake rubble. Unlike snake locomotion on flat surfaces which is inherently stable, when snakes traverse complex terrain by deforming their body out of plane, it becomes challenging to maintain stability. Here, we review our recent progress in understanding how snakes and snake robots traverse large, smooth obstacles such as boulders and felled trees that lack "anchor points" for gripping or bracing. First, we discovered that the generalist variable kingsnake combines lateral oscillation and cantilevering. Regardless of step height and surface friction, the overall gait is preserved. Next, to quantify static stability of the snake, we developed a method to interpolate continuous body in three dimensions (3D) (both position and orientation) between discrete tracked markers. By analyzing the base of support using the interpolated continuous body 3-D kinematics, we discovered that the snake maintained perfect stability during traversal, even on the most challenging low friction, high step. Finally, we applied this gait to a snake robot and systematically tested its performance traversing large steps with variable heights to further understand stability principles. The robot rapidly and stably traversed steps nearly as high as a third of its body length. As step height increased, the robot rolled more frequently to the extent of flipping over, reducing traversal probability. The absence of such failure in the snake with a compliant body inspired us to add body compliance to the robot. With better surface contact, the compliant body robot suffered less roll instability and traversed high steps at higher probability, without sacrificing traversal speed. Our robot traversed large step-like obstacles more rapidly than most previous snake robots, approaching that of the animal. The combination of lateral oscillation and body compliance to form a large, reliable base of support may be useful for snakes and snake robots to traverse diverse 3-D environments with large, smooth obstacles.


Asunto(s)
Locomoción , Robótica , Serpientes/fisiología , Animales , Fenómenos Biomecánicos
12.
Proc IEEE Sens ; 20202020 Oct.
Artículo en Inglés | MEDLINE | ID: mdl-34149973

RESUMEN

Several models incorporate needle shape prediction, however prediction in multi-layer tissue for complex needle shape remains an issue. In this work, we present a method for trajectory generation of flexible needles that allows for complex curvatures, extending upon a previous sensor-based model. This model combines curvature measurements from fiber Bragg grating (FBG) sensors and the mechanics of an inextensible elastic rod for shape-sensing. We evaluate the method's effectiveness in single- and double-layer isotropic tissue prediction. The results illustrate a valid trajectory generation method accounting for complex curvatures in flexible needles.

13.
Minim Invasive Ther Allied Technol ; 28(4): 199-205, 2019 Aug.
Artículo en Inglés | MEDLINE | ID: mdl-30822190

RESUMEN

Objective: Needle insertion is a common component of most diagnostic and therapeutic interventions. Needles with asymmetrically sharpened points such as the bevel point are ubiquitous. Their insertion path is typically curved due to the rudder effect at the point. However, the common planned path is straight, leading to targeting errors. We present a simple technique that may substantially reduce these errors. The method was inspired by practical experience, conceived mathematically, and refined experimentally. Methods: Targeting errors are reduced by flipping the bevel on the opposite side (rotating the needle 180° about its axis), at a certain depth during insertion. The ratio of the flip depth to the full depth of insertion is defined as the flip depth ratio (FDR). Based on a model, FDR is constant 0.3. Results: Experimentally, the ratio depends on the needle diameter, 0.35 for 20Ga and 0.45 for 18Ga needles. Thinner needles should be flipped a little shallower, but never less than 0.3. Conclusion: Practically, a physician may expect to reduce ∼80% of needle deflection errors by simply flipping the needle. The technique may be used by hand or with guidance devices.


Asunto(s)
Técnicas y Procedimientos Diagnósticos/instrumentación , Inyecciones/instrumentación , Inyecciones/métodos , Fenómenos Mecánicos , Agujas , Punciones/instrumentación , Punciones/métodos , Humanos , Modelos Teóricos
14.
Pediatr Allergy Immunol ; 30(2): 179-187, 2019 03.
Artículo en Inglés | MEDLINE | ID: mdl-30428138

RESUMEN

BACKGROUND: Exposure to air pollution aggravates symptoms of atopic dermatitis (AD) in children in the population studies. Variability in individual patient's response from individual susceptibility is needed to be explored. OBJECTIVE: This study aimed to investigate spectrum of individual variability in the associations between AD symptoms and air quality. METHODS: We enrolled 89 children aged 0-6 years with AD (22 890 person-days). Daily manifestation of symptoms was recorded for an average of 257 days (range 100-499). Both an individual analysis using logistic regression models and an overall analysis using a generalized estimating equation were performed. RESULTS: The odds ratios of an individual ranged 0.24-8.11 for particulate matter <10 µm in diameter (PM10 ), 0.09-101.92 for nitrogen oxide (NO2 ), 0.03-44.00 for ozone (O3 ), 0.11-58.30 for sulfur dioxide (SO2 ), 0.00-15.83 for carbon monoxide (CO), 0.00-39 446.94 for temperature, and 0.03-5.18 for relative humidity, demonstrating a wide individual variability. In the overall analysis, PM10 , NO2 , SO2 , and CO had a significantly positive association, whereas temperature and relative humidity were negatively associated with AD symptoms. Air pollution was responsible for aggravation of symptoms from 24.7% (O3 ) to 39.3% (SO2 ) of AD children. Overall, 71.9% of the AD children responded to at least one or more air pollution and weather variable. CONCLUSION: Responses of AD children to air pollution and weather variable were considerably variable among individuals. An individualized model would be useful to forecast and manage AD symptoms in patients.


Asunto(s)
Contaminantes Atmosféricos/inmunología , Contaminación del Aire/efectos adversos , Variación Biológica Poblacional/inmunología , Dermatitis Atópica/etiología , Exposición a Riesgos Ambientales/efectos adversos , Contaminantes Atmosféricos/análisis , Niño , Preescolar , Femenino , Humanos , Lactante , Recién Nacido , Masculino , República de Corea , Tiempo (Meteorología)
15.
IEEE Robot Autom Lett ; 3(3): 2129-2136, 2018 Jul.
Artículo en Inglés | MEDLINE | ID: mdl-30276269

RESUMEN

Fine needle deflection is a problem encountered during insertion into a soft tissue. Although an axial rotational insertion is an effective approach for minimizing this problem, needle deflection still depends on the insertion angle with respect to the tissue boundary. Since the human body consists of multi-layered tissues of various shapes and mechanical properties, preoperative planning of an optimal path is a key factor for achieving a successful insertion. In this paper, we propose an optimization-based preoperative path planning model that minimizes needle deflection during multi-layered tissue insertion. This model can determine the optimal path based on the sum of insertion angles with respect to each tissue boundary that the needle passes through. To increase the accuracy of the model, we incorporated the effect of distances from tissue boundaries and the probability that the deflection is acceptable by incorporating weighting factors into the model. To validate the model, we performed experiments involving four scenarios of two- and three-layered tissues. The results showed that the proposed model is capable of determining the optimal insertion path in all scenarios.

16.
J Comput Biol ; 25(1): 72-88, 2018 01.
Artículo en Inglés | MEDLINE | ID: mdl-29172668

RESUMEN

Assessing preferred relative rigid body position and orientation is important in the description of biomolecular structures (such as proteins) and their interactions. In this article, we extend and apply the "symmetrical parameterization," which we recently introduced in the kinematics community, to address problems in structural biology. We also review parameterization methods that are widely used in structural biology to describe relative rigid body motions (in particular, orientations) as a basis for comparison. The new symmetrical parameterization is useful in describing the relative biomolecular rigid body motions, where the parameters are symmetrical in the sense that the subunits of a complex biomolecular structure are described in the same way for the corresponding motion and its inverse. The properties of this new parameterization, singularity analysis, and inverse kinematics are also investigated in more detail. Finally, parameterization is applied to real biomolecular structures and a potential application to structure modeling of symmetric macromolecules to show the efficacy of the symmetrical parameterization in the field of computational structural biology.


Asunto(s)
Algoritmos , Biología Computacional/métodos , Análisis de Secuencia/métodos , Fenómenos Biomecánicos , Simulación de Dinámica Molecular , Movimiento (Física)
17.
J Comput Biol ; 24(1): 13-30, 2017 Jan.
Artículo en Inglés | MEDLINE | ID: mdl-27710115

RESUMEN

Cryo-electron microscopy (EM) and small angle X-ray scattering (SAXS) are two different data acquisition modalities often used to glean information about the structure of large biomolecular complexes in their native states. A SAXS experiment is generally considered fast and easy but unveils the structure at very low resolution, whereas a cryo-EM experiment needs more extensive preparation and postacquisition computation to yield a three-dimensional (3D) density map at higher resolution. In certain applications, we may need to verify whether the data acquired in the SAXS and cryo-EM experiments correspond to the same structure (e.g., before reconstructing the 3D density map in EM). In this article, a simple and fast method is proposed to verify the compatibility of the SAXS and EM experimental data. The method is based on averaging the two-dimensional correlation of EM images and the Abel transform of the SAXS data. Orientational preferences are known to exist in cryo-EM experiments, and we also consider these effects on our method. The results are verified on simulations of conformational states of large biomolecular complexes.


Asunto(s)
Algoritmos , Microscopía por Crioelectrón/normas , Procesamiento de Imagen Asistido por Computador/métodos , Modelos Moleculares , Difracción de Rayos X/normas , Humanos , Sustancias Macromoleculares/química , Conformación Proteica , Receptores de Glutamato/química , Dispersión del Ángulo Pequeño
18.
Trop Med Health ; 44: 23, 2016.
Artículo en Inglés | MEDLINE | ID: mdl-27524928

RESUMEN

BACKGROUND: Malaria is a significant public health issue in Papua New Guinea (PNG) as the burden is among the highest in Asia and the Pacific region. Though PNG's vulnerability to climate change and sensitivity of malaria mosquitoes to weather are well-documented, there are few in-depth epidemiological studies conducted on the potential impacts of climate on malaria incidence in the country. METHODS: This study explored what and how local weather and global climate variability impact on malaria incidence in five regions of PNG. Time series methods were applied to evaluate the associations of malaria incidence with weather and climate factors, respectively. Local weather factors including precipitation and temperature and global climate phenomena such as El Niño-Southern Oscillation (ENSO), the ENSO Modoki, the Southern Annular Mode, and the Indian Ocean Dipole were considered in analyses. RESULTS: The results showed that malaria incidence was associated with local weather factors in most regions but at the different lag times and in directions. Meanwhile, there were trends in associations with global climate factors by geographical locations of study sites. CONCLUSIONS: Overall heterogeneous associations suggest the importance of location-specific approaches in PNG not only for further investigations but also public health interventions in repose to the potential impacts arising from climate change.

19.
Anal Chem ; 88(24): 12241-12247, 2016 12 20.
Artículo en Inglés | MEDLINE | ID: mdl-28193033

RESUMEN

The components of sweat provide an array of potential biomarkers for health and disease. Sweat chloride is of interest as a biomarker for cystic fibrosis, electrolyte metabolism disorders, electrolyte balance, and electrolyte loss during exercise. Developing wearable sensors for biomarkers in sweat is a major technological challenge. Potentiometric sensors provide a relatively simple technology for on-body sweat chloride measurement, however, equilibration between reference and test solutions has limited the time over which accurate measurements can be made. Here, we report on a wearable potentiometric chloride sweat sensor. We performed parametric studies to show how the salt bridge geometry determines equilibration between the reference and test solutions. From these results, we show a sweat chloride sensor can be designed to provide accurate measurements over extended times. We then performed on-body tests on healthy subjects while exercising to establish the feasibility of using this technology as a wearable device.


Asunto(s)
Cloruros/análisis , Potenciometría/instrumentación , Sudor/química , Dispositivos Electrónicos Vestibles , Adulto , Fibrosis Quística/diagnóstico , Electrólitos/análisis , Diseño de Equipo , Ejercicio Físico , Femenino , Humanos , Masculino , Sudoración , Adulto Joven
20.
J Comput Biol ; 22(9): 787-805, 2015 Sep.
Artículo en Inglés | MEDLINE | ID: mdl-26244255

RESUMEN

Small-angle x-ray scattering (SAXS) is an experimental biophysical method used for gaining insight into the structure of large biomolecular complexes. Under appropriate chemical conditions, the information obtained from a SAXS experiment can be equated to the pair distribution function, which is the distribution of distances between every pair of points in the complex. Here we develop a mathematical model to calculate the pair distribution function for a structure of known density, and analyze the computational complexity of these calculations. Efficient recursive computation of this forward model is an important step in solving the inverse problem of recovering the three-dimensional density of biomolecular structures from their pair distribution functions. In particular, we show that integrals of products of three spherical-Bessel functions arise naturally in this context. We then develop an algorithm for the efficient recursive computation of these integrals.


Asunto(s)
Biología Computacional/métodos , Sustancias Macromoleculares/química , Estadística como Asunto/métodos , Difracción de Rayos X/métodos , Algoritmos , Modelos Teóricos , Dispersión del Ángulo Pequeño , Programas Informáticos
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