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A mathematical model of lung parenchyma.

The geometry of the proposed model of the parenchyma of a mammalian lung reproduces a cluster of alveoli arranged around a lowest-level air duct. The alveolar walls are assumed to be nonlinear elastic membranes, whose properties are described in terms of a strain energy function which reflects the hardening character of the stress-strain curve. The effect of the surfactant is included in terms of a variable (area-dependent) surface tension. Analyses of various mechanical processes in the parenchyma are performed with the aid of the finite element method, with the geometric and physical nonlinearities of the problem taken into account.

Biomechanical Phenomena↗

Heat and water vapor transport in the human upper airways at hyperbaric conditions.

Heat and mass transfer mechanisms have been characterized in physical models of human cadaver airways to simulated depths of 305 m with various gas mixtures. Such characterizations offer a detailed understanding of the effects of environmental pressures, gas composition, and respiratory rates (RMV) on the body cooling capacity of the respiratory airways. Empirical heat transfer relationships in the form -Nu = AReNPr1/3 are derived for the oral and nasal passageways during inhalation and exhalation flows. -Nu, Re, and Pr are the dimensionless Nusselt, Reynolds, and Prandtl numbers, respectively. The Nusselt and Reynolds numbers are based on the diameter and gas flow rate in the trachea and are applicable to Reynolds number values up to 70,000.

Air↗

An experimental study of velocity distribution in a human lung cast.

A mechanical lung model with branching up to five generations, developed from an actual human lung, is used to study experimentally the velocity profiles in the trachea and the main branches. Three different flow rates representing light, medium, and heavy breathings have been simulated for both inhalation and exhalation. The velocity profiles, except for the one in the trachea in the frontal direction due to exhalation, are in good agreement with the velocity profiles in simplified models of published literature.

Biomechanical Phenomena↗

A general method for determining the functional role of a muscle.

This paper presents a general classification method for determining the functional role of any muscle, and a procedure for determining the sensitivity of that role to small changes in system parameters. The classification method is based on the premise that the system model, when acted upon solely by the muscle of interest, will depart from any initial rest configuration in such a way as to decrease the muscle's length. This method is particularly useful for multiple-joint muscles, and is illustrated by examining a slider-crank mechanism and straight line muscle model to determine the functional role of the hamstrings during a constrained leg flexion motion.

Biomechanical Phenomena↗

Measurement of wall motion and wall shear in a compliant arterial cast.

Initial measurements of the time-varying wall shear rate at two sites in a compliant cast of a human aortic bifurcation are presented. The shear rates were derived from flow velocities measured by laser Doppler velocimetry (LDV) near the moving walls of the cast. To derive these shear rate values, the distance from the velocimeter sampling volume to the cast wall must be known. The time variation of this distance was obtained from LDV measurements of the velocity of the wall itself.

Aorta↗

Choking phenomena in a lung-like model.

A simple, continuous, one-dimensional model for the geometry and structure of the bronchial airways is used for the analysis of fluid flow patterns which have been observed in forced expiration maneuvers. Various phenomena within the conducting system associated with flow limitation are investigated: the conditions in which a "choke" (flow limitation) can occur in a compliant system; theoretical flows that are physically impossible; the possibility of having elastic jumps downstream of the choke point; perturbations in the physical parameters of the conducting system.

Airway Obstruction↗

An investigation of particle flow through capillary models with the resistive pulse technique.

The use of the resistive pulse technique for the measurement of microsphere and red cell transit times through single-pore "Nuclepore" membranes (with pore diameters of 3.5 to 7.0 microns and pore length of approximately 11 microns) is described. The investigation of the fluid mechanics and electrical characteristics of the experimental system provides methods for the determination of particle and cell size, and entrance and transit times. Experimental measurement of the position dependent velocity of spherical particles through the pore shows close agreement with theoretical models. Red cell size and transit time through different sized pores at physiological shear stresses is also measured.

Blood Flow Velocity↗

The physical dimensions of the human neonatal cardiovascular system.

To establish a data base for studies which seek to model and simulate the human perinatal cardiovascular system, we dissected three stillborn, full-term infants and measured the length, internal diameter, and wall thickness of over 1000 blood vessel segments. Cumulatively, these segments represent the major and minor vessels of the systemic and pulmonary circulation at birth. Statistical analysis showed that the methods used to obtain these physical dimensions were highly consistent and that storage of tissue samples in 10 percent formaldehyde solution caused a linear shrinkage of approximately 6.3 percent. A topological code was developed to illustrate the network relationships of blood vessel segments. An example of data utilization based on the topological code is presented and discussed.

Biomedical Engineering↗

Helical flow around arterial bends for varying body mass.

The three dimensionally curved aortic arch is modeled as a portion of a helical pipe. Pulsatile blood flow therein is calculated assuming helical symmetry and an experimentally measured pressure pulse. Appropriate values for the Womersley and Reynolds numbers are taken from allometric scaling relations for a variety of body masses. The flow structure is discussed with particular reference to the wall shear, which is believed to be important in the inhibition of atheroma. It is found that nonplanar curvature limits the severity of flow separation at the inner bend, and reduces spatial variation of wall shear.

Animals↗

Aerosol transport and deposition in sequentially bifurcating airways.

Deposition patterns and efficiencies of a dilute suspension of inhaled particles in three-dimensional double bifurcating airway models for both in-plane and 90 deg out-of-plane configurations have been numerically simulated assuming steady, laminar, constant-property air flow with symmetry about the first bifurcation. Particle diameters of 3, 5, and 7 microns were used in the simulation, while the inlet Stokes and Reynolds numbers varied from 0.037 to 0.23 and 500 to 2000, respectively. Comparisons between these results and experimental data based on the same geometric configuration showed good agreement. The overall trend of the particle deposition efficiency, i.e., an exponential increase with Stokes number, was somewhat similar for all bifurcations. However, the deposition efficiency of the first bifurcation was always larger than that of the second bifurcation, while in general the particle efficiency of the out-of-plane configuration was larger than that of the in-plane configuration. The local deposition patterns consistently showed that the majority of the deposition occurred in the carinal region. The distribution pattern in the first bifurcation for both configurations were symmetric about the carina, which was a direct result of the uniaxial flow at the inlet. The deposition patterns about the second carina showed increased asymmetry due to highly nonuniform flow generated by the first bifurcation and were extremely sensitive to bifurcation orientation. Based on the deposition variations between bifurcation levels and orientations, the use of single bifurcation models was determined to be inadequate to resolve the complex fluid-particle interactions that occur in multigenerational airways.

Aerosols↗

Surfactant transport over airway liquid lining of nonuniform depth.

Numerous effects (e.g., airway wall buckling, gravity, airway curvature, capillary instabilities) give rise to nonuniformities in the depth of the liquid lining of peripheral lung airways. The effects of such thickness variations on the unsteady spreading of a surfactant monolayer along an airway are explored theoretically here. Flow-induced film deformations are shown to have only a modest influence on spreading rates, motivating the use of a simplified model in which the liquid-lining depth is prescribed and the monolayer concentration satisfies a spatially inhomogeneous nonlinear diffusion equation. Two generic situations are considered: spreading along a continuous annular liquid lining of nonuniform depth, and spreading along a rivulet that wets the airway wall with zero contact angle. In both cases, transverse averaging at large times yields a one-dimensional approximation of axial spreading that is valid for the majority of the monolayer. However, a localized monolayer remains persistently two dimensional in a region at its leading edge having axial length scales comparable to the length scale of transverse depth variation. It is also shown how the transverse spreading of a monolayer may be arrested as it approaches a static contact line at the edge of a rivulet. Implications for Surfactant Replacement Therapy are discussed.

Biological Transport, Active↗

Viscoelastic behavior of a lung alveolar duct model.

A study is conducted into the oscillatory behavior of a finite element model of an alveolar duct. Its load-bearing components consist of a network of elastin and collagen fibers and surface tension acting over the air-liquid interfaces. The tissue is simulated using a visco-elastic model involving nonlinear quasi-static stress-strain behavior combined with a reduced relaxation function. The surface tension force is simulated with a time- and area-dependent model of surfactant behavior. The model was used to simulate lung parenchyma under three surface tension cases: air-filled, liquid-filled, and lavaged with 3-dimenthyl siloxane, which has a constant surface tension of 16 dyn/cm. The dynamic elastance (Edyn) and tissue resistance (Rti) were computed for sinusoidal tidal volume oscillations over a range of frequencies from 0.16-2.0 Hz. A comparison of the variation of Edyn and Rti with frequency between the model and published experimental data showed good qualitative agreement. Little difference was found in the model between Rti for the air-filled and lavaged models; in contrast, published data revealed a significantly higher value of Rti in the lavaged lung. The absence of a significant increase in Rti for the lavaged model can be attributed to only minor changes in the individual fiber bundle resistances with changes in their configuration. The surface tension was found to make an important contribution to both Edyn and Rti in the air-filled duct model. It was also found to amplify any existing tissue dissipative properties, despite exhibiting none itself over the small tidal volume cycles examined.

Biomechanical Phenomena↗

Three-dimensional computational model of left heart diastolic function with fluid-structure interaction.

Aided by advancements in computer speed and modeling techniques, computational modeling of cardiac function has continued to develop over the past twenty years. The goal of the current study was to develop a computational model that provides blood-tissue interaction under physiologic flow conditions, and apply it to a thin-walled model of the left heart. To accomplish this goal, the Immersed Boundary Method was used to study the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology. The fluid mass and momentum conservation equations were solved using Patankar's Semi-Implicit Method for Pressure Linked Equations (SIMPLE). A left heart model was developed to examine diastolic function, and consisted of the left ventricle, left atrium, and pulmonary flow. The input functions for the model included the pulmonary driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions for validation. The inflow velocities through the mitral valve corresponded with clinical values (E-wave = 74.4 cm/s, A-wave = 43 cm/s, and E/A = 1.73). The pressure traces for the atrium and ventricle, and the appearance of the ventricular flow fields throughout filling, agreed with those observed in the heart. In addition, the atrial flow fields could be observed in this model and showed the conduit and pump functions that current theory suggests. The ability to examine atrial function in the present model is something not described previously in computational simulations of cardiac function.

Biomedical Engineering↗

Simulating coronary arteries in x-ray angiograms.

Clinical validation of quantitative coronary angiography (QCA) algorithms is difficult due to the lack of a simple alternative method for accurately measuring in vivo vessel dimensions. We address this problem by embedding simulated coronary artery segments with known geometry in clinical angiograms. Our vessel model accounts for the profile of the vessel, x-ray attenuation in the original background, and noise in the imaging system. We have compared diameter measurements of our computer simulated arteries with measurements of an x-ray Telescopic-Shaped Phantom (XTSP) with the same diameters. The results show that for both uniform and anthropomorphic backgrounds there is good agreement in the measured diameters of XTSP compared to the simulated arteries (Pearson's correlation coefficient 0.99). In addition, the difference in accuracy and precision of the true diameter measures compared to the XTSP and simulated artery diameters was small (mean absolute error across all diameters was < or = 0.11 mm +/- 0.09 mm).

Algorithms↗

A three-dimensional deformable model for segmentation of human prostate from ultrasound images.

Segmentation of human prostate from ultrasound (US) images is a crucial step in radiation therapy, especially in real-time planning for US image-guided prostate seed implant. This step is critical to determine the radioactive seed placement and to ensure the adequate dose coverage of prostate. However, due to the low contrast of prostate and very low signal-to-noise ratio in US images, this task remains as an obstacle. The manual segmentation of this object is time consuming and highly subjective. In this work, we have proposed a three-dimensional (3D) deformable surface model for automatic segmentation of prostate. The model has a discrete structure made from a set of vertices in the 3D space that form triangle facets. The model converges from an initial shape to its equilibrium iteratively, by a weighted sum of the internal and external forces. Internal forces are based on the local curvature of the surface and external forces are extracted from the volumetric image data by applying an appropriate edge filter. We have also developed a method for initialization of the model from a few initial contours that are drawn on different slices. During the deformation, a resampling procedure is used to maintain the resolution of the model. The entire model is applied in a multiscale scheme, which increases the robustness and speed, and guarantees a better convergence. The model is tested on real clinical data and initial results are very promising.

Humans↗

Dynamic model of the left ventricle for use in simulation of myocardial perfusion SPECT and gated SPECT.

Simulation is a useful tool in cardiac SPECT to assess quantification algorithms. However, simple equation-based models are limited in their ability to simulate realistic heart motion and perfusion. We present a numerical dynamic model of the left ventricle, which allows us to simulate normal and anomalous cardiac cycles, as well as perfusion defects. Bicubic splines were fitted to a number of control points to represent endocardial and epicardial surfaces of the left ventricle. A transformation from each point on the surface to a template of activity was made to represent the myocardial perfusion. Geometry-based and patient-based simulations were performed to illustrate this model. Geometry-based simulations modeled (1) a normal patient, (2) a well-perfused patient with abnormal regional function, (3) an ischaemic patient with abnormal regional function, and (4) a patient study including tracer kinetics. Patient-based simulation consisted of a left ventricle including a realistic shape and motion obtained from a magnetic resonance study. We conclude that this model has the potential to study the influence of several physical parameters and the left ventricle contraction in myocardial perfusion SPECT and gated-SPECT studies.

Algorithms↗

Korean adult male voxel model KORMAN segmented from magnetic resonance images.

A voxel model of Korean adult male, KORMAN, was developed by processing whole-body magnetic resonance (MR) images of a healthy volunteer who represents an approximately average Korean in height and weight. Layer by layer the MR images were semi-automatically segmented and indexed using a graphic software and digitizer to construct data arrays consisting of 250 x 120 x 170 voxels of a size of 2 x 2 x 10 mm3. To assess the utility of the model, some illustrative dosimetric calculations were made to obtain organ absorbed doses and effective doses to the KORMAN placed in broad parallel photon fields with energies ranging from 0.05 to 10 MeV. The results were compared with those based on the medical internal radiation dose (MIRD)-type models given in ICRP74. The effective doses of ICRP74 were higher than those of KORMAN with percent differences ranging from 6% (LLAT, 10 MeV) to 30% (PA, 0.05 MeV). Significant differences of more than 40% were observed in organ absorbed doses for some organs including bone surface (AP), stomach (PA), and testes (LAT) for low photon energy. These are mainly caused by difference in trunk thickness between MIRD-type model and KORMAN, and differences in organ positions in the body.

Humans↗

Accuracy of finite element model-based multi-organ deformable image registration.

As more pretreatment imaging becomes integrated into the treatment planning process and full three-dimensional image-guidance becomes part of the treatment delivery the need for a deformable image registration technique becomes more apparent. A novel finite element model-based multiorgan deformable image registration method, MORFEUS, has been developed. The basis of this method is twofold: first, individual organ deformation can be accurately modeled by deforming the surface of the organ at one instance into the surface of the organ at another instance and assigning the material properties that allow the internal structures to be accurately deformed into the secondary position and second, multi-organ deformable alignment can be achieved by explicitly defining the deformation of a subset of organs and assigning surface interfaces between organs. The feasibility and accuracy of the method was tested on MR thoracic and abdominal images of healthy volunteers at inhale and exhale. For the thoracic cases, the lungs and external surface were explicitly deformed and the breasts were implicitly deformed based on its relation to the lung and external surface. For the abdominal cases, the liver, spleen, and external surface were explicitly deformed and the stomach and kidneys were implicitly deformed. The average accuracy (average absolute error) of the lung and liver deformation, determined by tracking visible bifurcations, was 0.19 (s.d.: 0.09), 0.28 (s.d.: 0.12) and 0.17 (s.d.: 0.07) cm, in the LR, AP, and IS directions, respectively. The average accuracy of implicitly deformed organs was 0.11 (s.d.: 0.11), 0.13 (s.d.: 0.12), and 0.08 (s.d.: 0.09) cm, in the LR, AP, and IS directions, respectively. The average vector magnitude of the accuracy was 0.44 (s.d.: 0.20) cm for the lung and liver deformation and 0.24 (s.d.: 0.18) cm for the implicitly deformed organs. The two main processes, explicit deformation of the selected organs and finite element analysis calculations, require less than 120 and 495 s, respectively. This platform can facilitate the integration of deformable image registration into online image guidance procedures, dose calculations, and tissue response monitoring as well as performing multi-modality image registration for purposes of treatment planning.

Algorithms↗