File Name: computational methods in physics and engineering wong .zip
Monte Carlo methods , or Monte Carlo experiments , are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle.
Garbozi, D. Bentz, and N. Martys, Digital Images and Computer Modelling.
Computational methods have played an important role in health care in recent years, as determining parameters that affect a certain medical condition is not possible in experimental conditions in many cases. Computational fluid dynamics CFD methods have been used to accurately determine the nature of blood flow in the cardiovascular and nervous systems and air flow in the respiratory system, thereby giving the surgeon a diagnostic tool to plan treatment accordingly.
Machine learning or data mining MLD methods are currently used to develop models that learn from retrospective data to make a prediction regarding factors affecting the progression of a disease. These models have also been successful in incorporating factors such as patient history and occupation.
MLD models can be used as a predictive tool to determine rupture potential in patients with abdominal aortic aneurysms AAA along with CFD-based prediction of parameters like wall shear stress and pressure distributions. A combination of these computer methods can be pivotal in bridging the gap between translational and outcomes research in medicine. This paper reviews the use of computational methods in the diagnosis and treatment of AAA. Rapid improvements in computational power coupled with better understanding of hemodynamics have spawned the interdisciplinary science of computational medicine.
A multidisciplinary effort with clinicians, radiologists, and biologists on the one hand and engineers and computer scientists on the other hand has greatly increased the ability to diagnose medical conditions and has improved delivery of healthcare. Computational methods have played a very important role in this, as experimentally determining parameters that affect a certain medical condition is not possible in many cases.
CFD methods can be used to accurately determine the nature of blood flow in the cardiovascular system [ 1 ] and the nervous system [ 2 ] and air flow in the respiratory system [ 3 ]. Some of these variables patient history, occupation, and family history are difficult to quantify directly and so, using methods such as machine learning, they can be incorporated into predictive models.
AAA is a condition affecting the aorta usually in its infra-renal segment and involves the abnormal dilatation of this artery Figure 1. The infrarenal aorta is a site predisposed to aneurysmal widening. The cyclic stress caused by the pulse wave in conjunction with factors which decrease the strength of the wall may lead to dilatation and ultimately to rupture [ 7 ]. It is the 13th most common cause of death in the United States [ 8 ]. There are several risk factors that have been known to affect the genesis, growth, and rupture of AAA: advanced age, greater height, coronary artery disease, atherosclerosis, high cholesterol levels, hypertension [ 10 ], and smoking [ 11 , 12 ].
AAAs are known to have an incidence that is approximately four to six times higher in men than in women. However, the incidence in women also rises with age, although it starts later in life than in men [ 13 ]. Initially, open surgery was the norm but since the introduction of EVAR [ 14 ], there has been a widespread acceptance of the procedure.
This is a less invasive procedure with a decrease in day mortality in patients when compared to open surgical repair. In addition, the current generation of devices approved has smaller delivery system profiles, tracks better, and can be used to treat difficult AAA morphology more easily [ 15 ]. Vascular surgeons have used lumen diameter as a metric to guide surgical intervention for some time now. A cutoff diameter of about 5—5.
Some studies like The UK Small Aneurysm Trial Participants, [ 17 ], have reinforced this value as a reasonable measure of the risk to benefit ratio between the risks of aneurysm rupture and those of surgical intervention. As a criterion, the use of the maximum diameter metric is a crude way to estimate the critical state of an AAA [ 18 ].
Vorp et al. They defined the critical state of an AAA as that at which the mechanical stress within the aneurysmal wall exceeds the tensile strength of the tissue. Other parameters such as wall tensile strength, length of aneurysm, and patient-specific pulsatile velocity and pressure boundary conditions also play an important role in the progress to rupture of the AAA.
Biomechanics of rupture in AAA is affected due to variations in a combination of these parameters. Hence, to account for the contributions of several parameters in what is essentially a patient-specific problem, computational methods could play a crucial role. This paper provides a summary of the different computational methods that can be used, a review of the literature that has incorporated computational methods to account for several parameters that lead to rupture in AAA, and suggestions on the direction that future research using these methods should take in order to improve our understanding of the rupture of AAA.
Computational methods in imaging are left out of this review as the focus is on the biomechanical analysis of AAA. Biomechanical analysis of an AAA system involves a series of steps to assess the factors that may influence the risk of rupture.
These are then put through a process of image segmentation to convert what are 2D slices into a 3D geometric model, suitable for use in a CFD code Figure 2. The pulsatile velocity and pressure boundary conditions for use in the CFD model are obtained during surgery. These are measured at the inlet and outlet of the aneurysm and at any other suitable point of interest for the researcher. CFD codes are then used to obtain the wall shear stress, pressure distributions, and the flow physics of blood in the aneurysm.
Computational methods in biomechanics incorporate the parameters mentioned in the previous section. Models are based on constitutive laws of continuum mechanics, such as the Law of Laplace that had been originally used in the analysis of bursting of cylindrical shells, the laws of rheology to describe the properties of blood, fluid mechanics in the analysis of vortex formation in the lumen, and material properties of stent grafts in a postsurgical aorta.
They describe the momentum field of the flow under investigation and need to be used in conjunction with the continuity equation that describes mass transport. FVM is generally seen to approximate the solution accurately to a large extent.
But FVM may not be the best way to understand the deformation of a tissue due to blood flow. FEM has been used to solve fluid mechanics based problems [ 20 , 21 ] and specifically for AAA simulations as well [ 22 , 23 ]. It has the capability to incorporate the displacement of the biological tissue in a medical simulation problem more accurately than a FVM-based solver where the fluid becomes the most important component in the solution unlike in FEM where the solid displacement is more important.
This would allow a fluid-structure interaction FSI model to be embedded in the resulting physics. FSI methods [ 24 , 25 ] have been demonstrated to be effective in the description of flow physics in aneurysms. The coupling of the aneurysmal wall motion and blood flow is commonly made by using the Arbitrary Lagrangian Eulerian ALE method. From a computational point of view, we have to incorporate the moving interface between the fluid and the rigid body. The ALE method has been successfully applied to such moving boundary problems, which arise in free surface problems and fluid-structure interaction problems.
Therefore it is natural to employ the mixed viewpoint of the Lagrangian and Eulerian descriptions [ 27 ]. Whilst the above method has been used for a rigid tissue, the ALE has been extended to the FSI problem as well [ 28 ].
Hirt et al. Significant experience over many years in the management of AAA amongst hospitals and clinicians has led to the availability of a large volume of data on patients who have undergone treatment for the condition. Statistical techniques such as univariate and multivariate logistic regression analyses have been successfully applied to risk prediction in clinical medicine. A commonly used instrument is the use of a prognostic score derived from logistic regression to classify a patient into a potential risk category [ 30 ].
This suggests that, using these techniques, an estimate of the associations between the various risk factors that cause rupture in an AAA can be encoded. Many techniques have been used for data mining in medical and biomedical studies. A popular data mining technique is decision tree induction. The dataset is recursively partitioned into discrete subcategories. These subcategories are based on the value of an attribute in the dataset.
The criteria for selecting these attributes in the dataset are based on its predictability within a certain subcategory. As a result of this, the final outcome is a set of series of categories based on values of the attributes. Each of these series generates a classification value. There are many algorithms developed for decision tree induction. Some clinical examples that apply this approach are diagnosis of central nervous system disorders [ 31 ], posttraumatic acute lung injury prediction [ 32 ], and acute cardiac ischemia [ 33 ].
Some of the parameters that may affect the ability to predict rupture risk in an untreated aneurysm are listed here. These parameters can be used in a model that learns from retrospective data and can be used in a prospective tool for patients. Calcification of the aortic wall and calcium volume and percentage of aneurysm sac volume.
Patient history smoking, diabetes, specific occupations, and family history of aneurysms. Whilst these may be some of the input variables for a machine learning model, the output is the risk of rupture that can be obtained as a result of training the model on such retrospectively gathered data.
The said model will learn about the parameters that play a part in the rupture or nonrupture of a patient-specific AAA. A great amount of classified data, that is, a suitable spread of ruptured and nonruptured retrospective cases, will allow the model to gauge the parameters that are the most important factors among many that lead to rupture in an AAA case.
This model can then be applied prospectively where the model, having learnt from a large amount of data in the past, can to a degree of accuracy make a prediction of rupture risk in the patient. When comparing different classifiers [ 34 , 35 ] the key issues to address in such a model are.
The risk of rupture of an AAA has been studied in several different ways. Some researchers have performed experiments on phantoms made of silicone rubber [ 36 ] and distensible tubes [ 37 — 39 ], on cadavers, and during surgery to ascertain the properties of the AAA configuration [ 18 ]. Some of them have come up with analytical approaches of a simplified AAA problem [ 40 — 42 ]. Experiments are difficult to set up due to ethical considerations of sample retrieval from patients.
Material properties need to be accurately obtained for the simulation to be of any use clinically. This has been a major challenge in AAA rupture studies. Unsteady boundary conditions of velocity and pressure are generally obtained from phase contrast MRI methods.
There is a paucity of such studies and, in most instances, a few waveforms that are available in literature are reused by others, thereby taking away the patient-specific nature of the problem being solved.
Figure 3 shows such a sample waveform that has been used by Soudah et al. Inlet velocity and pressure outlet waveforms [ 43 ]. Flow in the aorta is pulsatile in nature. Hence, time varying waveforms of velocity and pressure are needed in order to accurately model the flow physics. The inlet flow velocity profile has two peaks as seen in Figure 3 , each visualizing the systolic and diastolic phases in a pulse. The outlet pressure shows only one peak in the pulse.
Several different kinds of outlet boundary conditions have been used in literature such as constant pressure [ 44 , 45 ] and flow specification at particular instances [ 46 ]. The boundary conditions for the velocity V are imposed as follows: i no slip at the walls, ii uniform slug profile at the inlet, and iii zero-traction outflow at the exit.
For pulsatile flow, the inflow mean velocity is time dependent and the volume flow rate is oscillatory as suggested by Finol and Amon, [ 47 ]. Therefore, in the usage of Windkessel parameters based on patient-specific clinical data, the simulation takes into account the essential characteristics of the rest of the vasculature, which can be expected to improve the correlation between the simulation results and the true in vivo characteristics [ 48 ].
The Womersley number is a nondimensional number that describes the ratio of pulsatile flow to viscous effects and is used extensively in computations related to biofluids. Womersley profiles generally regard only the centerline velocity of the inlet. They incorporate the Bessel functions to derive the velocity profile in the inlet. But, it is not accurate as the geometry of the artery is patient-specific and affects the velocity values.
The Womersley number is as shown below [ 49 ]:. Flow boundary conditions are critical to computing the flow solution in AAA.
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Computational methods have played an important role in health care in recent years, as determining parameters that affect a certain medical condition is not possible in experimental conditions in many cases. Computational fluid dynamics CFD methods have been used to accurately determine the nature of blood flow in the cardiovascular and nervous systems and air flow in the respiratory system, thereby giving the surgeon a diagnostic tool to plan treatment accordingly. Machine learning or data mining MLD methods are currently used to develop models that learn from retrospective data to make a prediction regarding factors affecting the progression of a disease. These models have also been successful in incorporating factors such as patient history and occupation. MLD models can be used as a predictive tool to determine rupture potential in patients with abdominal aortic aneurysms AAA along with CFD-based prediction of parameters like wall shear stress and pressure distributions.
Once production of your article has started, you can track the status of your article via Track Your Accepted Article. Help expand a public dataset of research that support the SDGs. To encourage the development of formal computing methods , and their application in biomedical research and medical practice, by illustration of fundamental principles in biomedical informatics research; to stimulate basic research into application software design; to report the state of research of biomedical To encourage the development of formal computing methods , and their application in biomedical research and medical practice, by illustration of fundamental principles in biomedical informatics research; to stimulate basic research into application software design; to report the state of research of biomedical information processing projects; to report new computer methodologies applied in biomedical areas; the eventual distribution of demonstrable software to avoid duplication of effort; to provide a forum for discussion and improvement of existing software; to optimize contact between national organizations and regional user groups by promoting an international exchange of information on formal methods, standards and software in biomedicine. Computer Methods and Programs in Biomedicine covers computing methodology and software systems derived from computing science for implementation in all aspects of biomedical research and medical practice.
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Monte Carlo methods , or Monte Carlo experiments , are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes:  optimization , numerical integration , and generating draws from a probability distribution.
For personal use only. Includes bibliographical references and index. Physics Data processing. Mathematical physics.
Bryan M. Cameron Chevalier and Bryan M. Wong, and Jory A. Pandeeswar Makam, Sharma S. Yamijala, Linda J. Shimon, Bryan M.
For personal use only. Includes bibliographical references and index. Physics Data processing. Mathematical physics. Engineering - Data processing. Engineering mathematics.
Numerical methods in biomedical research is a rapidly development field to provide a state-of-the-art tool for biomedical research and applications. Reliable predictions will lead to patient-specific simulations in the next decade to improve the diagnoses and treatment of diseases. The main focus of this special issue will be on the interface between numerical methods and biomedical applications especially for cardiovascular dynamics and heat transfer problem in the human body. It is also interesting to have quantitative analysis from the molecular up to the organ level. The goal of this special issue is to bring together experts in related fields of computational biomedical engineering like multiscale flow modeling, blood flow propagation, fluid-solid coupling, inverse problems in biomechanics, high-performance computing of multiphysics discretization schemes, cardiovascular biomechanics, and porous media. In addition, advanced applications in the field of biomechanics problems as aneurysm modeling, valvular modeling, hemodynamics, transport phenomena, and the modeling of medical devices are welcome.
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