Biomedical Engineering and Bioengineering Commons^™

A Fractal Art Approach To The Three-Body Problem, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

This preliminary study explores a new search strategy for identifying relatively stable vs. unstable solutions to the planar three-body problem in astrophysics, starting from the perspective of computer-generated art. Here classical Newtonian accelerations, speeds, and positions of all three bodies in a fixed plane are calculated. All three bodies are stationary at time zero, and the fate of the system is classified as reflecting either a bound stable orbit, a likely collision, or the ejection of one body. The initial position of one of the three bodies is varied in the image plane, and the outcome coded as one of …

Model Based Analysis Of The Accuracy And Precision Of Auscultatory Blood Pressure Measurements In Patients With Atrial Fibrillation, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

Accurate measurement of blood pressure in the presence of atrial fibrillation remains an open problem. The present study combines the techniques of stochastic mathematical modeling with physiological models of the systemic circulation, cuff, and arm (1) to explore mechanisms underlying both the lack of accuracy and the lack of precision in cuff-based arterial pressure measurements during atrial fibrillation and (2) to develop strategies to correct for errors. Both the cardiovascular system and the measurement technique are described using mathematics, including both numerical techniques and analytical probability theory. Preliminary results with numerical models suggested that, despite variability, average systolic pressures tend …

Hypothesis Paper: Mechanism For Primary Blast Induced Traumatic Brain Injury With Minimal Head Motion, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

Transit of the human skull by blast waves produces diffuse brain injury. The exact mechanisms are unknown. This paper describes plausible mechanisms in which steep intracranial pressure gradients, demonstrated in prior computational models of blast-skull interaction, produce subsequent deformation and motion of the whole brain within the skull, without obvious movement of the head. Equations of motion are derived to describe the acceleration, velocity, and relative position of both the skull and the brain in response to known extracranial and intracranial pressures both during and several hundred milliseconds after blast wave passage. A finite element model is solved to visualize …

A Simple Mathematical Model For The Nonlinear Compliance Of Arteries, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

No abstract provided.

Brain Motion, Deformation, And Potential Injury During Soccer Heading, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

This paper addresses the problem of what is happening physically inside the skull during head-ball contact. Mathematical models based upon Newton’s laws of motion and numerical methods are used to create animations of brain motion and deformation inside the skull.

Initially a 1 cm gap filled with cerebrospinal fluid (CSF) separates the brain from the rigid skull in adults and older children. Whole head acceleration induces a pulse of artificial gravity within the skull. Because brain density differs slightly from that of CSF, the brain accelerates and strikes the inner aspect of the skull, undergoing viscoelastic deformation, ranging from 1 …

New Fractals For Computer Generated Art Created By Iteration Of Polynomial Functions Of A Complex Variable, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

Novel fractal forms can be created by iteration of higher order polynomials of the complex variable, z, with both positive and negative exponents, followed by optional integer power transformation, k zz . Such functions lead to an expanded universe of fascinating fractal patterns that can be incorporated into computer generated art.

Generalized Fractals For Computer Generated Art: Preliminary Results, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

This paper explores new types of fractals created by iteration of the functions xn+1 = f1(xn, yn) and yn+1 = f2(xn, yn) in a general plane, rather than in the complex plane. Iteration of such functions generates orbits with novel fractal patterns. Especially interesting are N-th order polynomials, raised to a positive or negative integer power, p.

Such functions create novel fractal patterns, including budding, spiked, striped, dragon head, and bat-like forms. The present faculty working paper shows how to create a rich variety of complex and fascinating fractals using this generalized approach, which is accessible to students with high …

Biomechanics Of Snoring And Sleep Apnea, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

To understand the mechanisms of snoring and sleep apnea a first-principles biomechanical analysis was done for airflow through branched parallel channels, separated by a freely movable soft palate, and converging to a common channel at the base of the tongue in a “Y-shaped” configuration. Branches of the Y describe slit-like passages on the nasal and oral sides of the soft palate, when the palate is pushed by backward movement of the tongue to form a wedge between the tongue surface and the posterior pharyngeal wall. The common channel of the Y describes the oropharyngeal passage between the base of the …

Valveless Pumping: The Reflected Pulse Wave Hypothesis, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

No abstract provided.

Meta-Analysis Of Studies On Cpr: A Better Route To New Practice Guidelines, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

Quantitative synthesis of research results multiple small clinical trials using the statistical techniques of meta-analysis yields conclusions in excellent agreement with large randomized “mega-trails”. The present paper introduces a simple yet powerful method of meta-analysis for combining results of any published studies of a proposed treatment compared with a suitable control. These may include pre-clinical or clinical models generating either continuous or dichotomous data.

Local Probability Based Transformations And Diagonal Projection: A New Support Vector Machine-Like Method For Classification Of Feature Vectors, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

No abstract provided.

Increased Risk Of Children For Subtle Closed Head Injury From Soccer Heading, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

No abstract provided.

Biomechanics Of Retinal Venous Pulsations As Indicators Of Intracranial Pressure, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

The origin of retinal venous pulsations remains an open problem in physiology and medicine; so too, their exact relationship to intracranial pressure. This study takes a mathematical modeling approach to explore details of blood flow through the eye to reveal the mechanism of pulsations. The intravaginal, intraneural, and intraocular segments of the retinal arteries and veins are modeled as connected resistive-capacitive segments. The analysis incorporates two critical mechanical properties of these small blood vessels, not heretofore studied, which become significant under conditions of negative transmural pressures: (1) dramatically reduced compliance during flattening and (2) cross-sectional shape change as internal volume …

Clinical Roc Studies Of Digital Stereo Mammography, Tarek Z. Elabbady, Charles F. Babbs, Valerie P. Jackson, Edward J. Delp, David M. Chelberg, Zygmunt Pizlo, Leslie A. Geddes

Weldon School of Biomedical Engineering Faculty Working Papers

The objective of this study was to explore and document the diagnostic utility of digital stereo mammography for the detection of localized breast cancer in women. In it we character­ized the ability of experienced mammographers, general radiologists, and non-radiologists to detect three types of tumor masses embedded within a heterogeneous background of normal tis­sue elements in numerically simulated digital mammograms. The simulated mammograms were displayed to the subjects on a high resolution video display, both in stereo mode and in mono mode. Half of the mammograms contained a single tumor, ranging from 0.3 to 0.8 cm in maxi­mal diameter. Each …

A Prototype Computational Phantom To Create Digital Images For Research And Training In Diagnostic Radiology, Charles F. Babbs

Weldon School of Biomedical Engineering Faculty Working Papers

Research in the processing, compression, transmission, and interpretation of digital radiographic images require the testing and evaluation of a wide variety of images, varying both in format and in spatial resolution. If receiver operating characteristic (ROC) analysis or a related method is used to evaluate the performance of observers using novel vs. conventional displays, large numbers of test images containing known abnormalities are required. This report describes a convenient, inexpensive, and reproducible source of test images, having any desired resolution and containing precisely defined abnormalities of unlimited subtlety. The images are generated by computing x-ray transmission through mathematically defined, three …

Toward Virtual Digital Mammograms For Research And Training In Tumor Detection, Charles F. Babbs, Leslie A. Geddes

Weldon School of Biomedical Engineering Faculty Working Papers

Research in the processing, compression, transmission, and interpretation of digital radiographic images requires evaluation of a wide variety of test images, varying in format, in spatial resolution, and in anatomic content. To evaluate the diagnostic performance of observers using novel versus conventional image formats, large numbers of test images containing known abnormalities are required. This report describes a method for creating high resolution, virtual digital mammograms from computational models of the human breast that include branched lobulated ducts and suspensory ligaments embedded in fatty subcutaneous tissue. Breast phantoms may include any of three types of simulated tumors (fibroadenomas, invasive ductal …

Oxidative Mechanisms In Arterial Distension Injury: Observations Relevant To Restenosis After Angioplasty, Charles F. Babbs, Yuan Zhong

Weldon School of Biomedical Engineering Faculty Working Papers

Background: To explore the hypothesis that tissue iron and reactive oxygen species, including superoxide (O2), mediate acute inflammatory and late hyperplastic responses to vascular injury, we studied experimental overdistension of normal carotid and femoral arteries in dogs. Experimental design: Arterial segments isolated in situ were distended with Ringer solution at 2 atmospheres pressure. In initial experiments the arteries were excised immediately after distension and immersed in diaminobenzidine solutions containing Mn++ ions to initiate histochemical reactions for O2. In other experiments distended arterial segments were reperfused with arterial blood in the presence or absence of the iron chelator, deferoxamine, or the …

Evidence That Free Fatty Acid-Iron Complexes Directly Initiate Lipid Peroxidation In Vitro And In Vivo: A New Mechanism Of Oxidative Stress, Steven C. Salaris, Charles F. Babbs, Joann Pham, John J. Turek

Weldon School of Biomedical Engineering Faculty Working Papers

Through a series of biochemical and histochemical experiments we explored the novel hypothesis that iron and free fatty acids, liberated after tissue injury, combine to form liposoluble complexes that directly initiate lipid peroxidation. The addition of 100 M ferric iron to 30 mM linoleate suspensions at pH 7.4 produced time dependent lipid peroxidation, measured as conjugated diene formation. Complexes of 100 M ferric iron and 600 M pentanoate also initiated formation of conjugated dienes in linoleate suspensions and formation of malondialdehyde-like materials in rat liver slices. A histochemical stain for free fatty acids revealed positive reactions within cell membranes in …