Intraluminal thrombus may play a role in abdominal aortic aneurysm pathogenesis and rupture. The purpose of this work was to demonstrate the feasibility of a new non-invasive method for the determination of the biomechanical features of the aortic wall and luminal boundary in abdominal aortic aneurysm containing intraluminal thrombus. Automated ultrasonographic measures of infrarenal aortic cross-sectional area ( A) were obtained on-line along with non-invasive arterial pressure ( p) from eight patients of mean(s.e.m.) age 74(3) years, with abdominal aortic aneurysm (mean dimensions 5.9(0.4) × 5.3(0.5) cm) containing intraluminal thrombus. Luminal boundary and abdominal aortic aneurysm wall were scanned separately. Compliance ( C) was computed as C = (A max — A min )/[ A max ( p max — p min )], where ‘max’ and ‘min’ represent maximum and minimum values, respectively. Mean compliance was lower for the abdominal aortic aneurysm wall alone than for the luminal surface enclosed by intraluminal thrombus: 4.0(0.9) × 10 −4 /mmHg versus 9.8(1.7) × 10 −4 /mmHg ( P < 0.01). Intraluminal thrombus area was nearly constant over the cardiac cycle, indicating that the thrombus is virtually incompressible. This non-invasive method to assess biomechanical features of abdominal aortic aneurysm has potential to further the understanding of the influences of intraluminal thrombus on aneurysm disease.
Proportional, integral, and derivative (PID) controllers have proven to be robust in controlling many applications, and remain the most widely used control system architecture. The purpose of this work was to use this architecture for designing and tuning two PID controllers. The first was used to control the physiologic arterial circumferential wall stress (CWS) and the second to control the physiologic arterial shear stress (SS) imposed on intact vascular segments that were implanted into an ex vivo vascular perfusion system (EVPS). In order to most accurately control the stresses imposed onto vascular segments perfused ex vivo, analytical models were derived to calculate the CWS and SS. The mid-vein-wall CWS was calculated using the classical Lame solution for thick-walled cylinders in combination with the intraluminal pressure and outer diameter measurements. Similarly, the SS was calculated using the Hagen-Poiseuille equation in combination with the flow rate and outer diameter measurements. Performance of each controller was assessed by calculating the root mean square of the error (RMSE) between the desired and measured process variables. The performance experiments were repeated ten times (N=10) and an average RMSE was reported for each controller. RMSE standard deviations were calculated to demonstrate the reproducibility of the results. Sterile methods were utilized for making blood gas and temperature measurements in order to maintain physiologic levels within the EVPS. Physiologic blood gases (pH, pO(2), and pCO(2)) and temperature within the EVPS were very stable and controlled manually. Blood gas and temperature levels were recorded hourly for several (N=9) 24 h perfusion experiments. RMSE values for CWS control (0.427+/-0.027 KPa) indicated that the system was able to generate a physiologic CWS wave form within 0.5% error of the peak desired CWS over each cardiac cycle. RMSE values for SS control (0.005+/-0.0007 dynescm(2)) indicated that the system was able to generate a physiologic SS wave form within 0.3% error of the peak desired SS over each cardiac cycle. Physiologic pH, pO(2), pCO(2), and temperature levels were precisely maintained within the EVPS. The built-in capabilities and overall performance of the EVPS described in this study provide us with a novel tool for measuring molecular responses of intact vascular segments exposed to precisely simulated arterial biomechanical conditions.
Numerical algorithms for subspace system identification (N4SID) are a powerful tool for generating the state space (SS) representation of any system. The purpose of this work was to use N4SID to generate SS models of the flowrate and pressure generation within an ex vivo vascular perfusion system (EVPS). Accurate SS models were generated and converted to transfer functions (TFs) to be used for proportional integral and derivative (PID) controller design. By prescribing the pressure and flowrate inputs to the pumping components within the EVPS and measuring the resulting pressure and flowrate in the system,_four TFs were estimated;_two for a flowrate controller (H(RP,f) and H(RPP,f)) and two for a pressure controller (H(RP,p) and H(RPP,p)). In each controller,_one TF represents a roller pump (H(RP,f) and H(RP,p)),_and the other represents a roller pump and piston in series (H(RPP,f) and H(RPP,p)). Experiments to generate the four TFs were repeated five times (N=5) from which average TFs were calculated. The average model fits, computed as the percentage of the output variation (to_the_prescribed_inputs) reproduced by the model, were 94.93+/-1.05% for H(RP,p), 81.29+/-0.20% for H(RPP,p), 94.45+/-0.73% for H(RP,f), and 77.12+/-0.36% for H(RPP,f). The simulated step, impulse, and frequency responses indicate that the EVPS is a stable system and can respond to signals containing power of up to 70_Hz.
Arterial hemodynamics and wall mechanics are important considerations for the vascular clinician for a number of reasons. Hemodynamics and wall mechanics both have been shown to be affecters of disease formation. It is important for the practicing vascular surgeon to know how disease affects both blood flow and wall mechanics and to understand the consequence of hemodynamics on arterial reconstructions. In this article, we summarize the basic concepts of arterial hemodynamics and wall mechanics as they relate to the development of arterial pathology. A few practical mathematical relationships and examples are provided for both illustration and utilization. We also discuss the use of computer models for the estimation of wall stresses in individual abdominal aortic aneurysms.