A Numerical study of fluid flow in peristaltic pumps and polymeric elastic pipes

This thesis work deals with a mathematical description of flow in polymeric pipe and in a specific peristaltic pump. This study involves fluid-structure interaction analysis in presence of complex-turbulent flows treated in an arbitrary Lagrangian-Eulerian (ALE) framework. The flow simulations are performed in COMSOL 4.4, as 2D axial symmetric model, and ABAQUS 6.14.1, as 3D model with symmetric boundary conditions. In COMSOL, the fluid and structure problems are coupled by monolithic algorithm, while ABAQUS code links ABAQUS CFD and ABAQUS Standard solvers with single block-iterative partitioned algorithm. For the turbulent features of the flow, the fluid model in both codes is described by RNG k-ϵ. The structural model is described, on the basis of the pipe material, by Elastic models or Hyperelastic Neo-Hookean models with Rayleigh damping properties. In order to describe the pulsatile fluid flow after the pumping process, the available data are often defective for the fluid problem. Engineering measurements are normally able to provide average pressure or velocity at a cross-section. This problem has been analyzed by McDonald's and Womersley's work for average pressure at fixed cross section by Fourier analysis since '50, while nowadays sophisticated techniques including Finite Elements and Finite Volumes exist to study the flow. Finally, we set up peristaltic pipe simulations in ABAQUS code, by using the same model previously tested for the fl uid and the structure.

A systems approach to cardiovascular health and disease with a focus on aortic wave dynamics

Cardiovascular diseases (CVDs) have reached an epidemic proportion in the US and worldwide with serious consequences in terms of human suffering and economic impact. More than one third of American adults are suffering from CVDs. The total direct and indirect costs of CVDs are more than $500 billion per year. Therefore, there is an urgent need to develop noninvasive diagnostics methods, to design minimally invasive assist devices, and to develop economical and easy-to-use monitoring systems for cardiovascular diseases. In order to achieve these goals, it is necessary to gain a better understanding of the subsystems that constitute the cardiovascular system. The aorta is one of these subsystems whose role in cardiovascular functioning has been underestimated. Traditionally, the aorta and its branches have been viewed as resistive conduits connected to an active pump (left ventricle of the heart). However, this perception fails to explain many observed physiological results. My goal in this thesis is to demonstrate the subtle but important role of the aorta as a system, with focus on the wave dynamics in the aorta.

The operation of a healthy heart is based on an optimized balance between its pumping characteristics and the hemodynamics of the aorta and vascular branches. The delicate balance between the aorta and heart can be impaired due to aging, smoking, or disease. The heart generates pulsatile flow that produces pressure and flow waves as it enters into the compliant aorta. These aortic waves propagate and reflect from reflection sites (bifurcations and tapering). They can act constructively and assist the blood circulation. However, they may act destructively, promoting diseases or initiating sudden cardiac death. These waves also carry information about the diseases of the heart, vascular disease, and coupling of heart and aorta. In order to elucidate the role of the aorta as a dynamic system, the interplay between the dominant wave dynamic parameters is investigated in this study. These parameters are heart rate, aortic compliance (wave speed), and locations of reflection sites. Both computational and experimental approaches have been used in this research. In some cases, the results are further explained using theoretical models.

The main findings of this study are as follows: (i) developing a physiologically realistic outflow boundary condition for blood flow modeling in a compliant vasculature; (ii) demonstrating that pulse pressure as a single index cannot predict the true level of pulsatile workload on the left ventricle; (iii) proving that there is an optimum heart rate in which the pulsatile workload of the heart is minimized and that the optimum heart rate shifts to a higher value as aortic rigidity increases; (iv) introducing a simple bio-inspired device for correction and optimization of aortic wave reflection that reduces the workload on the heart; (v) deriving a non-dimensional number that can predict the optimum wave dynamic state in a mammalian cardiovascular system; (vi) demonstrating that waves can create a pumping effect in the aorta; (vii) introducing a system parameter and a new medical index, Intrinsic Frequency, that can be used for noninvasive diagnosis of heart and vascular diseases; and (viii) proposing a new medical hypothesis for sudden cardiac death in young athletes.

PROTEIN-TRIGGERED SUSTAINED DRUG RELEASE CONTROLLED BY APTAMERS BOUND TO OLIGOMER-CROSSLINKED ALGINATE

Sustained drug release systems provide many advantages over traditional delivery methods such as extending the time in which the drug is found to be within an effective concentration within the therapeutic window, which decreases the frequency of administration of the drug, and increases patient compliance. Research using polyacrylamide crosslinked by oligomers containing an aptamer sequence, has demonstrated a pulsatile release over 50 minutes triggered by a 2 mM target adenosine concentration. This thesis aims to build off this concept by designing a system that delivers in a sustained manner when triggered by micromolar target concentrations reflective of disease in vivo, using macromolecular targets. For example, the disease wet age related macular degeneration (wet AMD) is associated with increased concentrations of the protein vascular endothelial growth factor (VEGF-A) – a macromolecule. Patients with wet AMD would benefit from the implantation of devices or microspheres that release drugs in a sustained manner in response to local VEGF concentrations. In this thesis, we hypothesize that the protein lysozyme, used to demonstrate proof-of-concept, could trigger the increased release of drugs from oligomer-crosslinked alginate. The objectives are to (i) demonstrate sustained release from alginate, (ii) design oligomer crosslinked alginate that degrades in response to lysozyme, and then (iii) use these systems to control the release of FITC-dextran with and without lysozyme. A series of control experiments and analyses were used to optimize the crosslinking of alginate by annealed oligomers. The cumulative release of FITC-dextran (MW 20,000) from oligomer crosslinked alginate increased by 3.4 μg when lysozyme (3 μM) was introduced at 48 hours, as opposed to controls which released only 0.2 μg. FITC-loaded alginate microspheres coated by oligomer-crosslinked alginate released 15% more FITC-dextran over 120 hours when placed into 3 μM of lysozyme than without lysozyme. Controls of alginate crosslinked with PEG or control oligomers (without a lysozyme aptamer sequence) had no changes in release with lysozyme. The incorporation of a lysozyme aptamer onto oligomers used to crosslink alginate disks or alginate coatings on microspheres resulted in different diffusion and release of FITC-dextran into PBS with or without lysozyme. This approach could be adapted for the delivery of drugs to diseases with specific protein profiles such as wet AMD.

Soluzione analitica di un modello semplificato per la circolazione sistemica

La circolazione sanguigna nell’organismo umano sfrutta un meccanismo ad hoc per trasportare gli scarti e tutte le sostanze necessarie al metabolismo cellulare. Il cuore rappresenta la pompa che dà al sangue la spinta per scorrere nei vasi e il ventricolo sinistro è la cavità cardiaca che contribuisce di più allo svolgimento di questo lavoro. Il modello pulsatile utilizzato in questo elaborato per la circolazione sistemica deriva dalla semplificazione di un modello a parametri concentrati precedentemente pubblicato. Nell’analogo elettrico di questo modello sono state incluse la resistenza al ritorno venoso, la resistenza al deflusso aortico e la resistenza arteriolare sistemica. Inoltre, la funzione di pompa del ventricolo è definita dalla complianza ventricolare tempo-variante e dal suo inverso, l’elastanza. Le valvole ventricolari sono simulate da due diodi e le capacità venose e arteriose tengono conto del comportamento elastico dei rispettivi compartimenti. Considerando il lavoro delle valvole, il ciclo cardiaco è stato suddiviso in sette intervalli temporali, per ciascuno dei quali è stato disegnato un analogo elettrico che descrive il comportamento degli elementi circuitali in quello specifico intervallo temporale. Attraverso l’applicazione delle leggi di Kirchoff agli analoghi elettrici sopra citati si scrivono le equazioni differenziali nelle funzioni incognite carica elettrica sulla complianza ventricolare e tensione arteriosa. Per ottenere le espressioni analitiche della soluzione delle equazioni differenziali si approssima l’elastanza con una funzione lineare a tratti e si utilizzano i teoremi per la risoluzione delle equazioni differenziali di ordine uno non omogenee. Le espressioni analitiche vengono implementate su Matlab, che consente di ottenere dei grafici della pressione venosa, arteriosa e ventricolare, dell’elastanza, del volume ventricolare e della portata aortica anche in risposta ad una diminuzione della resistenza arteriolare sistemica.