Factoring estimates for a 1024-bit RSA modulus

We estimate the yield of the number field sieve factoring algorithm when applied to the 1024-bit composite integer RSA-1024 and the parameters as proposed in the draft version [17] of the TWIRL hardware factoring device [18]. We present the details behind the resulting improved parameter choices from [18]

Non-invasive assessment of leaflet deformation and mechanical properties in heart valve tissue engineering

Tissue-engineered heart valves are a promising alternative for mechanical and bioprosthetic heart valve replacements. Despite their relative success, current valvular implants are made of non-living material and, therefore, do not have the ability to grow, adapt or remodel in response to a change in the valvular environment. This especially has a negative effect on the treatment of congenital valve defects in adolescent and pediatric patients. Heart valve tissue engineering seeks to overcome these limitations by creating functional, autologous and living heart valves. The in-vitro formation of aortic heart valves has proven to be a significant engineering challenge. Although the mechanical properties of tissue-engineered valves may be sufficient, they may need improvement. When compared with native aortic valves, cultured valves are relatively stiff and less anisotropic in the physiological strain range. Mechanical stimulation of the developing tissue in a bioreactor system is reported to enhance tissue formation and quality, and is widely used in cardiovascular tissue engineering. More particular, inducing strains in the cultured tissue by load application appears to be an important enhancer of tissue development. However, optimal conditioning protocols in heart valve tissue engineering have not been identified, yet. Documented bioreactor systems have been unable to sufficiently control the load to induce predefined or controlled deformations to the cultured heart valves. In addition, the mechanical properties of the engineered valves have been generally examined by sacrificing the heart valves at the end-stage of tissue culture to perform traditional single or multi-axial tensile experiments. To investigate the mechanical behavior of the heart valves during culture as a non-invasive quality check, it is also desired to assess the mechanical properties non-destructively in real-time. During tissue culture the mechanical properties of the heart valves change with time. To subject the valve to a predefined deformation pattern via the application of a pressure difference over the valve, a feedback controlled bioreactor system is needed. The objective of this thesis is to develop a bioreactor system in which induced heart valve leaflet deformations are measured and controlled and resulting mechanical properties are assessed during culture, non-invasively and non-destructively. For this purpose, an inverse experimental-numerical approach was developed to measure volumetric and local heart valve leaflet deformations during culture. Volumetric deformation was defined as the amount of fluid displaced by the deformed heart valve leaflets in a stented configuration in response to the valvular pressure difference. This volume was measured non-invasively using a flow sensor. A computational model was employed to relate volumetric deformation to local tissue strains in various regions of the leaflets; e.g. belly and commissures. Consecutively, the experimental-numerical approach was further developed and applied to assess the mechanical properties of the tissue-engineered heart valves. A range of increasing pressure differences was applied and the corresponding induced volumetric deformations of the engineered heart valve leaflets were measured during culture. The correlation between the pressure difference and deformation data served as input for the estimation of mechanical properties using the computational model. To validate the method, six heart valves were cultured, and the estimated mechanical properties were in good agreement with uniaxial tensile test data. In addition, the diastolic functionality of the heart valve leaflets was assessed in the bioreactor by studying the deformation and leakage of the cultured heart valves under physiological aortic diastolic pressure differences. As a second step towards a controlled bioreactor system, the above described deformation assessment method was extended by addition of a feedback control mechanism. The resulting technique enabled both measurement and control of the heart valve deformation in real-time. Functionality of this approach was demonstrated in two tissue engineering experiments in which a total of eight heart valves were cultured by application of two different deformation protocols. Results indicated a good correlation between the measured and the prescribed deformation values in both experiments. In addition, the cultured heart valves showed mechanical properties in the range of previous tissue engineering studies. However, no significant differences in mechanical properties were found between the valves cultured by the dissimilar protocols. Tissue analyses provide a broader understanding of the development of engineered heart valves during culture. In addition to the mechanical and functional evaluations, analyzing tissue composition on a microscopic and macroscopic level may provide further insight into the relation between mechanical conditioning and tissue development. Consequently, the tissue of the engineered heart valves was analyzed qualitatively; macroscopic appearance and histology, and quantitatively; biochemical assays. The 14 heart valves cultured in four independent experiments all showed a dense, homogeneous tissue with a smooth surface. Tissue composition was comparable to previously performed cardiovascular tissue engineering studies. Collagen type I and III were demonstrated throughout the tissue, as well as striated structure fragments of elastin, both of which are the main structural matrix components of natural heart valves. The next step towards preclinical application of the controlled bioreactor system was to optimize the system to culture tissue-engineered heart valves suitable for minimal invasive implantation. First, implantable stented heart valves were successfully cultured in the bioreactor system. Thereafter, the bioreactor system was employed to create ovine tissue-engineered heart valves suitable for animal studies. Complete realization of the bioreactor functionality was demonstrated for one of the three cultured ovine heart valves. The presence of leakage along the heart valves was still an issue in the other valves and needs further investigation. Finally, a further advanced bioreactor design was addressed, which extends the revised bioreactor with systolic flow capabilities. This bioreactor system would allow the independent application of both controlled strain-based and physiological flow-based loads to tissue-engineered heart valves

Non-invasive assessment of leaflet deformation and mechanical properties in heart valve tissue engineering

Tissue-engineered heart valves are a promising alternative for mechanical and bioprosthetic heart valve replacements. Despite their relative success, current valvular implants are made of non-living material and, therefore, do not have the ability to grow, adapt or remodel in response to a change in the valvular environment. This especially has a negative effect on the treatment of congenital valve defects in adolescent and pediatric patients. Heart valve tissue engineering seeks to overcome these limitations by creating functional, autologous and living heart valves. The in-vitro formation of aortic heart valves has proven to be a significant engineering challenge. Although the mechanical properties of tissue-engineered valves may be sufficient, they may need improvement. When compared with native aortic valves, cultured valves are relatively stiff and less anisotropic in the physiological strain range. Mechanical stimulation of the developing tissue in a bioreactor system is reported to enhance tissue formation and quality, and is widely used in cardiovascular tissue engineering. More particular, inducing strains in the cultured tissue by load application appears to be an important enhancer of tissue development. However, optimal conditioning protocols in heart valve tissue engineering have not been identified, yet. Documented bioreactor systems have been unable to sufficiently control the load to induce predefined or controlled deformations to the cultured heart valves. In addition, the mechanical properties of the engineered valves have been generally examined by sacrificing the heart valves at the end-stage of tissue culture to perform traditional single or multi-axial tensile experiments. To investigate the mechanical behavior of the heart valves during culture as a non-invasive quality check, it is also desired to assess the mechanical properties non-destructively in real-time. During tissue culture the mechanical properties of the heart valves change with time. To subject the valve to a predefined deformation pattern via the application of a pressure difference over the valve, a feedback controlled bioreactor system is needed. The objective of this thesis is to develop a bioreactor system in which induced heart valve leaflet deformations are measured and controlled and resulting mechanical properties are assessed during culture, non-invasively and non-destructively. For this purpose, an inverse experimental-numerical approach was developed to measure volumetric and local heart valve leaflet deformations during culture. Volumetric deformation was defined as the amount of fluid displaced by the deformed heart valve leaflets in a stented configuration in response to the valvular pressure difference. This volume was measured non-invasively using a flow sensor. A computational model was employed to relate volumetric deformation to local tissue strains in various regions of the leaflets; e.g. belly and commissures. Consecutively, the experimental-numerical approach was further developed and applied to assess the mechanical properties of the tissue-engineered heart valves. A range of increasing pressure differences was applied and the corresponding induced volumetric deformations of the engineered heart valve leaflets were measured during culture. The correlation between the pressure difference and deformation data served as input for the estimation of mechanical properties using the computational model. To validate the method, six heart valves were cultured, and the estimated mechanical properties were in good agreement with uniaxial tensile test data. In addition, the diastolic functionality of the heart valve leaflets was assessed in the bioreactor by studying the deformation and leakage of the cultured heart valves under physiological aortic diastolic pressure differences. As a second step towards a controlled bioreactor system, the above described deformation assessment method was extended by addition of a feedback control mechanism. The resulting technique enabled both measurement and control of the heart valve deformation in real-time. Functionality of this approach was demonstrated in two tissue engineering experiments in which a total of eight heart valves were cultured by application of two different deformation protocols. Results indicated a good correlation between the measured and the prescribed deformation values in both experiments. In addition, the cultured heart valves showed mechanical properties in the range of previous tissue engineering studies. However, no significant differences in mechanical properties were found between the valves cultured by the dissimilar protocols. Tissue analyses provide a broader understanding of the development of engineered heart valves during culture. In addition to the mechanical and functional evaluations, analyzing tissue composition on a microscopic and macroscopic level may provide further insight into the relation between mechanical conditioning and tissue development. Consequently, the tissue of the engineered heart valves was analyzed qualitatively; macroscopic appearance and histology, and quantitatively; biochemical assays. The 14 heart valves cultured in four independent experiments all showed a dense, homogeneous tissue with a smooth surface. Tissue composition was comparable to previously performed cardiovascular tissue engineering studies. Collagen type I and III were demonstrated throughout the tissue, as well as striated structure fragments of elastin, both of which are the main structural matrix components of natural heart valves. The next step towards preclinical application of the controlled bioreactor system was to optimize the system to culture tissue-engineered heart valves suitable for minimal invasive implantation. First, implantable stented heart valves were successfully cultured in the bioreactor system. Thereafter, the bioreactor system was employed to create ovine tissue-engineered heart valves suitable for animal studies. Complete realization of the bioreactor functionality was demonstrated for one of the three cultured ovine heart valves. The presence of leakage along the heart valves was still an issue in the other valves and needs further investigation. Finally, a further advanced bioreactor design was addressed, which extends the revised bioreactor with systolic flow capabilities. This bioreactor system would allow the independent application of both controlled strain-based and physiological flow-based loads to tissue-engineered heart valves

Tissue-engineered heart valves develop native-like collagen fiber architecture

Creating autologous tissues with on-demand and native-like biomechanical properties is the ultimate challenge in functional heart valve tissue engineering. A promising approach toward this goal is to induce development of native-like tissue structure in vitro by mimicking the diastolic loading phase in a bioreactor. Heart valves cultured with this approach showed in vitro sufficient strength to withstand systemic pressures. This study aims to link global functioning of these valves to the development of a native-like fiber architecture induced by in vitro diastolic loading. It is hypothesized that increased loading magnitude during culture will lead to increased collagen fiber alignment. To test this hypothesis, 10 tissue-engineered heart valves were subjected to different loading protocols in vitro. Local fiber distribution and mechanics were determined in an inverse numerical–experimental approach, combining indentation tests with confocal imaging. Indentation tests on native ovine heart valves were used as a comparison. Although the effect of loading magnitude was small within the tested range, results indicated that the local fiber architecture indeed developed toward native structural properties for all loading protocols. However, apparent fiber mechanics were much stiffer compared with native. This confirms that in vitro mechanical conditioning induces development of a native-like tissue architecture, which underlines its importance for functional heart valve tissue engineering

Deformation-controlled load application in heart valve tissue engineering

In cardiovascular tissue engineering, mechanical stimulation of tissue-engineered constructs is known to improve tissue properties. During tissue culture, the mechanical properties of the tissue construct change. To impose a predefined deformation protocol and to avoid negative effects of excessive strain, it is desired to monitor and control deformations during load application. In a previous study, load application and resulting deformation of tissue-engineered heart valve leaflets were monitored during culture inside a bioreactor in real time and noninvasively. A combined experimental-numerical approach was applied to assess volumetric and local leaflet deformation of the cultured heart valve in a diastolic configuration. In this study, this approach was further developed and a feedback controller to regulate deformation was incorporated into the bioreactor system. Functionality of this technique was demonstrated in two tissue engineering experiments in which a total of eight heart valves were cultured by application of two different deformation protocols. Results indicated a good correspondence between the measured and the prescribed deformation values in both experiments. In addition, the cultured heart valves showed mechanical properties in the range of previous tissue engineering studies. The bioreactor system including the deformation measurement and control features has promising possibilities of systematically elucidating the effects of loading protocols on tissue properties. In conclusion, it facilitates the development of an optimal conditioning protocol for tissue engineering of aortic heart valves. © 2009 Mary Ann Liebert, Inc