<p>Assessment of left ventricular (LV) deformation is essential for clinical evaluation of LV function and cardiac images are frequently used to evaluate the LV motion and function. By combining the images with mathematical models more information may be extracted from the images. The work presented in this thesis has focused on using the finite element (FE) method to describe the LV and its deformation and combining this method with images of the heart to extract more information about the deformation.</p><p>We developed a method that estimated the LV deformation by manually tracking distinct anatomical landmarks (fiducial markers) through the cardiac cycle in 3 dimensional (3D) images of the heart. The motion of the nodal parameters of an FE mesh shaped to the geometry of the LV was fitted to the motion of the fiducial markers and thus provided a means to describe the motion. The sparsity of the fiducial markers made the fitting problem under-constrained so a parameter distribution model (PDM) of likely motions were constructed from a historical database of cases where FE meshes had been fitted to the motion of magnetic resonance (MR) tagged data. The estimated deformation from the fiducial marker fitting was filtered through the PDM and the resulting deformation corresponded well when compared to the deformation obtained from MR tagging in 13 normal subjects.</p><p>A method that decomposed the LV deformation into different deformation modes such as longitudinal shortening, wall thickening, and twisting was developed. The nodes of a subject’s LV FE mesh were displaced according to each deformation mode and the relative contribution of each mode to the total deformation measured by MR tagging was quantified by calculating a coefficient for each mode. A study that compared 13 young normal subjects with 13 older diabetes patients showed that the patients had a significantly lower degree of longitudinal shortening and wall thickening but a higher degree of longitudinal twist.</p><p>The LV deformation is influenced by cardiac disease via the material properties of the myocardium. We investigated the effects of the material parameter values on the LV deformation in a simulation study using an FE model of the LV. A description of the myocardial microstructure and a passive and active constitutive law was included in the model. The cardiac cycle was simulated from the beginning of diastasis through to the end of ejection by applying appropriate boundary conditions. The different deformation modes between end diastole and end systole were extracted and quantified for different sets of material parameters. We found that stiffer material properties particularly in the myocardial sheet direction impaired longitudinal shortening and wall thickening.</p><p>A sensitivity analysis was carried out to look at the various material parameters’ influence on LV wall strains during passive inflation. The analysis showed a high degree of coupling of the parameters in the constitutive law, which indicated an overparameterization of the law. A parameter estimation study revealed the same problem. Most of the parameters were set to constant values and only one parameter in each of the three microstructural directions were estimated during the passive inflation phase using synthetic strain data as measurements. This still gave good estimates of the stress-strain relationships in the fiber and sheet directions.</p> / Papers I and II reprinted with kind permission of Elsevier, ScienceDirect

Assessment of left ventricular (LV) deformation is essential for clinical evaluation of LV function and cardiac images are frequently used to evaluate the LV motion and function. By combining the images with mathematical models more information may be extracted from the images. The work presented in this thesis has focused on using the finite element (FE) method to describe the LV and its deformation and combining this method with images of the heart to extract more information about the deformation. We developed a method that estimated the LV deformation by manually tracking distinct anatomical landmarks (fiducial markers) through the cardiac cycle in 3 dimensional (3D) images of the heart. The motion of the nodal parameters of an FE mesh shaped to the geometry of the LV was fitted to the motion of the fiducial markers and thus provided a means to describe the motion. The sparsity of the fiducial markers made the fitting problem under-constrained so a parameter distribution model (PDM) of likely motions were constructed from a historical database of cases where FE meshes had been fitted to the motion of magnetic resonance (MR) tagged data. The estimated deformation from the fiducial marker fitting was filtered through the PDM and the resulting deformation corresponded well when compared to the deformation obtained from MR tagging in 13 normal subjects. A method that decomposed the LV deformation into different deformation modes such as longitudinal shortening, wall thickening, and twisting was developed. The nodes of a subject’s LV FE mesh were displaced according to each deformation mode and the relative contribution of each mode to the total deformation measured by MR tagging was quantified by calculating a coefficient for each mode. A study that compared 13 young normal subjects with 13 older diabetes patients showed that the patients had a significantly lower degree of longitudinal shortening and wall thickening but a higher degree of longitudinal twist. The LV deformation is influenced by cardiac disease via the material properties of the myocardium. We investigated the effects of the material parameter values on the LV deformation in a simulation study using an FE model of the LV. A description of the myocardial microstructure and a passive and active constitutive law was included in the model. The cardiac cycle was simulated from the beginning of diastasis through to the end of ejection by applying appropriate boundary conditions. The different deformation modes between end diastole and end systole were extracted and quantified for different sets of material parameters. We found that stiffer material properties particularly in the myocardial sheet direction impaired longitudinal shortening and wall thickening. A sensitivity analysis was carried out to look at the various material parameters’ influence on LV wall strains during passive inflation. The analysis showed a high degree of coupling of the parameters in the constitutive law, which indicated an overparameterization of the law. A parameter estimation study revealed the same problem. Most of the parameters were set to constant values and only one parameter in each of the three microstructural directions were estimated during the passive inflation phase using synthetic strain data as measurements. This still gave good estimates of the stress-strain relationships in the fiber and sheet directions. / Papers I and II reprinted with kind permission of Elsevier, ScienceDirect

This thesis presents two novel algorithms for converting a normalised binary floating point number into a binary logarithmic number with the single-precision of a floating point number. The thesis highlights the importance of logarithmic number systems in real-time DSP applications. A real-time cross-correlation application where logarithmic signal processing is used to simplify the complex computation is presented. The first algorithm presented in this thesis comprises two stages. A piecewise linear approximation to the original logarithmic curve is performed in the first stage and a scaled-down normalised error curve is stored in the second stage. The algorithm requires less than 20 kbits of ROM and a maximum of three small multipliers. The architecture is implemented on Xilinx's Spartan3 and Spartan6 FPGA family. Synthesis results confirm that the algorithm operates at a frequency of 42.3 MHz on a Spartan3 device and 127.8 MHz on a Spartan6. Both solutions have a pipeline latency of two clocks. The operating speed increases to 71.4 MHz and 160 MHz respectively when the pipeline latencies increase to eight clocks. The proposed algorithm is further improved by using a PWL (Piece-Wise Linear) approximation of the transform curve combined with a PWL approximation of a scaled version of the normalized segment error. A hardware approach for reducing the memory with additional XOR gates in the second stage is also presented. The architecture presented uses just one 18k bit Block RAM (BRAM) and synthesis results indicate operating frequencies of 93 and 110 MHz when implemented on the Xilinx Spartan3 and Spartan6 devices respectively. Finally a novel prototype of an FPGA-based four channel correlation velocimetry system is presented. The system operates at a higher sampling frquency than previous published work and outputs the new result after every new sample it receives. The system works at a sampling frequency of 195.31 kHz and a sample resolution of 12 bits. The prototype system calculates a delay in a range of 0 to 2.6 ms with a resolution of 5.12 us.