Medical ultrasound is crucial in modern healthcare, with high-frame-rate imaging expanding its applications to both high blood velocities over large fields-of-view and slow-moving blood. Accurate flow measurements require high temporal and spatial resolution, necessitating the use of matrix transducers, which face several challenges depending on the application. For monitoring the brains of preterm babies, challenges include designing ASIC-integrated matrices that meet clinical needs and minimizing cables to ensure unrestricted mother-child contact. For atherosclerosis screening, challenges involve sensor-ASIC integration, developing high-frame-rate data acquisition, and addressing high side-lobe levels in sparse matrices. The objective of this thesis is to address these challenges and develop the necessary technology to enable the use of ultrasound matrix transducers for quantifying blood flow and detecting physiologically abnormal flow patterns and velocities in the two mentioned applications.@en

For over 50 years, medical ultrasound has been a pioneering force in healthcare, seamlessly blending diagnostic and therapeutic applications. In diagnostics, ultrasound reveals intricate internal structures based on the generation of acoustic pressure waves in the human body and capturing reflections from tissue and body structures, enabling precise anomaly identification. Simultaneously, in therapy, ultrasound utilizes its acoustic prowess for targeted interventions and submillimeter localization in unconventional cancer treatments like proton therapy. The field has shifted significantly with the advent of nonlinear acoustics, exploring wave propagation phenomena. Contrast agents marked a revolutionary leap, enhancing the specificity, sensitivity, and efficiency of diagnostic and therapeutic ultrasound. Microbubbles, as the most conventionally used agents, exhibit strong nonlinear scattering under ultrasonic excitation, making them suitable for CEUS applications. @en

In this thesis two topics are discussed. The covariant formulation ofMaxwell’s equations of electromagnetism and the formulation of said equations in the context of a rotating frame of reference. Through the development of the necessary theories of Differential Geometry and Special Relativity we show how to formulateMaxwell’s equations in terms of the covariant derivative and in terms of the hodge operator and differential operator. Using this formulation we study the transformation properties of these equations under Lorentz transformations and we conclude that they remain invariant under said transformations. Secondly,we discuss literature concerning the problem of electromagnetism in the context of a rotating frame of reference. We show that the method of direct transformation to a rotating frame results in an unobservable frame of reference and we show that it is impossible to reconstruct Coriolis like forces in an observable frame of reference.

This thesis produces a pre-characterization numerical model capable of handling and calculating electromagnetic fields within a rectangular reverberation chamber near its lowest usablefrequency at 200 MHz. As reverberation chambers strive to have high electric field uniformityto meet field uniformity standards, high electric fields, having the property of being naturallymore uniform, are out of the scope of interest. Additionally high frequencies require more computational memory and CPU time.The model is made using a finite element method based modelling software called Comsol Multiphysics. The modelled reverberation chamber consisting of an antenna, a reflectiveshielded chamber and a Z-fold mode-stirrer is gradually build up. This means that first ananalysis of only the antennas will be made, thereafter the antennas will be put into a reflec-tive shielded chamber environment and finally the antennas are put into a reflective shieldedchamber environment with a z-fold mode stirrer. Furthermore, an extra situation will be considered in which a dielectric object will be added to a shielded chamber environment excited by an antenna without mode stirrer. The effect of an added dielectric object will be studied because of physical interest and completeness and not as added intermediate step to build a reverberation chamber environment. As all situations have similar difficulties in modelling and measuring, the gradual development of the reverberation chamber will allow for the best error analysis of the model. The model replicates the setup of a real reverberation chamber located at Comtest, Zoeterwoude. The reliability and accuracy of the model is studied by comparing the modelled electric field to the measured one. It was found that all models showed a good resemblance between simulated and measured electric fields above 60 MHz except the most complex reverberation chamber model. The simulated field uniformity expressed as standard deviationis twice as high as measurements suggest. The model can therefore only be used as worst-case scenario prediction for the field uniformity. Two kinds of antennas are used during the modelling and measuring phase, a 3104c biconical antenna used in the frequency range 25-200 MHz and the 3146a log-periodic dipole array antenna in the frequency range 200-1000 MHz. The electromagnetic radiation pattern in the far field domain was modelled and corresponded to the expected omni-directional and directional field pattern respectively. Next the antennas were placed in a highly reflective shielded chamber with dimensions (4.05 m×2.55 m×2.925 m). By taking data in specific slices from the model and comparing these to the measurements at the same points it was concluded that the model does not ac-curately predict the electric fields below 60 MHz. Above 60 MHz the model does predict the general electric field pattern in the chamber. It however does not predict local maxima or minima of the electric field.The same comparison was done for the situation in which a dielectric object was added to the setup. The dielectric object was chosen to be a container filled with water (0.27 m×0.565 m×0.269 m). This container is placed in the formerly empty shielded chamber to change the inner electric field. Water was used due to its favourable properties for reflectivity. The same behaviour of the model was observed with this added dielectric object. Finally the electric field in the reverberation chamber at Comtest (5.03 m×3.97 m×2.85 m) was modelled and solved using a GMRES algorithm with geometric multigrid preconditioning.The preconditioning in the GMRES allows for faster convergence. The field uniformity wascomputed for both the model and the measurements as outlined by IEC 61000-4-21. This wasdone for 4 and 12 stirrer rotation positions. Both showed that the model had a less uniform field compared to the Comtest reverberation chamber. The Comtest reverberation chamber complied with the electromagnetic compatibility requirements for measurements using 12 stirrer positions whereas the model did not. However the 4 stirrer position model, which made use of perfect electric conductor boundary conditions, showed a maximum of 13% increase in field uniformity when steel walls were used instead. To show a glimpse of an innovation that put the Delft University of Technology on the map, the shifted laplacian preconditioner is briefly discussed. As an intermediate step in solving a problem with little to no damping, a complex preconditioning matrix is used. It is shown that for an increasing imaginary shift in the Helmholtz problem, expressed as an increasing electrical conductivity σ, the number of iterations needed to reach a relative tolerance smaller than 0.01 decreases. At last, the effect of a shifted laplacian contribution to a multigrid preconditioning on the convergence speed is studied for an non-damped pressure acoustic Helmholtz problem. It is shown that the added contribution slows convergence in a simple geometry, while a more complex geometry cannot be solved without this contribution.

In this thesis, we investigate a sparse basis for ultrasound images, so that we can use sparse regularization in imaging. Actually, there are few previous researches explicitly demonstrating that medical ultrasound images can be sparsified for some dictionary. We consider various orthogonal transforms such as wavelet transforms, cosine transforms and wave atom transforms. Then, we perform those transforms on various ultrasound images and analyzes their sparsity. These ultrasound images include the images of two computer ultrasound phantoms and beamformed ultrasound images with good quality from real people. We looked at sparsity of the true pre-beamformed images, as well as beamformed images. We also consider constructing a specific ultrasound image dictionary using the K-SVD algorithm. We observed that, the pre-beamformed images hardly haVe no sparse basis, and the sparsity of beamformed images will only increase slightly if we use different 1D-DWT in each direction. We also found that the wide overdetermined dictionary generated by K-SVD significantly increases sparsity. After this, we simulate the ultrasound image reconstruction from the ultrasound RF measurements, and we analyze the effects of the different sparse spaces on the reconstruction performance. We observed that, the L1-regularization can work for ultrasound imaging better than L2-regularization, but the orthogonal transforms as well as the dictionary do not improve the reconstruction image quality much.

In medical ultrasound imaging phased array transducers are used for non-invasive imaging. For 3D intra-cardiac-echography technical borders are reached since blood vessel size limits the dimensions of the array. This dimensional limitation lowers lateral resolution. To solve part of the problem, non conventional ways of lateral resolution improvements are needed. For linear arrays R. Reeg [1] proposed null subtraction imaging (NSI), which resulted at best in 30 dB lower side lobes and a width reduction of up to 25 times for the main lobe. This is a non-linear image processing technique based on implementing multiple apodizations in post-processing. Three images are made from which one has a sharp drop to zero in the middle which can be exploited by subtracting it from the other images. This results in a improvement over a regular apodization scheme.
To verify the technique for 2D phased array imaging, simulations are done using Field-II [2, 3] while taking array dimension into account. Measurements take place on an artificial phantom with evenly spaced line scatter targets. For the experiment a P4-l phased array transducer was used in combination with a Verasonics Vantage 256TMwhere a sub-aperture of 30 elements is used. The experiment is done on a CIRS 040GSE Phantom, where evenly spaced line scatter targets and lateral resolution targets are looked at. To form an image a simple delay-and-sum (DAS) algorithm was used. The effect of NSI on the speckle in an image is also measured, where for normal developed speckle a signal to noise ratio (SNR) of 1.91 is expected. Results for simulation were as expected with an average beamwidth reduction of 22.5 times and on average higher main lobe to side lobe ratio (MSR) of 33.4 dB for NSI imaging opposed to using a rectangular apodization. Experimentally an average beamwidth reduction of 5 times and an on average higher MSR of 20.5 dB are realised. The beamwidth reduction is lower then expected, this is due to rounding errors in the DAS algorithm, where data can only be delayed by integer elements. For the lateral scatter targets no extra targets can be distinguished when using NSI imaging opposed to rectangular apodization imaging, only the targets that where already visible show reduction in beamwidth and side lobe levels. When using NSI speckle SNR is reduced from 1.78 to on average 0.50 and seems to scale with energy present in the image. An hybrid image between the NSI image and rectangular apodization image is made to solve this. It results in reduced beamwidth, restored speckle SNR but the MSR is reduced. It can be concluded that the method works for phased array imaging under perfect conditions, the simulation. To get the full potential of the technique more research is needed towards the effects of improper sampling. Which in this case resulted in less then ideal ’sharp’ drops, lowering the reduction in beamwidth. Also the reduced speckle needs further research to understand it well. Once this is all achieved the next step to 3D imaging can be made.

Currently a lot of effort is put into developing matrix arrays which allow for volumetric imaging and new applications. There are however multiple problems. Compared to arrays currently in use which have in the order of 128 elements, matrix arrays can easily contain 1000 to 10000 elements. If all elements would be connected independently, the cable would become very thick. Therefore, beamforming methods are required that can operate with fewer transmit and receive channels. Furthermore, the room for electronics on the chip is limited. So, the required electronics for the beamforming methods should be kept simple.

In this thesis we will propose beamforming methods that are able to operate with fewer channels. This will be done separately for the transmit and receive part, but they do in no way exclude each other. To be able to focus pulsed waves in transmit we propose a method based on Fresnel zone plates which are used in optics to focus continuous wave light. Our method only requires a single continuous-wave excitation signal to be present, which is connected and disconnected on demand to each element. We have evaluated our method with measurements and simulations. As compared to the conventional focusing method, the spatial resolution is not affected by our method, but the Contrast-to-Noise ratio is 5\% lower for shallow depths and up to 20\% lower deeper into the medium. Overall though, the differences were relatively small and so it is clear that our new focusing method works very well. If needed, better results can be obtained by trading in frame rate. In this case the results are almost indistinguishable from the conventional focusing method.

To solve the problem with image formation, we have developed a frequency domain two stage beamforming method for use with matrix arrays, which does not require all element data to be present. This has been done for two matrix types. For the first method we have confirmed with simulations that it performs similar to the respective results obtained with two 2D frequency domain two stage beamforming method that have already been experimentally verified. For the second method we have evaluated the performance with simulations and measurements. Our method was able to obtain a 25\% better spatial resolution as compared to Dynamic Receive Focusing(DRF), without additional artefacts. As an alternative to the last method, we have also developed a frequency domain beamforming method that does require all element data, but only requires a single insonification by a spherical wave. This method did perform worse than the method discussed before in both simulations and measurements, but it does outperform DRF applied to spherical wave data.