Guiding Ultrasound with a Selective Contrast

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Photoacoustic Eect

While thermoacoustic imaging can be implemented in many cases without consideration for the intricacies of the thermoacoustic eect, it will become clear in the course of this document that the use of photoacoustic signal from deep in the human body is a challenging endeavour. A successful implementation of such a system depends on the careful optimisation of the various parameters of the system. An awareness of the dominating factors and of the physical assumptions made in the derivations of the mathematical description of the thermoacoustic eect is therefore indispensable. The objective of this section (in conjunction with Appendices A and B on page 167) is to provide a complete derivation of the thermoacoustic problem in uids from rst principle and some exemplary solutions. It represents an attempt to provide a statement of the theoretical background of thermoacoustics using valid physical assumptions, explicit statement of the assumptions made and consistent mathematical notation. Many yet unresolved questions that were encountered in the course of the work for this thesis, require a detailed understanding of the thermodynamic processes involved in the thermoacoustic eect. Apart from providing the reader with an understanding of the photoacoustic eect, this section and the corresponding appendices are intended to serve as a basis for further work. With regard to the results presented in this thesis, the most immediate applications were to gain a better understanding of the frequency spectrum of thermoacoustic waves, the conditions for ecient illumination and the energy balance of the photoacoustic eect.

Light Source

To generate the energy needed for the photoacoustic eect, a combination of a laser and an optical parametric oscillator was chosen. This allows illumi-nation of samples in a wide range of dierent wavelengths, in particular in the diagnostic window.

Continuum Surelite II-10

The pump laser used for this work was a Surelite II-10 laser by Continuum, CA, USA. The Surelite II-10 is a ashlight-pumped, Q-switched Nd:YAG laser. The optical layout of the Surelite II-10 is illustrated in Figure 3.1. The cavity is dened by the rear mirror (1) and the output coupler (7). The laser comprises a Nd3+-doped YAG rod (5) as gain medium which is pumped by a ash lamp driven by 􀀀1800V electrical pulses resulting in a ash with a duration of approximately 200 µs. The primary transition in Nd:YAG crystals emits light at a wavelength of 1064 nm.

Q-Switch

Generally the cavity is blocked by a Q-Switch: a combination of a polariser (4), a =4 plate (3) and a Pockels cell (2). The Pockels cell exploits the Pockels electro-optic eect to induce birefringence in a non-linear optical medium with an electric eld to create an electrically controlled wave plate. At approximately 3600V this results in a =4 rotation of the phase of photons at 1064nm while at 0V no rotation is induced. The polariser is transparent for horizontally polarised light and reective for vertically polarised light.When the Pockels cell is not electrically polarised, a photon generated in the Nd:YAG rod (5) travelling towards the rear mirror (1) is polarised horizontally by the polariser (4). Its polarisation is then changed to circular by the wave plate (3) and passes unaected through the inactive Pockels cell (2). After being reected by the rear mirror, the photon passes the inactive Pockels cell a second time and its polarisation is changed from circular to vertical by the wave plate. It is therefore reected by the polariser (4) and oscillation in the cavity is prevented.
On the other hand, when the Pockels cell is electrically polarised, on each pass through the active Pockels cell a photon’s polarisation is changed an additional time from circular to linear or vice versa. A photon’s polarisation is therefore identical upon completion of the entire path between the rst and second pass through the polariser. In other words, the photon now has horizontal polarisation when it encounters the polariser a second time and passes unimpeded, permitting oscillation in the cavity.
By pumping the gain medium with closed cavity, energy can be stored through population inversion since the life-time for spontaneous emission is much greater than for stimulated emission, the later being only possible with an open cavity. By carefully selecting the delay between activation of the ash lamp and the opening of the cavity with respect to the life-time for spontaneous emission, an optimal degree of population inversion can be achieved and the stored energy be released in a very short but intense light pulse.After passing the output coupler (7), the light has a wavelength of 1064 nm, a pulse energy of approximately 650 mJ, a pulse width of 5 􀀀 7 ns and is horizontally polarised.

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Second Harmonic Generation

As illustrated in Section 2.1, at 1064nm light absorption in water is nonnegligible. To achieve maximum penetration depth in biological tissues, wavelengths between 700nm and 900nm would be desirable. The wavelength of the photons generated by the Nd:YAG crystal is therefore transformed in two steps, the rst of which is second harmonic generation, also known as frequency doubling.
Second harmonic generation describes a non-linear optical process in which two photons interacting with a non-linear medium are eectively combined, resulting in a doubling of the energy (and thus frequency) of the photons in a beam.
The second harmonic generation assembly (9) implements a Type I second harmonic generation resulting in a rotation of the polarisation of the beam by 90°. It operates with a maximum eciency of approximately 50%. Phase matching is achieved by automated temperature control and manual angular ne-tuning of the Crystal orientation.
The light exiting the Surelite II-10 therefore consists to 50% of light at 1064nm horizontally polarised (300 mJ) and to 50% of light at 532 nmvertically polarised (300 mJ) with 4 􀀀 6 ns pulse duration. According to Continuum (2002) the beam is approximately 7mm in diameter and has a divergence of 0:3 mrads 1.

Table of contents :

Abstract
Résumé Français
Contents
I Introduction 
1 Introduction 
1.1 Structure of this Document
1.2 State of the Art
History of Medical Ultrasound
High Intensity Focused Ultrasound
Time-Reversal
Photoacoustics
Time-Reversal Using Photoacoustic Signals
1.3 Objective and Motivation for this Thesis
Photoacoustics for HIFU Aberration Correction
Targeting of Tumours at Unknown Locations
2 Theoretical Background 
2.1 Light Propagation in Tissues
Absorption Coecient
Scattering Coecient
Anisotropy Factor
Coecients Combining Absorption and Scattering
2.2 Medical Limits on Illumination
2.3 Photoacoustic Eect
Fundamental Principles
Linear Acoustics without Sources
The Linear Thermoacoustic Problem
Solution of the Thermoacoustic Problem
Solution for an Innite Medium
Solutions Under Stress Connement
Solution for Spherically Symmetrical Sources
Solutions for Specic Geometries
Concluding Remarks
II Experimental Section 
3 Instruments 
3.1 Light Source
Continuum Surelite II-10
Optical Parametric Oscillator
Beam Characteristics and Control
3.2 Beam Shaping and Beam Delivery
Beam Homogenisation
Choice of Light Guides
3.3 Ultrasound Electronics
Lecoeur Open System
Supersonic Imagine Brain Therapy System
3.4 Ultrasound Probes
Diagnostic Ultrasound Probe
Imasonic HIFU-Compatible Probe
4 Proof of Principle & Challenges 
4.1 Guiding Ultrasound with a Selective Contrast
4.2 Experimental Setup
4.3 Photoacoustic Results & Target Signal Isolation
4.4 Time-Reversal Results
4.5 Identication of Problem Areas
Sampling Noise
Target Signal Isolation
Feasibility with HIFU Compatible Devices
Feasibility in Biological Samples
Technological Challenges for Clinical Applications
5 Denoising and Target Isolation 
5.1 Denoising of Photoacoustic Signals
Analysis of Dominant Noise Sources
Deterministic Noise Contributions
Random Noise Contributions
Methods for Denoising
Optimal Bandwidth Filtering
Radon Filtering
5.2 Isolation of Optically Selective Sources
Basic Target Isolation Algorithm
Physical Interpretation of the Algorithm
Performance of the algorithm
On the Problem of Spectroscopic Approaches
5.3 Conclusion
6 Photoacoustic Guidance of HIFU 
6.1 Evaluation of Transducer Prototypes
Reception Characteristics
Heating Characteristics
Conclusion on HIFU Prototype Transducers
6.2 Characterisation of the Imasonic Transducer
Pressure & Thermal Characteristics
Ability to Necrose Tissue
6.3 Photoacoustic Guidance of HIFU
Photoacoustic Acquisition
Denoising and Target Isolation
Photoacoustic Guidance of HIFU by Time-Reversal
6.4 Conclusion
7 Towards in Vivo Applications 
7.1 Development of Contrast Agents
Choice of Contrast Agents
Synthesis and Vectorisation of Contrast Agents
Evaluation of the Properties of the Compounds
7.2 Experiments on Biological Materials
Verication of Cellular Targeting
Injection with Vectorised Contrast Agents
7.3 Conclusion
IIIConclusions 
8 Review & Perspectives 
8.1 Review of Contributions
8.2 Perspectives for Future Work
Improvement of the Signal-to-Noise Ratio
Development of Targeted Contrast Agents
Improvements to Target Isolation Algorithms
8.3 Conclusion
IVAppendices 
A Reminder of Linear Acoustic Theory 
A.1 Introduction
A.2 Conservation of Momentum
A.3 Conservation of Mass
A.4 Relation of Change in Variables of State
A.5 Wave Equation
A.6 Velocity Potential
B Green’s Function Solutions 
B.1 Statement and Solution of the General Problem
Statement of the General Problem
Simplifying Assumptions
Choice of Constants
B.2 Recasting a Source Term Problem
C Principles of Optical Parametric Oscillators 
C.1 Optical Parametric Processes
C.2 Optical Parametric Amplication
C.3 Spontaneous Parametric Down-Conversion
C.4 Optical Parametric Oscillation
D Wiener Filters 
D.1 Derivation of a Linearly Optimised Filter Function
D.2 Application to the Problem of Additive Noise
E Résumé Substantiel en Français 
Introduction
Bases Théoriques
Instruments
Preuve de Principe & Identication des Dés
Réduction de Bruit & Extraction de Cible
Guidage Photoacoustique de HIFU
Vers des Applications in Vivo
Conclusions & Perspectives
Nomenclature
Bibliography 

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