Sensitivity of quantitative photoacoustic tomography inversion schemes to experimental uncertainty

The ability to accurately quantify chromophore concentration from photoacoustic images would have a major impact on pre-clinical and clinical imaging. Recent years have seen significant advances in the theoretical understanding of quantitative photoacoustic imaging and in the development of model-based inversion strategies that overcome issues such as non-uniqueness and non-linearity. Nevertheless, their full in vivo implementation has not successfully been achieved, partially because experimental uncertainties complicate the transition. In this study, a sensitivity analysis is performed to assess the impact on accuracy of having uncertainty in critical experimental parameters such as scattering, beam diameter, beam position and calibration factor. This study was performed using two virtual phantoms, at one illumination and four optical wavelengths. The model-based inversion was applied in 3 variants - one just inverting for chromophores and two others further inverting for either a scaling factor or the scatterer concentration. The performance of these model-based inversions is also compared to linear unmixing strategies - with and without fluence correction. The results show that experimental uncertainties in a priori fixed parameters - especially calibration factor and scatterer concentration - significantly affect accuracy of model-based inversions and therefore measures to ameliorate this uncertainty should be considered. Including a scaling parameter in the inversion appears to improve quantification estimates. Furthermore, even with realistic levels of experimental uncertainty in model-based input parameters, they outperform linear unmixing approaches. If parameter uncertainty is large and has significant impact on accuracy, the parameter can be included as an unknown in model-based schemes

Exploiting statistical independence for quantitative photoacoustic tomography

To unlock the full capability of photoacoustic tomography as a quantitative, high resolution, molecular imaging modality, the problem of quantitative photoacoustic tomography must be solved. The aim in this is to extract clinically relevant functional information from photoacoustic images by finding the concentrations of the chromophores in the tissue. This is a challenging task due to the effect of the unknown but spatially and spectrally varying light fluence within the tissue. Many inversion schemes that include a model of the fluence have been proposed, but these have yet to make an impact in pre-clinical or clinical imaging. In this study, the statistical independence of the chromophore's distributions is proposed as a means of improving the robustness and hence the usefulness of the model-based inversion methods. This was achieved by minimising the mutual information between the estimated chromophore distributions in addition to the least squares data error within a gradient-based optimisation scheme. By applying the proposed inversion scheme to simulated multiwavelength photoacoustic images, it was shown that more accurate estimates for the concentrations of independent chromophores could be obtained in the presence of errors in the model parameters

CLSM method for the dynamic observation of pH change within polymer matrices for oral delivery

If acid-sensitive drugs or cells are administered orally, there is often a reduction in efficacy associated with gastric passage. Formulation into a polymer matrix is a potential method to improve their stability. The visualization of pH within these materials may help better understand the action of these polymer systems and allow comparison of different formulations. We herein describe the development of a novel confocal laser-scanning microscopy (CLSM) method for visualizing pH changes within polymer matrices and demonstrate its applicability to an enteric formulation based on chitosan-coated alginate gels. The system in question is first shown to protect an acid-sensitive bacterial strain to low pH, before being studied by our technique. Prior to this study, it has been claimed that protection by these materials is a result of buffering, but this has not been demonstrated. The visualization of pH within these matrices during exposure to a pH 2.0 simulated gastric solution showed an encroachment of acid from the periphery of the capsule, and a persistence of pHs above 2.0 within the matrix. This implies that the protective effect of the alginate-chitosan matrices is most likely due to a combination of buffering of acid as it enters the polymer matrix and the slowing of acid penetration

Less is often more : applied inverse problems using hp-forward models

To solve an applied inverse problem, a numerical forward model for the problem’s physics is required. Commonly, the finite element method is employed with discretizations consisting of elements with variable size h and polynomial degree p. Solutions to hp-forward models are known to converge exponentially by simultaneously decreasing h and increasing p. On the other hand, applied inverse problems are often ill-posed and their minimization rate exhibits uncertainty. Presently, the behavior of applied inverse problems incorporating hp elements of differing p, h, and geometry is not fully understood. Nonetheless, recent research suggests that employing increasingly higher-order hp-forward models (increasing mesh density and p) decreases reconstruction errors compared to inverse regimes using lower-order hp-forward models (coarser meshes and lower p). However, an affirmative or negative answer to following question has not been provided, “Does the use of higher order hp-forward models in applied inverse problems always result in lower error reconstructions than approaches using lower order hp-forward models?” In this article we aim to reduce the current knowledge gap and answer the open question by conducting extensive numerical investigations in the context of two contemporary applied inverse problems: elasticity imaging and hydraulic tomography – nonlinear inverse problems with a PDE describing the underlying physics. Our results support a negative answer to the question – i.e. decreasing h (increasing mesh density), increasing p, or simultaneously decreasing h and increasing p does not guarantee lower error reconstructions in applied inverse problems. Rather, there is complex balance between the accuracy of the hp-forward model, noise, prior knowledge (regularization), Jacobian accuracy, and ill-conditioning of the Jacobian matrix which ultimately contribute to reconstruction errors. As demonstrated herein, it is often more advantageous to use lower-order hp-forward models than higherorder hp-forward models in applied inverse problems. These realizations and other counterintuitive behavior of applied inverse problems using hp-forward models are described in detail herein

Statistical independence in nonlinear model-based inversion for quantitative photoacoustic tomography

The statistical independence between the distributions of different chromophores in tissue has previously been used for linear unmixing with independent component analysis (ICA). In this study, we propose exploiting this statistical property in a nonlinear model-based inversion method. The aim is to reduce the sensitivity of the inversion scheme to errors in the modelling of the fluence, and hence provide more accurate quantification of the concentration of independent chromophores. A gradient-based optimisation algorithm is used to minimise the error functional, which includes a term representing the mutual information between the chromophores in addition to the standard least-squares data error. Both numerical simulations and an experimental phantom study are conducted to demonstrate that, in the presence of experimental errors in the fluence model, the proposed inversion method results in more accurate estimation of the concentrations of independent chromophores compared to the standard model-based inversion

CLSM Method for the Dynamic Observation of pH Change within Polymer Matrices for Oral Delivery

If acid-sensitive drugs or cells are administered orally, there is often a reduction in efficacy associated with gastric passage. Formulation into a polymer matrix is a potential method to improve their stability. The visualization of pH within these materials may help better understand the action of these polymer systems and allow comparison of different formulations. We herein describe the development of a novel confocal laser-scanning microscopy (CLSM) method for visualizing pH changes within polymer matrices and demonstrate its applicability to an enteric formulation based on chitosan-coated alginate gels. The system in question is first shown to protect an acid-sensitive bacterial strain to low pH, before being studied by our technique. Prior to this study, it has been claimed that protection by these materials is a result of buffering, but this has not been demonstrated. The visualization of pH within these matrices during exposure to a pH 2.0 simulated gastric solution showed an encroachment of acid from the periphery of the capsule, and a persistence of pHs above 2.0 within the matrix. This implies that the protective effect of the alginate-chitosan matrices is most likely due to a combination of buffering of acid as it enters the polymer matrix and the slowing of acid penetration