title: Completeness, conservation and error in SPH for fluids

authors: Vaughan, G.L.

subjects: mathematics

abstract: Smoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ensuring completeness conditions (low-order polynomials are interpolated exactly) are enforced when estimating property gradients, but the consequences on errors have not been investigated. Here, we present an expression for the error in an SPH estimate, accounting for completeness, an expression that applies to SPH generally. We revisit the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. We find that a common method for enforcing completeness violates a property required of the kernel gradients, namely that gradients with respect the two position variables be equal and opposite. In such models this means conservation principles are not enforced and we present results that show this. As an aside we show the summation interpolant for density is a solution of, and may be used in the place of, the discretized, symmetrized continuity equation. Finally, we examine two examples of discretization errors, namely numerical boundary layers and the existence of crystallized states. Copyright ©2007 John Wiley & Sons, Ltd.

text: Completeness, conservation and error in SPH for fluids Smoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ensuring completeness conditions (low-order polynomials are interpolated exactly) are enforced when estimating property gradients, but the consequences on errors have not been investigated. Here, we present an expression for the error in an SPH estimate, accounting for completeness, an expression that applies to SPH generally. We revisit the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. We find that a common method for enforcing completeness violates a property required of the kernel gradients, namely that gradients with respect the two position variables be equal and opposite. In such models this means conservation principles are not enforced and we present results that show this. As an aside we show the summation interpolant for density is a solution of, and may be used in the place of, the discretized, symmetrized continuity equation. Finally, we examine two examples of discretization errors, namely numerical boundary layers and the existence of crystallized states. Copyright ©2007 John Wiley & Sons, Ltd.

year: 2008

title: The cost-effectiveness of active surveillance compared to watchful waiting and radical prostatectomy for low risk localised prostate cancer

authors: Lao, Chunhuan

subjects: Active surveillance

abstract: Background: Radical prostatectomy is the most common treatment for localised prostate cancer in New Zealand. Active surveillance was introduced to prevent overtreatment and reduce costs while preserving the option of radical prostatectomy. This study aims to evaluate the cost-effectiveness of active surveillance compared to watchful waiting and radical prostatectomy.
Methods: Markov models were constructed to estimate the life-time cost-effectiveness of active surveillance compared to watchful waiting and radical prostatectomy for low risk localised prostate cancer patients aged 45–70 years, using national datasets in New Zealand and published studies including the SPCG-4 study. This study was from the perspective of the Ministry of Health in New Zealand.
Results: Radical prostatectomy is less costly than active surveillance in men aged 45–55 years with low risk localised prostate cancer, but more costly for men aged 60–70 years. Scenario analyses demonstrated significant uncertainty as to the most cost-effective option in all age groups because of the unavailability of good quality of life data for men under active surveillance. Uncertainties around the likelihood of having radical prostatectomy when managed with active surveillance also affect the cost-effectiveness of active surveillance against radical prostatectomy.
Conclusions: Active surveillance is less likely to be cost-effective compared to radical prostatectomy for younger men diagnosed with low risk localised prostate cancer. The cost-effectiveness of active surveillance compared to radical prostatectomy is critically dependent on the ‘trigger’ for radical prostatectomy and the quality of life in men on active surveillance. Research on the latter would be beneficial.

text: The cost-effectiveness of active surveillance compared to watchful waiting and radical prostatectomy for low risk localised prostate cancer Background: Radical prostatectomy is the most common treatment for localised prostate cancer in New Zealand. Active surveillance was introduced to prevent overtreatment and reduce costs while preserving the option of radical prostatectomy. This study aims to evaluate the cost-effectiveness of active surveillance compared to watchful waiting and radical prostatectomy.
Methods: Markov models were constructed to estimate the life-time cost-effectiveness of active surveillance compared to watchful waiting and radical prostatectomy for low risk localised prostate cancer patients aged 45–70 years, using national datasets in New Zealand and published studies including the SPCG-4 study. This study was from the perspective of the Ministry of Health in New Zealand.
Results: Radical prostatectomy is less costly than active surveillance in men aged 45–55 years with low risk localised prostate cancer, but more costly for men aged 60–70 years. Scenario analyses demonstrated significant uncertainty as to the most cost-effective option in all age groups because of the unavailability of good quality of life data for men under active surveillance. Uncertainties around the likelihood of having radical prostatectomy when managed with active surveillance also affect the cost-effectiveness of active surveillance against radical prostatectomy.
Conclusions: Active surveillance is less likely to be cost-effective compared to radical prostatectomy for younger men diagnosed with low risk localised prostate cancer. The cost-effectiveness of active surveillance compared to radical prostatectomy is critically dependent on the ‘trigger’ for radical prostatectomy and the quality of life in men on active surveillance. Research on the latter would be beneficial.

year: 2017

title: A walking stick in one hand and a chainsaw in the other: Patients’ perspectives of living with multimorbidity

authors: Signal, Louise

abstract: AIMS: Multimorbidity is common, yet there are major gaps in research, particularly among younger and indigenous populations. This research aimed to understand patients’ perspectives of living with multimorbidity. 

METHODS: A qualitative study of 61 people living with multimorbidity, 27 of whom were Māori and a third aged under 65, from urban and rural regions in New Zealand. Six focus groups and 14 interviews were conducted, recorded, transcribed and analysed. 
RESULTS: For many participants, living with multimorbidity disrupted their ‘normal’ lives, posing challenges in everyday activities such as eating and toileting, working and managing medications. Dealing with the health system posed challenges such as accessing appointments and having enough time in consultations. Cultural competency, good communication and continuity of care from healthcare providers were all valued. Participants had many recommendations to improve management, including a professional single point of contact to coordinate all specialist care. 
CONCLUSIONS: Living with multimorbidity is often challenging requiring people to manage their conditions while continuing to live their lives. This research suggests changes are needed in the health system in New Zealand and elsewhere to better manage multimorbidity thus improving patient’s lives and reducing costs to the health sector and wider society.

text: A walking stick in one hand and a chainsaw in the other: Patients’ perspectives of living with multimorbidity AIMS: Multimorbidity is common, yet there are major gaps in research, particularly among younger and indigenous populations. This research aimed to understand patients’ perspectives of living with multimorbidity. 

METHODS: A qualitative study of 61 people living with multimorbidity, 27 of whom were Māori and a third aged under 65, from urban and rural regions in New Zealand. Six focus groups and 14 interviews were conducted, recorded, transcribed and analysed. 
RESULTS: For many participants, living with multimorbidity disrupted their ‘normal’ lives, posing challenges in everyday activities such as eating and toileting, working and managing medications. Dealing with the health system posed challenges such as accessing appointments and having enough time in consultations. Cultural competency, good communication and continuity of care from healthcare providers were all valued. Participants had many recommendations to improve management, including a professional single point of contact to coordinate all specialist care. 
CONCLUSIONS: Living with multimorbidity is often challenging requiring people to manage their conditions while continuing to live their lives. This research suggests changes are needed in the health system in New Zealand and elsewhere to better manage multimorbidity thus improving patient’s lives and reducing costs to the health sector and wider society.

year: 2017