Minimally invasive surgical procedures offer advantages of smaller incisions, decreased hospital length of stay, and  rapid postoperative recovery to the patient.  Surgical robots improve access and visualization intraoperatively and have expanded the indications for minimally invasive procedures.  A limitation of the DaVinci surgical robot is a lack of sensory feedback to the operative surgeon.  Experienced robotic surgeons use visual interpretation of tissue and suture deformation as a surrogate for tactile feedback. A difficulty encountered during robotic surgery is maintaining adequate suture tension while tying knots or following a running anastomotic suture.  Displaying suture strain in real time has potential to decrease the learning curve and improve the performance and safety of robotic surgical procedures.  Conventional strain measurement methods involve installation of complex sensors on the robotic instruments. This paper presents a noninvasive video processing-based method to determine strain in surgical sutures. The method accurately calculates strain in suture by processing video from the existing surgical camera, making implementation uncomplicated.  The video analysis method was developed and validated using video of suture strain standards  on a servohydraulic testing system. The video-based suture strain algorithm is shown capable of measuring suture strains of 0.2% with subpixel resolution and proven reliability under various conditions.

John Martell

Thomas Elmer

Nachappa Gopalsami

Young Soo Park

Visual Measurement of Suture Strain for Robotic Surgery

We describe how scale space methods can be used for quantitative analysis of blood glucose concentrations from type 2 diabetes patients. Blood glucose values were recorded voluntarily by the patients over one full year as part of a self-management process, where the time and frequency of the recordings are decided by the patients. This makes a unique dataset in its extent, though with a large variation in reliability of the recordings. Scale space and frequency space techniques are suited to reveal important features of unevenly sampled data, and useful for identifying medically relevant features for use both by patients as part of their self-management process, and provide useful information for physicians.

Stein Olav Skrøvseth

Fred Godtliebsen

Scale Space Methods for Analysis of Type 2 Diabetes Patients' Blood Glucose Values

We present the optimal campaigns in the smoking dynamics. Assuming
that the giving up smoking model is described by the simplified <svg style="vertical-align:-1.90608pt;width:42.837502px;" id="M1" height="12.9375" version="1.1" viewBox="0 0 42.837502 12.9375" width="42.837502"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,12.9375)">
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				<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
				<tspan style="font-size: 12.50px; " x="7.4267821" y="0">𝐿</tspan>
				<tspan style="font-size: 12.50px; " x="16.278906" y="0">𝑆</tspan>
				<tspan style="font-size: 12.50px; " x="24.405855" y="0">𝑄</tspan>
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		</g>
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</svg> (potential-light-smoker-quit smoker) model, we consider two possible control variables in the form of
education and treatment campaigns oriented to decrease the attitude towards smoking. 
In order to do this we minimize the number of light (occasional) and persistent smokers
and maximize the number of quit smokers in a community. We first show the existence
of an optimal control for the control problem and then derive the optimality system by
using the Pontryagin maximum principle. Finally numerical results of real epidemic are
presented to show the applicability and efficiency of this approach.

Gul Zaman

Optimal Campaign in the Smoking Dynamics

We formulate a mathematical model for the cointeraction of schistosomiasis and HIV/AIDS in order to assess their synergistic relationship in the presence of therapeutic measures. Comprehensive mathematical techniques are used to analyze the model steady states. The disease-free equilibrium is shown to be locally asymptotically stable when the associated disease threshold parameter known as the basic reproduction number for the model is less than unity. Centre manifold theory is used to show that the schistosomiasis-only and HIV/AIDS-only endemic equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. The impact of schistosomiasis and its treatment on the dynamics of HIV/AIDS is also investigated. To illustrate the analytical results, numerical simulations using a set of reasonable parameter values are provided, and the results suggest that schistosomiasis treatment will always have a positive impact on the control of HIV/AIDS.

S. Mushayabasa

C. P. Bhunu

Modeling Schistosomiasis and HIV/AIDS Codynamics

Two datasets of points of known spatial positions and an associated absorbed dose value are often compared for quality assurance purposes in External Beam Radiation Therapy (EBRT). Some problems usually arise regarding the pass fail criterion to accept both datasets as close enough for practical purposes. Instances of this kind of comparisons are fluence or dose checks for intensity modulated radiation therapy, modelling of a treatment unit in a treatment planning system, and so forth. The gamma index is a figure of merit that can be obtained from both datasets; it is widely used, as well as other indices, as part of a comparison procedure. However, it is recognized that false negatives may take place (there are acceptable cases where a certain number of points do not pass the test) due in part to
computation and experimental uncertainty. This work utilizes mathematical methods to analyse comparisons, so that uncertainty can be taken into account. Therefore, false rejections due to uncertainty do not take place and there is no need to expand tolerances to take uncertainty into account. The methods provided are based on the rules of uncertainty propagation and help obtain rigorous pass/fail criteria, based on experimental information.

Francisco Cutanda Henríquez

Silvia Vargas Castrillón

A Probability Approach to the Study on Uncertainty Effects on Gamma Index Evaluations in Radiation Therapy


		The mathematical model for the dynamics of the hepatitis C proposed in Avenda&#xf1;o et al. (2002), with four populations (healthy and unhealthy hepatocytes, the viral load of the hepatitis C virus, and T killer cells), is revised. Showing that the reduced model obtained by considering only the first three of these populations, known as basic model, has two possible equilibrium states: the uninfected one where viruses are not present in the individual, and the endemic one where viruses and infected cells are present. A threshold parameter (the basic reproductive virus number) is introduced, and in terms of it, the global stability of both two possible equilibrium states is established. Other central result consists in showing, by model numerical simulations, the feasibility of monitoring liver damage caused by HCV, avoiding unnecessary biopsies and the undesirable related inconveniences/imponderables to the patient; another result gives a mathematical modelling basis to recently developed techniques for the disease assessment based essentially on viral load measurements.

J. Alavez-Ram&#237;rez

J. L. Fuentes-Allen

J. L&#243;pez-Estrada

Noninvasive Monitoring of Hepatic Damage from Hepatitis C Virus Infection

Pamela Jones

Sivabal Sivaloganathan

Computational and Mathematical Methods in Medicine

Researchers have suggested that the fate of a shock-induced wave front at the
edge of a “virtual anode” (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.

Nicholas P. Charteris

Bradley J. Roth

How Hyperpolarization and the Recovery of Excitability Affect Propagation through a Virtual Anode in the Heart


		The goal of this paper is to construct a new algorithm for the numerical simulations of the evolution of tumour invasion and metastasis. 
By means of mathematical model equations and their numerical solutions we investigate how cancer cells can produce and secrete matrix
degradative enzymes, degrade extracellular matrix, and invade due to diffusion and haptotactic migration. For the numerical simulations
of the interactions between the tumour cells and the surrounding tissue, we apply numerical approximations, which are spectrally accurate
and based on small amounts of grid-points. Our numerical experiments illustrate the metastatic ability of tumour cells.

M. Kolev

B. Zubik-Kowal

Numerical Solutions for a Model of Tissue Invasion and Migration of Tumour Cells

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<p><em>Computational and Mathematical Methods in Medicine</em> publishes research and review articles focused on the application of mathematics to problems arising from the biomedical sciences.</p>


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Computational and Mathematical Methods in Medicine