Lessons from dynamic cadaver and invasive bone pin studies: do we know how the foot really moves during gait?

Background: This paper provides a summary of a Keynote lecture delivered at the 2009 Australasian Podiatry Conference. The aim of the paper is to review recent research that has adopted dynamic cadaver and invasive kinematics research approaches to better understand foot and ankle kinematics during gait. It is not intended to systematically cover all literature related to foot and ankle kinematics (such as research using surface mounted markers). Since the paper is based on a keynote presentation its focuses on the authors own experiences and work in the main, drawing on the work of others where appropriate Methods: Two approaches to the problem of accessing and measuring the kinematics of individual anatomical structures in the foot have been taken, (i) static and dynamic cadaver models, and (ii) invasive in-vivo research. Cadaver models offer the advantage that there is complete access to all the tissues of the foot, but the cadaver must be manipulated and loaded in a manner which replicates how the foot would have performed when in-vivo. The key value of invasive in-vivo foot kinematics research is the validity of the description of foot kinematics, but the key difficulty is how generalisable this data is to the wider population. Results: Through these techniques a great deal has been learnt. We better understand the valuable contribution mid and forefoot joints make to foot biomechanics, and how the ankle and subtalar joints can have almost comparable roles. Variation between people in foot kinematics is high and normal. This includes variation in how specific joints move and how combinations of joints move. The foot continues to demonstrate its flexibility in enabling us to get from A to B via a large number of different kinematic solutions. Conclusion: Rather than continue to apply a poorly founded model of foot type whose basis is to make all feet meet criteria for the mechanical 'ideal' or 'normal' foot, we should embrace variation between feet and identify it as an opportunity to develop patient-specific clinical models of foot function

In vivo, intrinsic kinematics of the foot and ankle

ISSN:1757-114

Automated quantification of steatosis: agreement with stereological point counting

Background: Steatosis is routinely assessed histologically in clinical practice and research. Automated image analysis can reduce the effort of quantifying steatosis. Since reproducibility is essential for practical use, we have evaluated different analysis methods in terms of their agreement with stereological point counting (SPC) performed by a hepatologist. Methods: The evaluation was based on a large and representative data set of 970 histological images from human patients with different liver diseases. Three of the evaluated methods were built on previously published approaches. One method incorporated a new approach to improve the robustness to image variability. Results: The new method showed the strongest agreement with the expert. At 20× resolution, it reproduced steatosis area fractions with a mean absolute error of 0.011 for absent or mild steatosis and 0.036 for moderate or severe steatosis. At 10× resolution, it was more accurate than and twice as fast as all other methods at 20× resolution. When compared with SPC performed by two additional human observers, its error was substantially lower than one and only slightly above the other observer. Conclusions: The results suggest that the new method can be a suitable automated replacement for SPC. Before further improvements can be verified, it is necessary to thoroughly assess the variability of SPC between human observers

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case