Causal stroke

For 2-port TF and GY elements causal patterns must be as displayed in Fig. B.5. A TF relates efforts. That is, if the effort at one port is an input, the effort at the other port must be an output. Since the constitutive equations of GY elements relate the effort of one port to the flow of the other one, both causal strokes must either point to the element or away from it. 

At 0-junctions the effort at all incident bonds is the same. Consequently, one causal stroke can point to the junction, while aU others must point away from it (cf. Fig. B.5). For the dual 1-junctions, the role of effort and flow is interchanged. That is, at one bond the causal stroke may be pointing away from the junction. At all other bonds it must point towards the 1-junction. This causal pattern reflects the fact that one effort is equal to the sum of all other efforts and simultaneously it indicates that... 

For resistors with linear constitutive relations, causal strokes may be either on the side of a port (conductance causality), or pointing away from the port (resistance causality). In some cases, however, there is no such choice. For a resistor representing dry friction, only the effort (force) can be the output. 

Definition B.2 Causal path) A sequence of bonds from one power port of an element to a power port of another element is called a causal path if there is no 2-port gyrator in between and if all bonds have their causal stroke at the same end. 

A cascade of bonds between two power ports with a gyrator in between is called a causal path if aU bonds on one side of the gyrator have there causal stroke at the same end, while aU bonds on the other side of the gyrator have their causal stroke on the opposite end. That is, the gyrator switches the direction of efforts on one of its sides. ... 

From the fact that one of the variables on a port is an independent variable of the constitutive relation and the other one a dependent variable, it follows that the computational direction of the two conjugate variables at a bond is always bi-directional and can in principle be expanded into two opposite signals, in other words, a bond can be considered a bilateral signal flow. The effort is the input of the multiport node at the one side and the output of the node at the other side. Only after a particular choice is made about the two possibilities of these directions, this can be represented by causally augmenting the (multi)bond with a so-called causal stroke, a little line drawn orthogonal to the bond at the end of the bond where the effort serves as an output of the bond from a computational point of view. This implicates that it serves as an input for the port that is connected to that side of the bond. Similarly the conjugate flow at that side of the bond is an output of this port and an input to... 

Fig. 1.4 Meaning of the causal stroke direction of the bilateral signals...

There is a constraint between the causality of two or more ports of a node. This is the case for the elementary two port nodes (M)TF and (M)GY the (M)TF always has only one stroke at the node, while the (M)GY has either both strokes at the node or both open ends. The junctions also have such a causal constraint an -port 0-junction has one stroke at the node and n - 1 open ends, while an -port 1-junction has one open end at the node and n - 1 causal strokes. The same holds for the XO and the XI in principle, but in many cases they will be given a fixed causality, given the discontinuous and consequently non-invertible nature of their constitutive relations. 

Straightforward application of the causality assignment to the bond graph in Fig. 1.7 results in Fig. 1.8, where the numbers refer to the sequential order in which the causal strokes were assigned. Note that the two I-type storage elements representing the pendulum point mass do not get their preferred causality. Section 1.5 will explain... 

The graphic trick to represent bicausality in a bond graph breaks the causal stroke into two half strokes each dedicated to the assignment of one of the two conjugate power variables (here the flow variable is on the half arrow side and the effort variable on the opposite side). The assignment rule remains in agreement with the one of causality since a flow is imposed on the subsystem far from the flow-dedicated half stroke while an effort is imposed on the subsystem closed to the effort-dedicated half stroke [18] (Fig. 6.6). 

Some of the association between atrial fibrillation and stroke must be coincidental because atrial fibrillation can be caused by coronary and hypertensive heart disease, both of which may be associated with atheromatous disease or primary intracerebral hemorrhage. Although anticoagulation markedly reduces the risk of first or recurrent stroke, this is not necessarily evidence for causality because this treatment may be working in other ways, such as by inhibiting artery-to-artery embolism, although trials of warfarin in secondary prevention of stroke in sinus rhythm have shown no benefit over aspirin (Ch. 24). 

Homocysteine and cardiovascular disease evidence on causality from a meta-analysis. British Medical Journal 325 1202-1206 Wald DS, Law M, Morris JK (2004). The dose-response relationship between serum homocysteine and cardiovascular disease implications for treatment and screening. European Journal of Cardiovascular Prevention and Rehabilitation 11 250-253 Wang X, Qin X, Demirtas H et al. (2007). Efficacy of folic acid supplementation in stroke prevention a meta-analysis. Lancet 369 1876-1882... 

Calcification, and possibly sclerosis, of the aortic and mitral valves may be a cause of embolism of calcific or complicating thrombotic material. However, these degenerative disorders of heart valves are so common, particularly in the elderly, that it has been very difficult to associate them causally with stroke (Boon et al. 1996). 

There is also good evidence that inflammation has a causal role in carotid plaque instability (van der Wal et al. 1994 Redgrave et al. 2006). Visualization of plaque macrophages by MRI after their uptake of ultra-small particles of iron oxide is now possible (Trivedi et al. 2004 Tang et al. 2006). However, large prospective studies are required to determine whether these imaging characteristics predict the risk of stroke. 

Acetazolamide toxicity was suspected, because of the temporal association between drug treatment and the onset of the neurological sjmptoms, together with metabolic acidosis. Gerstmann sjmdrome is usually due to an acute stroke. Although a brain CT scan was negative, such an event was likely in this patient, who had a history of cerebrovascular disease and multiple risk factors, and a causal relation to acetazolamide must be considered tenuous. 

Five patients developed ischemic stroke within 2-5 days of finishing a 4-day course of fluorouracil plus low-dose cispla-tin by continuous infusion (57). Whilst cisplatin has been implicated as having produced central ischemic events, most commonly in combination with vindesine and bleomycin, there has only been one other report involving fluorouracil. Although the causal link was not conclusive, the circumstantial evidence was strong. 

Even though it is impossible to establish causality in this case, it is conceivable that the stroke was the result of over-anticoagulation induced by the herbal medication (11). 

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