to make its necess ity evident and its meaning easy to grasp. Thus the book is not intended as a complete exposition of the theory of Vector Analysis, bu t as a. Fundamentals of Vector Analysis. Abstract The purpose of this appendix is to present a consistent but brief introduction to vector calculus. For the sake of. Quantities with magnitude and direction are labeled vector quantities. .. ond definition is adequate for the vector analysis of this chapter.
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This chapter departs from the study and analysis of electromag- netic concepts where 1D scalar quantities was sufficient. Voltage, current, time, and 1D position . PDF Drive is your search engine for PDF files. As of today we have 78,, eBooks for you to download for free. No annoying ads, no download limits, enjoy . PDF | On Jan 1, , Ivan Avramidi and others published Lecture Notes Vector Analysis MATH
The full text of this article hosted at iucr. Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. This chapter contains sections titled: Vector Algebra: Geometric Method.
Clinical detection of fluid overload as oedema is insensitive and requires the accumulation of 4—5 L before detection [ 7 ].
Finally, deuterium dilution studies, which are the gold standard for total body water TBW assessment, are not feasible on a daily basis in the ICU setting [ 8 ]. Bioelectrical impedance vector analysis BIVA is a rapid, non-invasive bedside technique to measure fat-free TBW that correlates closely with the deuterium dilution technique [ 9 , 10 ].
BIVA has been reported to be useful to monitor hydration status during fluid removal in patients with decompensated heart failure [ 11 , 12 ] and during intermittent haemodialysis [ 13 — 17 ]. Thus, it may also prove useful in patients who are critically ill.
However, there is a paucity of studies of the feasibility and validity of BIVA-derived measurements in critically ill patients, and no study to date has examined the association between BIVA-measured hydration status and changes in fluid balance or clinician-driven fluid management.
Accordingly, we conducted a prospective, clinician-blinded, observational study to assess the feasibility and validity of BIVA in critically ill patients.
Materials and methods Study design We conducted a prospective, clinician-blinded, observational study from August to February to evaluate BIVA-measured hydration status in adult ICU patients at a tertiary hospital. Informed consent was obtained from the person legally responsible for the patient.
Inclusion and exclusion criteria We enrolled a consecutive convenience sample of screened patients by eligibility on weekdays only. We excluded patients with end-stage kidney disease undergoing long-term dialysis, pregnant patients, patients admitted to the ICU following elective cardiac surgery, patients with pacemakers or implantable defibrillators and patients with diaphragmatic pacing.
At the time of each BIVA measurement, we recorded mean arterial pressure MAP , central venous pressure CVP , vasopressor requirements, gas exchange, arterial lactate, creatinine and cumulative fluid balance. BIVA results were not made available to treating clinicians at any time during the study.
It combines bioelectrical impedance with capacitance measures i. Whole-body impedance is considered as a combination of resistance R and reactance Xc. BIVA is safe and non-invasive and can be performed at the bedside, giving a result within minutes. It is based on the electrical principle that the body is a circuit with a given resistance opposition of current flow through intracellular and extracellular solution and reactance capacitance of the cells to store energy [ 19 ].
Through the application of a kHz current to the body via a pair of electrodes one placed on the dorsum of the wrist and the other on the ipsilateral ankle , it gives a measurement of TBW in fat-free tissues. The accuracy of the test rests on careful placement of the BIVA electrodes and the connecting cable clips.
Describing the globe position with a 3D vector method could be also useful for orbital decompression surgery in TED.
Having a more accurate measurement method could help evaluate postoperative changes of the axial globe position in different directions. What is more, new onset strabismus is an important complication after orbital decompression surgery, and the 3D vector method might help in studying the eyeball motion and tilt change.
The 3D reconstruction technique provides a more comprehensive view of the orbit and improves the ability to analyze in orbital diseases [ 9 , 10 ]. In the following study, we established a coordinate system based on 3D CT images, defined the globe vector, and discussed the reliability of this method. We also compared the globe vector with the results of traditional two-dimensional 2D CT measurement, Hertel exophthalmometry, and clinical strabismus tests. Patients and Methods 2.
There were 30 females and 29 males, and the average age was The exclusion criteria included the patients with orbital rim or zygomatic change from fracture or surgery, orbital tumor, and orbital inflammation.
The research adhered to the tenets of the Declaration of Helsinki and was approved by the Ethics Committee of Fudan University. Informed consent was obtained from all the patients. The patients were instructed to look straight with fixed eyes during scanning.
The axial image including the thickest lens was chosen, and a line between the lateral orbital rims was drawn; then, the perpendicular distance between the corneal apex and this line was defined as the 2D CT exophthalmos. The landmarks were pointed to the volume-rendering image and adjusted on the axial, coronal, and sagittal images.
The intersection of the three reference planes was set as the origin 0, 0, 0 , and positive x, y, and z coordinate values indicated the front, left, and superior orientations, respectively Figure 1. Table 1: The landmarks, reference points, and planes of the 3D coordinate system. Figure 1: The landmarks and reference coordinate system.
The positive x, y, and z coordinate values indicated the front, left, and superior orientation, respectively. The points of the corneal apex C and the eyeball center E were marked using the following procedure. The cursor was adjusted and positioned on the middle point of the cornea section in the axial and sagittal images simultaneously; this was then named as point C. A sphere was created with the CAD computer-aided design function and was made to overlap with the eyeball wall on the axial, sagittal, and coronal images; then, the center of this sphere was named point E.
A 3D vector was defined to present the position of the globe in the reference coordinate system.