well my calculations prove that writing and speaking are important in engineering. Throughout your career, you will confront many writing situations, including proposals, formal reports, and journal articles. Proposals are important documents in engineering. What does a proposal do? A proposal presents a strategy for solving a problem. A successful proposal needs two elements: a statement of a problem and a proposed solution to that problem. When a proposal works well, these two elements fit as pieces of a jigsaw puzzle. The audiences of proposals include technical readers, who consider the technical merits of the proposal, and management readers, who evaluate the benefits of the proposal.
While proposals often serve as the beginnings of projects in engineering, formal reports and journal articles often serve as the completion points of projects. Formal reports are usually split into three sections: front matter, main text, and back matter. The front matter includes the front cover, title page, contents page, and informative summary. The main text portion of your formal report contains the introduction, discussion, and conclusion sections. The back matter portion of your report contains your appendices, glossary, and references. The front matter and back matter allow you to target multiple audiences. Journal articles are similar to formal reports in content, but because of format differences, generally target only one type of audience.
In all of the situations discussed in these guidelines, you might have to write or present as part of a group. Although collaboration on a document or presentation presents a challenge to the group members, it also has advantages. One advantage is that working in a group broadens the range of ideas that the document or presentation can incorporate. Another advantage is that collaborative work allows the group to draw from the various writing and editing strengths of the members. In a successful group effort, you find a strategy that accents the advantages and mitigates the disadvantages.
No single course can prepare you for every communication situation that you will face as an engineer or scientist. Nonetheless, you should be able to handle most situations if you will first sit down and examine your constraints. One of these constraints is format. Included in these guidelines were some professional examples of format so that you could practice creating documents. You should understand that there are no universal formats for engineering and science. While there may be similarities, the formats that engineers and scientists use at Sandia National Laboratories are not the same formats that engineers and scientists use at IBM or Dow Chemical.
You cannot treat scientific writing in the same way that you treat thermodynamics or anatomy or quantum chemistry. Writing is a craft, not a science. The process of learning to write effectively does not end with these guidelines, or any guidelines for that matter; it continues throughout your career. Hemingway wasn't speaking of scientific writing when he remarked, "We are apprentices of a craft where no one becomes a master." However, Hemingway's remark describes accurately the writing that we as engineers and scientists do.
nerd Consider a piece of a dendrite decomposed in short cylindric segments of length dx each. The schematic drawing in Fig. 2.16 shows the corresponding circuit diagram. Using Kirchhoff's laws we find equations that relate the voltage u(x) across the membrane at location x with longitudinal and transversal currents. First, a longitudinal current i(x) passing through the dendrite causes a voltage drop across the longitudinal resistor RL according to Ohm's law,
u(t, x + dx) - u(t, x) = RL i(t, x) , (2.23)
where u(t, x + dx) is the membrane potential at the neighboring point x + dx. Second, the transversal current that passes through the RC-circuit is given by C u(t, x)/t + u(t, x)/RT. Kirchhoff's law regarding the conservation of current at each node leads to
i(t, x + dx) - i(t, x) = C u(t, x) + - Iext(t, x) . (2.24)
The values of the longitudinal resistance RL, the transversal conductivity R-1T, the capacity C, and the externally applied current can be expressed in terms of specific quantities per unit length rL, r-1T, c, and iext, respectively, viz.
RL = rL dx , R-1T = r-1T dx , C = c dx , Iext(t, x) = iext(t, x) dx . (2.25)
These scaling relations express the fact that the longitudinal resistance and the capacity increase with the length of the cylinder, whereas the transversal resistance is decreasing, simply because the surface the current can pass through is increasing. Substituting these expressions in Eqs. (2.24) and (2.25), dividing by dx, and taking the limit dx 0 leads to
Taking the derivative of these equations with respect to x and crosswise substitution yields
We introduce the characteristic length scale = rT/rL (``electrotonic length scale''馃槈 and the membrane time constant = rT c. If we multiply Eq. (2.28) by we get
After a transformation to unit-free coordinates,
x = x/ , t = t/ , (2.29)
and rescaling the current variables,
i = i , iext = rT iext , (2.30)
we obtain the cable equations (where we have dropped the hats)
in a symmetric, unit-free form. Note that it suffices to solve one of these equations due to the simple relation between u and i given in Eq. (2.27a).
The cable equations can be easily interpreted. These equations describe the change in time of voltage and longitudinal current. Both equations contain three different contributions. The first term on the right-hand side of Eq. (2.32) is a diffusion term that is positive if the voltage (or current) is a convex function of x. The voltage at x thus tends to decrease, if the values of u are lower in a neighborhood of x than at x itself. The second term on the right-hand side of Eq. (2.32) is a simple decay term that causes the voltage to decay exponentially towards zero. The third term, finally, is a source term that acts as an inhomogeneity in the otherwise autonomous differential equation. This source can be due to an externally applied current, to synaptic input, or to other (non-linear) ion channels; cf.Section 2.5.3.
2.5.1.1 Example: Stationary solutions of the cable equation
In order to get an intuitive understanding of the behavior of the cable equation we look for stationary solutions of Eq. (2.32a), i.e., for solutions with u(t, x)/t = 0. In that case, the partial differential equation reduces to an ordinary differential equation in x, viz.
u(t, x) - u(t, x) = - iext(t, x) . (2.32)
The general solution to the homogenous equation with iext(t, x) 0 is
u(t, x) = c1 sinh(x) + c2 cosh(x) , (2.33)
as can easily be checked by taking the second derivative with respect to x. Here, c1 and c2 are constants that are determined by the boundary conditions.
Solutions for non-vanishing input current can be found by standard techniques. For a stationary input current iext(t, x) = (x) localized at x = 0 and boundary conditions u(卤) = 0 we find
u(t, x) = e-x , (2.34)
cf. Fig. 2.17. This solution is given in units of the intrinsic length scale = (rT/rL)1/2. If we re-substitute the physical units we see that is the length over which the stationary membrane potential drops by a factor 1/e. In the literature is refered to as the electrotonic length scale (Rall, 1989). Typical values for the specific resistance of intracellular medium and the cell membrane are 100 cm and 30 k cm2, respectively. In a dendrite with radius = 1 m this amounts to a transversal and a longitudinal resistance of rL = 100 cm/() = 3 . 105 m-1 and rT = 30 k cm2/(2) = 5 . 1011 m. The corresponding electrotonic length scale is = 1.2 mm. Note that the electrotonic length can be significantly smaller if the transversal conductivity is increased, e.g., due to open ion channels.
Figure 2.17: Stationary solution of the cable equation with a constant current of unit strength being injected at x = 0, i.e., iext(t, x) = (x). The electrotonic length scale is the distance over which the membrane potential drops to 1/e of its initial value.
For arbitrary stationary input current iext(x) the solution of Eq. (2.32a) can be found by a superposition of translated fundamental solutions (2.35), viz.,
u(t, x) = dx' e-x - x' iext(x'馃槈 . (2.35)
This is an example of the Green's function approach applied here to the stationary case. The general time-dependent case will be treated in the next section.
2.5.2 Green's Function (*)
In the following we will concentrate on the equation for the voltage and start our analysis by deriving the Green's function for a cable extending to infinity in both directions. The Green's function is defined as the solution of a linear equation such as Eq. (2.32) with a Dirac -pulse as its input. It can be seen as an elementary solution of the differential equation because - due to linearity - the solution for any given input can be constructed as a superposition of these Green's functions.
In order to find the Green's function for the cable equation we thus have to solve Eq. (2.32a) with iext(t, x) replaced by a impulse at x = 0 and t = 0,
u(t, x) - u(t, x) + u(t, x) = (t) (x) . (2.36)
Fourier transformation with respect to the spatial variable yields
u(t, k) + k2 u(t, k) + u(t, k) = (t)/ . (2.37)
This is an ordinary differential equation in t and has a solution of the form
u(t, k) = exp - 1 + k2 t/ (t) (2.38)
with (t) denoting the Heaviside function. After an inverse Fourier transform we obtain the desired Green's function G(t, x),
u(t, x) = exp - t - G(t, x) . (2.39)
The general solution for an infinitely long cable is therewith given through
u(t, x) = dt'dx' G(t - t', x - x'馃槈 iext(t', x'馃槈 . (2.40)
2.5.2.1 Example: Checking the Green's property
We can check the validity of Eq. (2.40) by substituting G(t, x) into the left-hand side of Eq. (2.37). After a short calculation we find
- + 1 G(t, x) = exp - t - (t) , (2.41)
where we have used (t)/t = (t). As long as t 0 the right-hand side of Eq. (2.42) vanishes, as required by Eq. (2.37). For t 0 we find
exp - t - = (x) , (2.42)
which proves that the right-hand side of Eq. (2.42) is indeed equivalent to the right-hand side of Eq. (2.37).
Having established that
- + 1 G(t, x) = (x) (t) , (2.43)
we can readily show that Eq. (2.41) is the general solution of the cable equation for arbitrary input currents iext(t0, x0). We substitute Eq. (2.41) into the cable equation, exchange the order of integration and differentiation, and find
2.5.2.2 Example: Finite cable
Real cables do not extend from - to + and we have to take extra care to correctly include boundary conditions at the ends. We consider a finite cable extending from x = 0 to x = L with sealed ends, i.e., i(t, x = 0) = i(t, x = L) = 0 or, equivalently, u(t, x = 0) = u(t, x = L) = 0.
The Green's function G0, L for a cable with sealed ends can be constructed from G by applying a trick from electro-statics called ``mirror charges'' (Jackson, 1962). Similar techniques can also be applied to treat branching points in a dendritic tree (Abbott, 1991). The cable equation is linear and, therefore, a superposition of two solutions is also a solution. Consider a current pulse at time t0 and position x0 somewhere along the cable. The boundary condition u(t, x = 0) = 0 can be satisfied if we add a second, virtual current pulse at a position x = - x0 outside the interval [0, L]. Adding a current pulse outside the interval [0, L] comes for free since the result is still a solution of the cable equation on that interval. Similarly, we can fulfill the boundary condition at x = L by adding a mirror pulse at x = 2 L - x0. In order to account for both boundary conditions simultaneously, we have to compensate for the mirror pulse at - x0 by adding another mirror pulse at 2 L + x0 and for the mirror pulse at x = 2 L - x0 by adding a fourth pulse at -2 L + x0 and so forth. Altogether we have
We emphasize that in the above Green's function we have to specify both (t0, x0) and (t, x) because the setup is no longer translation invariant. The general solution on the interval [0, L] is given by
u(t, x) = dt0 dx0 G0, L(t0, x0;t, x) iext(t0, x0) . (2.44)
An example for the spatial distribution of the membrane potential along the cable is shown in Fig. 2.18A, where a current pulse has been injected at location x = 1. In addition to Fig. 2.18A, subfigure B exhibits the time course of the membrane potential measured in various distances from the point of injection. It is clearly visible that the peak of the membrane potential measured at, e.g., x = 3 is more delayed than at, e.g., x = 2. Also the amplitude of the membrane potential decreases significantly with the distance from the injection point. This is a well-known phenomenon that is also present in neurons.
Originally posted by MC Mike
nerd Consider a piece of a dendrite decomposed in short cylindric segments of length dx each. The schematic drawing in Fig. 2.16 shows the corresponding circuit diagram. Using Kirchhoff's laws we find equations that relate the voltage u(x) across the membrane at location x with longitudinal and transversal currents. First, a longitudinal current i(x) passing through the dendrite causes a voltage drop across the longitudinal resistor RL according to Ohm's law,u(t, x + dx) - u(t, x) = RL i(t, x) , (2.23)
where u(t, x + dx) is the membrane potential at the neighboring point x + dx. Second, the transversal current that passes through the RC-circuit is given by C u(t, x)/t + u(t, x)/RT. Kirchhoff's law regarding the conservation of current at each node leads to
i(t, x + dx) - i(t, x) = C u(t, x) + - Iext(t, x) . (2.24)
The values of the longitudinal resistance RL, the transversal conductivity R-1T, the capacity C, and the externally applied current can be expressed in terms of specific quantities per unit length rL, r-1T, c, and iext, respectively, viz.
RL = rL dx , R-1T = r-1T dx , C = c dx , Iext(t, x) = iext(t, x) dx . (2.25)
These scaling relations express the fact that the longitudinal resistance and the capacity increase with the length of the cylinder, whereas the transversal resistance is decreasing, simply because the surface the current can pass through is increasing. Substituting these expressions in Eqs. (2.24) and (2.25), dividing by dx, and taking the limit dx 0 leads to
Taking the derivative of these equations with respect to x and crosswise substitution yields
We introduce the characteristic length scale = rT/rL (``electrotonic length scale''馃槈 and the membrane time constant = rT c. If we multiply Eq. (2.28) by we get
After a transformation to unit-free coordinates,
x = x/ , t = t/ , (2.29)
and rescaling the current variables,
i = i , iext = rT iext , (2.30)
we obtain the cable equations (where we have dropped the hats)
in a symmetric, unit-free form. Note that it suffices to solve one of these equations due to the simple relation between u and i given in Eq. (2.27a).
The cable equations can be easily interpreted. These equations describe the change in time of voltage and longitudinal current. Both equations contain three different contributions. The first term on the right-hand side of Eq. (2.32) is a diffusion term that is positive if the voltage (or current) is a convex function of x. The voltage at x thus tends to decrease, if the values of u are lower in a neighborhood of x than at x itself. The second term on the right-hand side of Eq. (2.32) is a simple decay term that causes the voltage to decay exponentially towards zero. The third term, finally, is a source term that acts as an inhomogeneity in the otherwise autonomous differential equation. This source can be due to an externally applied current, to synaptic input, or to other (non-linear) ion channels; cf.Section 2.5.3.2.5.1.1 Example: Stationary solutions of the cable equation
In order to get an intuitive understanding of the behavior of the cable equation we look for stationary solutions of Eq. (2.32a), i.e., for solutions with u(t, x)/t = 0. In that case, the partial differential equation reduces to an ordinary differential equation in x, viz.u(t, x) - u(t, x) = - iext(t, x) . (2.32)
The general solution to the homogenous equation with iext(t, x) 0 is
u(t, x) = c1 sinh(x) + c2 cosh(x) , (2.33)
as can easily be checked by taking the second derivative with respect to x. Here, c1 and c2 are constants that are determined by the boundary conditions.
Solutions for non-vanishing input current can be found by standard techniques. For a stationary input current iext(t, x) = (x) localized at x = 0 and boundary conditions u(卤) = 0 we findu(t, x) = e-x , (2.34)
cf. Fig. 2.17. This solution is given in units of the intrinsic length scale = (rT/rL)1/2. If we re-substitute the physical units we see that is the length over which the stationary membrane potential drops by a factor 1/e. In the literature is refered to as the electrotonic length scale (Rall, 1989). Typical values for the specific resistance of intracellular medium and the cell membrane are 100 cm and 30 k cm2, respectively. In a dendrite with radius = 1 m this amounts to a transversal and a longitudinal resistance of rL = 100 cm/() = 3 . 105 m-1 and rT = 30 k cm2/(2) = 5 . 1011 m. The corresponding electrotonic length scale is = 1.2 mm. Note that the electrotonic length can be significantly smaller if the transversal conductivity is increased, e.g., due to open ion channels.
Figure 2.17: Stationary solution of the cable equation with a constant current of unit strength being injected at x = 0, i.e., iext(t, x) = (x). The electrotonic length scale is the distance over which the membrane potential drops to 1/e of its initial value.
For arbitrary stationary input current iext(x) the solution of Eq. (2.32a) can be found by a superposition of translated fundamental solutions (2.35), viz.,
u(t, x) = dx' e-x - x' iext(x'馃槈 . (2.35)
This is an example of the Green's function approach applied here to the stationary case. The general time-dependent case will be treated in the next section.
2.5.2 Green's Function (*)
In the following we will concentrate on the equation for the voltage and start our analysis by deriving the Green's function for a cable extending to infinity in both directions. The Green's function is defined as the solution of a linear equation such as Eq. (2.32) with a Dirac -pulse as its input. It can be seen as an elementary solution of the differential equation because - due to linearity - the solution for any given input can be constructed as a superposition of these Green's functions.In order to find the Green's function for the cable equation we thus have to solve Eq. (2.32a) with iext(t, x) replaced by a impulse at x = 0 and t = 0,
u(t, x) - u(t, x) + u(t, x) = (t) (x) . (2.36)
This is an ordinary differential equation in t and has a solution of the form
u(t, k) = exp - 1 + k2 t/ (t) (2.38)
with (t) denoting the Heaviside function. After an inverse Fourier transform we obtain the desired Green's function G(t, x),
u(t, x) = exp - t - G(t, x) . (2.39)
The general solution for an infinitely long cable is therewith given through
u(t, x) = dt'dx' G(t - t', x - x'馃槈 iext(t', x'馃槈 . (2.40)
2.5.2.1 Example: Checking the Green's property
We can check the validity of Eq. (2.40) by substituting G(t, x) into the left-hand side of Eq. (2.37). After a short calculation we find- + 1 G(t, x) = exp - t - (t) , (2.41)
where we have used (t)/t = (t). As long as t 0 the right-hand side of Eq. (2.42) vanishes, as required by Eq. (2.37). For t 0 we find
exp - t - = (x) , (2.42)
which proves that the right-hand side of Eq. (2.42) is indeed equivalent to the right-hand side of Eq. (2.37).
Having established that- + 1 G(t, x) = (x) (t) , (2.43)
we can readily show that Eq. (2.41) is the general solution of the cable equation for arbitrary input currents iext(t0, x0). We substitute Eq. (2.41) into the cable equation, exchange the order of integration and differentiation, and find
2.5.2.2 Example: Finite cable
Real cables do not extend from - to + and we have to take extra care to correctly include boundary conditions at the ends. We consider a finite cable extending from x = 0 to x = L with sealed ends, i.e., i(t, x = 0) = i(t, x = L) = 0 or, equivalently, u(t, x = 0) = u(t, x = L) = 0.The Green's function G0, L for a cable with sealed ends can be constructed from G by applying a trick from electro-statics called ``mirror charges'' (Jackson, 1962). Similar techniques can also be applied to treat branching points in a dendritic tree (Abbott, 1991). The cable equation is linear and, therefore, a superposition of two solutions is also a solution. Consider a current pulse at time t0 and position x0 somewhere along the cable. The boundary condition u(t, x = 0) = 0 can be satisfied if we add a second, virtual current pulse at a position x = - x0 outside the interval [0, L]. Adding a current pulse outside the interval [0, L] comes for free since the result is still a solution of the cable equation on that interval. Similarly, we can fulfill the boundary condition at x = L by adding a mirror pulse at x = 2 L - x0. In order to account for both boundary conditions simultaneously, we have to compensate for the mirror pulse at - x0 by adding another mirror pulse at 2 L + x0 and for the mirror pulse at x = 2 L - x0 by adding a fourth pulse at -2 L + x0 and so forth. Altogether we have
We emphasize that in the above Green's function we have to specify both (t0, x0) and (t, x) because the setup is no longer translation invariant. The general solution on the interval [0, L] is given by
u(t, x) = dt0 dx0 G0, L(t0, x0;t, x) iext(t0, x0) . (2.44)
An example for the spatial distribution of the membrane potential along the cable is shown in Fig. 2.18A, where a current pulse has been injected at location x = 1. In addition to Fig. 2.18A, subfigure B exhibits the time course of the membrane potential measured in various distances from the point of injection. It is clearly visible that the peak of the membrane potential measured at, e.g., x = 3 is more delayed than at, e.g., x = 2. Also the amplitude of the membrane potential decreases significantly with the distance from the injection point. This is a well-known phenomenon that is also present in neurons.
NERD!
nitroglycerin,
also called GLYCERYL TRINITRATE, a powerful explosive and an important ingredient of most forms of dynamite. It is also used with nitrocellulose in some propellants, especially for rockets and missiles, and it is employed as a vasodilator in the easing of cardiac pain.
Pure nitroglycerin is a colourless, oily, somewhat toxic liquid having a sweet, burning taste. It was first prepared in 1846 by the Italian chemist Ascanio Sobrero by adding glycerol to a mixture of concentrated nitric and sulfuric acids. The hazards involved in preparing large quantities of nitroglycerin have been greatly reduced by widespread adoption of continuous nitration processes.
Nitroglycerin, with the molecular formula C3H5(ONO2)3, has a high nitrogen content (18.5 percent) and contains sufficient oxygen atoms to oxidize the carbon and hydrogen atoms while nitrogen is being liberated, so that it is one of the most powerful explosives known. Detonation of nitroglycerin generates gases that would occupy more than 1,200 times the original volume at ordinary room temperature and pressure; moreover, the heat liberated raises the temperature to about 5,000 C (9,000 F). The overall effect is the instantaneous development of a pressure of 20,000 atmospheres; the resulting detonation wave moves at approximately 7,700 m per second (more than 17,000 miles/h). Nitroglycerin is extremely sensitive to shock and to rapid heating; it begins to decompose at 50 -60 C (122 -140 F) and explodes at 218 C (424 F).
The safe use of nitroglycerin as a blasting explosive became possible after the Swedish chemist Alfred Nobel developed dynamite in the 1860s by combining liquid nitroglycerin with an inert porous material such as charcoal or diatomaceous earth. Nitroglycerin plasticizes collodion (a form of nitrocellulose) to form blasting gelatin, a very powerful explosive. Nobel's discovery of this action led to the development of ballistite, the first double-base propellant and a precursor of cordite.
A serious problem in the use of nitroglycerin results from its high freezing point (13 C [55 F]) and the fact that the solid is even more shock-sensitive than the liquid. This disadvantage is overcome by using mixtures of nitroglycerin with other polynitrates; for example, a mixture of nitroglycerin and ethylene glycol dinitrate freezes at -29 C (-20 F).
Continuous nitroglycerin use leads to development of nitroglycerin tolerance and loss of effectiveness. Intravenous (iv) N-acetyl cysteine (NAC), during short-term studies of people receiving continuous nitroglycerin, was reported to reverse nitroglycerin tolerance.1 2 In a double-blind study of patients with unstable angina, transdermal nitroglycerin plus oral NAC (600 mg three times per day) was associated with fewer failures of medical treatment than placebo, NAC, or nitroglycerin alone. However, when combined with nitroglycerin use, NAC has led to intolerable headaches.3 4 In two double-blind, randomized trials of angina patients treated with transdermal nitroglycerin, oral NAC 200 mg or 400 mg three times per day failed to prevent nitroglycerin tolerance.5 6
Vitamin C may help maintain the blood vessel dilation response to nitroglycerin. A double-blind study found that individuals taking 2 grams of vitamin C three times per day did not tend to develop nitroglycerin tolerance over time compared to those taking placebo.7 In another controlled clinical trial, similar protection was achieved with 500 mg three times daily.8
People using long-acting nitroglycerin can avoid tolerance with a ten- to twelve-hour hour nitroglycerin-free period every day. People taking long-acting nitroglycerin should ask their prescribing doctor or pharmacist about preventing nitroglycerin tolerance.
Blood returning from the body in the veins must be pumped by the heart through the lungs and into the arteries against the high pressure in the arteries. In order to accomplish this work, the heart's muscle must produce and use energy ("fuel"馃槈. The production of energy requires oxygen. Angina pectoris (angina) or "heart pain" is due to an inadequate flow of blood (and oxygen) to the muscle of the heart. It is believed that all nitrates, including nitroglycerin, correct the imbalance between the flow of blood and oxygen to the heart and the work that the heart must do by dilating the arteries and veins in the body. Dilation of the veins reduces the amount of blood that returns to the heart that must be pumped . Dilation of the arteries lowers the pressure in the arteries against which the heart must pump. As a consequence, the heart works less and requires less blood and oxygen.
Additionally, in patients with angina, nitroglycerin preferentially dilates blood vessels that supply the areas of the heart where there is not enough oxygen, thereby delivering oxygen to the heart tissue that needs it most.
PRESCRIPTION: yes
GENERIC AVAILABLE: yes (for some dosage forms)
PREPARATIONS: extended-release capsules containing 2.5, 6.5, 9, or 13 mg; 2% ointment with tape for application; patches (or transdermal delivery systems) which deliver 0.1, 0.2, 0.3, 0.4, 0.6, or 0.8 mg of nitroglycerin per hour; buccal tablets containing 1, 2, or 3 mg of nitroglycerin in an extended-release formulation; a translingual spray which delivers 0.4 mg of nitroglycerin per spray; sublingual tablets containing 0.15 or 0.3mg.
STORAGE: All formulations should be kept at room temperature, 15-30掳C (59-86掳F). The sublingual tablets are especially susceptible to moisture. They should NOT be kept in bathrooms or kitchens because of the higher degrees of moisture there. Care should be taken to replace the sublingual tablets every six months.
PRESCRIBED FOR: Nitroglycerin is indicated for the acute treatment and prevention of angina.
DOSING: For the treatment of acute angina attacks or for acute prevention (i.e. immediately before encountering situations likely to bring on an anginal attack): one tablet is allowed to dissolve under the tongue or in the buccal pouch (between the cheek and gums), or one spray is given of the lingual spray. (Nitroglycerin for sublingual or buccal use as well as spray are rapidly absorbed from the lining of the mouth for immediate effects.) This may be repeated every 5 minutes as needed. If angina is not relieved after a total of 3 doses, the patient should be taken to a hospital or a physician should be contacted. If lingual spray is used, the canister of spray should not be shaken prior to use, and it should be sprayed onto or under the tongue and then the mouth closed.
For prevention of angina, ointment may be applied using special dose-measuring application papers provided with the ointment. The appropriate amount of ointment is squeezed as a thin layer onto the paper, and the paper is used to spread the ointment onto nonhairy area of skin. The ointment should not be allowed to come into contact with the hands so that there is no absorption from the hands. Transdermal patches also are used for prevention. Patches may be applied to any hairless site but should not be applied to areas with cuts or calluses. Firm pressure should be used over the patch to ensure contact with the skin. The patch should not be cut or trimmed . Patches are waterproof and should not be affected by showering or bathing. Capsules of long-acting nitroglycerin also are used for prevention. They usually are prescribed 2 to 3 times per day and are taken 1 to 2 hours after a meal.
DRUG INTERACTIONS: Since nitroglycerin can cause hypotension (low blood pressure), other medications which also cause hypotension may produce an unwanted additive effect. Such drugs might include medicines used to treat high blood pressure, some antidepressants; some anti-psychotics, quinidine, procainamide, benzodiazepines such as diazepam (Valium) or opiates (e.g. morphine). Since alcohol also may intensify the blood pressure lowering effect of nitroglycerin, patients receiving nitroglycerin should be advised to drink alcoholic beverages with caution.
Ergot alkaloids (e.g. Cafergot) and Imitrex can oppose the vasodilatory actions of nitroglycerin and may precipitate angina. A similar effect can occur with ephedrine and the decongestants pseudoephedrine (Sudafed) and propanolamine.
PREGNANCY: Since most persons who use nitroglycerin are over 50 years of age, experience with the use of nitroglycerin during pregnancy is limited. Nitroglycerin can be used during pregnancy if in the judgment of the physician the potential benefits justify the potential (though unknown) risks to the fetus.
NURSING MOTHERS: It is not known if nitroglycerin is secreted in breast milk.
SIDE EFFECTS: A persistent, throbbing headache commonly occurs with nitroglycerin therapy. Aspirin, acetaminophen, or ibuprofen may be used to relieve the pain. Flushing of the head and neck can occur with nitroglycerin therapy as can an increase in heart rate or palpitations. This can be associated with a drop in blood pressure which can be accompanied by dizziness or weakness. To reduce the risk of low blood pressure, patients often are told to sit or lie down during and immediately after taking nitroglycerin
Originally posted by HockeyHorror
nitroglycerin,
also called GLYCERYL TRINITRATE, a powerful explosive and an important ingredient of most forms of dynamite. It is also used with nitrocellulose in some propellants, especially for rockets and missiles, and it is employed as a vasodilator in the easing of cardiac pain.
Pure nitroglycerin is a colourless, oily, somewhat toxic liquid having a sweet, burning taste. It was first prepared in 1846 by the Italian chemist Ascanio Sobrero by adding glycerol to a mixture of concentrated nitric and sulfuric acids. The hazards involved in preparing large quantities of nitroglycerin have been greatly reduced by widespread adoption of continuous nitration processes.Nitroglycerin, with the molecular formula C3H5(ONO2)3, has a high nitrogen content (18.5 percent) and contains sufficient oxygen atoms to oxidize the carbon and hydrogen atoms while nitrogen is being liberated, so that it is one of the most powerful explosives known. Detonation of nitroglycerin generates gases that would occupy more than 1,200 times the original volume at ordinary room temperature and pressure; moreover, the heat liberated raises the temperature to about 5,000 C (9,000 F). The overall effect is the instantaneous development of a pressure of 20,000 atmospheres; the resulting detonation wave moves at approximately 7,700 m per second (more than 17,000 miles/h). Nitroglycerin is extremely sensitive to shock and to rapid heating; it begins to decompose at 50 -60 C (122 -140 F) and explodes at 218 C (424 F).
The safe use of nitroglycerin as a blasting explosive became possible after the Swedish chemist Alfred Nobel developed dynamite in the 1860s by combining liquid nitroglycerin with an inert porous material such as charcoal or diatomaceous earth. Nitroglycerin plasticizes collodion (a form of nitrocellulose) to form blasting gelatin, a very powerful explosive. Nobel's discovery of this action led to the development of ballistite, the first double-base propellant and a precursor of cordite.
A serious problem in the use of nitroglycerin results from its high freezing point (13 C [55 F]) and the fact that the solid is even more shock-sensitive than the liquid. This disadvantage is overcome by using mixtures of nitroglycerin with other polynitrates; for example, a mixture of nitroglycerin and ethylene glycol dinitrate freezes at -29 C (-20 F).
Continuous nitroglycerin use leads to development of nitroglycerin tolerance and loss of effectiveness. Intravenous (iv) N-acetyl cysteine (NAC), during short-term studies of people receiving continuous nitroglycerin, was reported to reverse nitroglycerin tolerance.1 2 In a double-blind study of patients with unstable angina, transdermal nitroglycerin plus oral NAC (600 mg three times per day) was associated with fewer failures of medical treatment than placebo, NAC, or nitroglycerin alone. However, when combined with nitroglycerin use, NAC has led to intolerable headaches.3 4 In two double-blind, randomized trials of angina patients treated with transdermal nitroglycerin, oral NAC 200 mg or 400 mg three times per day failed to prevent nitroglycerin tolerance.5 6
Vitamin C may help maintain the blood vessel dilation response to nitroglycerin. A double-blind study found that individuals taking 2 grams of vitamin C three times per day did not tend to develop nitroglycerin tolerance over time compared to those taking placebo.7 In another controlled clinical trial, similar protection was achieved with 500 mg three times daily.8
People using long-acting nitroglycerin can avoid tolerance with a ten- to twelve-hour hour nitroglycerin-free period every day. People taking long-acting nitroglycerin should ask their prescribing doctor or pharmacist about preventing nitroglycerin tolerance.
Blood returning from the body in the veins must be pumped by the heart through the lungs and into the arteries against the high pressure in the arteries. In order to accomplish this work, the heart's muscle must produce and use energy ("fuel"馃槈. The production of energy requires oxygen. Angina pectoris (angina) or "heart pain" is due to an inadequate flow of blood (and oxygen) to the muscle of the heart. It is believed that all nitrates, including nitroglycerin, correct the imbalance between the flow of blood and oxygen to the heart and the work that the heart must do by dilating the arteries and veins in the body. Dilation of the veins reduces the amount of blood that returns to the heart that must be pumped . Dilation of the arteries lowers the pressure in the arteries against which the heart must pump. As a consequence, the heart works less and requires less blood and oxygen.
Additionally, in patients with angina, nitroglycerin preferentially dilates blood vessels that supply the areas of the heart where there is not enough oxygen, thereby delivering oxygen to the heart tissue that needs it most.
PRESCRIPTION: yes
GENERIC AVAILABLE: yes (for some dosage forms)
PREPARATIONS: extended-release capsules containing 2.5, 6.5, 9, or 13 mg; 2% ointment with tape for application; patches (or transdermal delivery systems) which deliver 0.1, 0.2, 0.3, 0.4, 0.6, or 0.8 mg of nitroglycerin per hour; buccal tablets containing 1, 2, or 3 mg of nitroglycerin in an extended-release formulation; a translingual spray which delivers 0.4 mg of nitroglycerin per spray; sublingual tablets containing 0.15 or 0.3mg.
STORAGE: All formulations should be kept at room temperature, 15-30掳C (59-86掳F). The sublingual tablets are especially susceptible to moisture. They should NOT be kept in bathrooms or kitchens because of the higher degrees of moisture there. Care should be taken to replace the sublingual tablets every six months.
PRESCRIBED FOR: Nitroglycerin is indicated for the acute treatment and prevention of angina.
DOSING: For the treatment of acute angina attacks or for acute prevention (i.e. immediately before encountering situations likely to bring on an anginal attack): one tablet is allowed to dissolve under the tongue or in the buccal pouch (between the cheek and gums), or one spray is given of the lingual spray. (Nitroglycerin for sublingual or buccal use as well as spray are rapidly absorbed from the lining of the mouth for immediate effects.) This may be repeated every 5 minutes as needed. If angina is not relieved after a total of 3 doses, the patient should be taken to a hospital or a physician should be contacted. If lingual spray is used, the canister of spray should not be shaken prior to use, and it should be sprayed onto or under the tongue and then the mouth closed.
For prevention of angina, ointment may be applied using special dose-measuring application papers provided with the ointment. The appropriate amount of ointment is squeezed as a thin layer onto the paper, and the paper is used to spread the ointment onto nonhairy area of skin. The ointment should not be allowed to come into contact with the hands so that there is no absorption from the hands. Transdermal patches also are used for prevention. Patches may be applied to any hairless site but should not be applied to areas with cuts or calluses. Firm pressure should be used over the patch to ensure contact with the skin. The patch should not be cut or trimmed . Patches are waterproof and should not be affected by showering or bathing. Capsules of long-acting nitroglycerin also are used for prevention. They usually are prescribed 2 to 3 times per day and are taken 1 to 2 hours after a meal.
DRUG INTERACTIONS: Since nitroglycerin can cause hypotension (low blood pressure), other medications which also cause hypotension may produce an unwanted additive effect. Such drugs might include medicines used to treat high blood pressure, some antidepressants; some anti-psychotics, quinidine, procainamide, benzodiazepines such as diazepam (Valium) or opiates (e.g. morphine). Since alcohol also may intensify the blood pressure lowering effect of nitroglycerin, patients receiving nitroglycerin should be advised to drink alcoholic beverages with caution.
Ergot alkaloids (e.g. Cafergot) and Imitrex can oppose the vasodilatory actions of nitroglycerin and may precipitate angina. A similar effect can occur with ephedrine and the decongestants pseudoephedrine (Sudafed) and propanolamine.
PREGNANCY: Since most persons who use nitroglycerin are over 50 years of age, experience with the use of nitroglycerin during pregnancy is limited. Nitroglycerin can be used during pregnancy if in the judgment of the physician the potential benefits justify the potential (though unknown) risks to the fetus.
NURSING MOTHERS: It is not known if nitroglycerin is secreted in breast milk.
SIDE EFFECTS: A persistent, throbbing headache commonly occurs with nitroglycerin therapy. Aspirin, acetaminophen, or ibuprofen may be used to relieve the pain. Flushing of the head and neck can occur with nitroglycerin therapy as can an increase in heart rate or palpitations. This can be associated with a drop in blood pressure which can be accompanied by dizziness or weakness. To reduce the risk of low blood pressure, patients often are told to sit or lie down during and immediately after taking nitroglycerin
nerd 2.6 Compartmental Models
We have seen that analytical solutions can be given for the voltage along a passive cable with uniform geometrical and electrical properties. If we want to apply the above results in order to describe the membrane potential along the dendritic tree of a neuron we face several problems. Even if we neglect `active' conductances formed by non-linear ion channels a dendritic tree is at most locally equivalent to an uniform cable. Numerous bifurcations and variations in diameter and electrical properties along the dendrite render it difficult to find a solution for the membrane potential analytically (Abbott et al., 1991).
Numerical treatment of partial differential equations such as the cable equation requires a discretization of the spatial variable. Hence, all derivatives with respect to spatial variables are approximated by the corresponding quotient of differences. Essentially we are led back to the discretized model of Fig. 2.16, that has been used as the starting point for the derivation of the cable equation. After the discretization we have a large system of ordinary differential equations for the membrane potential at the chosen discretization points as a function of time. This system of ordinary differential equations can be treated by standard numerical methods.
In order to solve for the membrane potential of a complex dendritic tree numerically, compartmental models are used that are the result of the above mentioned discretization (Bower and Beeman, 1995; Yamada et al., 1989; Ekeberg et al., 1991). The dendritic tree is divided into small cylindric compartments with an approximatively uniform membrane potential. Each compartment is characterized by its capacity and transversal conductivity. Adjacent compartments are coupled by the longitudinal resistance that are determined by their geometrical properties (cf. Fig. 2.19).
Figure 2.19: Multi-compartment neuron model. Dendritic compartments with membrane capacitance C and transversal resistance RT are coupled by a longitudinal resistance r = (RL + RL)/2. External input to compartment is denoted by I. Some or all compartments may also contain nonlinear ion channels (variable resistor in leftmost compartment).
Once numerical methods are used to solve for the membrane potential along the dendritic tree, some or all compartments can be equipped with nonlinear ion channels as well. In this way, effects of nonlinear integration of synaptic input can be studied (Mel, 1994). Apart from practical problems that arise from a growing complexity of the underlying differential equations, conceptual problems are related to a drastically increasing number of free parameters. The more so, since almost no experimental data regarding the distribution of any specific type of ion channel along the dendritic tree is available. To avoid these problems, all nonlinear ion channels responsible for generating spikes are usually lumped together at the soma and the dendritic tree is treated as a passive cable. For a review of the compartmental approach we refer the reader to the book of Bower and Beeman (Bower and Beeman, 1995). In the following we illustrate the compartmental approach by a model of a cerebellar granule cell.
2.6.0.1 A multi-compartment model of cerebellar granule cells
As an example for a realistic neuron model we discuss a model for cerebellar granule cells in turtle developed by Gabbiani and coworkers (Gabbiani et al., 1994). Granule cells are extremely numerous tiny neurons located in the lowest layer of the cerebellar cortex. These neurons are particularly interesting because they form the sole type of excitatory neuron of the whole cerebellar cortex (Ito, 1984).
Figure 2.20 shows a schematic representation of the granule cell model. It consists of a spherical soma and four cylindrical dendrites that are made up of two compartments each. There is a third compartment at the end of each dendrite, the dendritic bulb, that contains synapses with mossy fibers and Golgi cells.
Figure 2.20: Schematic representation of the granule cell model (not to scale). The model consists of a spherical soma (radius 5.0 m) and four cylindrical dendrites (diameter 1.2 m, length 88.1 m) made up of two compartments each. There is a third compartment at the end of each dendrite, the dendritic bulb, that contains synapses with mossy fibers (mf) and Golgi cells (GoC). The active ion channels are located at the soma. The dendrites are passive. The axon of the granule cell, which rises vertically towards the surface of the cerebellar cortex before it undergoes a T-shaped bifurcation, is not included in the model.
One of the major problems with multi-compartment models is the fact that the spatial distribution of ion channels along the surface of the neuron is almost completely unknown. In the present model it is therefore assumed for the sake of simplicity that all active ion channels are concentrated at the soma. The dendrites, on the other hand, are described as a passive cable.
The granule cell model contains a fast sodium current INa and a calcium-activated potassium current IK(Ca) that provide a major contribution for generating action potentials. There is also a high-voltage activated calcium current ICa(HVA) similar to the IL-current discussed in Section 2.3.4. Finally, there is a so-called delayed rectifying potassium current IKDR that also contributes to the rapid repolarization of the membrane after an action potential (Hille, 1992).
Cerebellar granule cells receive excitatory input from mossy fibers and inhibitory input from Golgi cells. Inhibitory input is conveyed by fast GABA-controlled ion channels with a conductance that is characterized by a bi-exponential decay; cf. Section . Excitatory synapses contain both fast AMPA and voltage-dependent NMDA-receptors. How these different types of synapse can be handled in the context of conductance-based neuron models has been explained in Section 2.4.
Figure 2.21 shows a simulation of the response of a granule cell to a series of excitatory and inhibitory spikes. The plots show the membrane potential measured at the soma as a function of time. The arrows indicate the arrival time of excitatory and inhibitory spikes, respectively. Figure 2.21A shows nicely how subsequent EPSPs add up almost linearly until the firing threshold is finally reached and an action potential is triggered. The response of the granule cell to inhibitory spikes is somewhat different. In Fig. 2.21B a similar scenario as in subfigure A is shown, but the excitatory input has been replaced by inhibitory spikes. It can be seen that the activation of inhibitory synapses does not have a huge impact on the membrane potential. The reason is that the reversal potential of the inhibitory postsynaptic current of about -75 mV is close to the resting potential of -68 mV. The major effect of inhibitory input therefore is a modification of the membrane conductivity and not so much of the membrane potential. This form of inhibition is also called `silent inhibition'.
Figure 2.21: Simulation of the response of a cerebellar granule cell to three subsequent excitatory (A) and inhibitory (B) spikes. The arrival time of each spike is indicated by an arrow. A. Excitatory postsynaptic potentials nicely sum up almost linearly until the firing threshold is reached and an action potential is fired. B. In granule cells the reversal potential of the inhibitory postsynaptic current is close to the resting potential. The effect of inhibitory spikes on the membrane potential is therefore almost negligible, though there is a significant modification of the membrane conductivity (`silent inhibition'馃槈.
A final example shows explicitly how the spatial structure of the neuron can influence the integration of synaptic input. Figure 2.22 shows the simulated response of the granule cell to an inhibitory action potential that is followed by a short burst of excitatory spikes. In Fig. 2.22A both excitation and inhibition arrive on the same dendrite. The delay between the arrival time of inhibitory and excitatory input is chosen so that inhibition is just strong enough to prevent the firing of an action potential. If, on the other hand, excitation and inhibition arrive on two different dendrites, then there will be an action potential although the timing of the input is precisely the same; cf. Fig. 2.22B. Hence, excitatory input can be suppressed more efficiently by inhibitory input if excitatory and inhibitory synapses are closely packed together.
This effect can be easily understood if we recall that the major effect of inhibitory input is an increase in the conductivity of the postsynaptic membrane. If the activated excitatory and inhibitory synapses are located close to each other on the same dendrite (cf. Fig. 2.22A), then the excitatory postsynaptic current is `shunted' by nearby ion channels that have been opened by the inhibitory input. If excitatory and inhibitory synapses, however, are located on opposite dendrites (cf. Fig. 2.22B), then the whole neuron acts as a `voltage divider'. The activation of an inhibitory synapse `clamps' the corresponding dendrite to the potassium reversal potential which is approximately equal to the resting potential. The excitatory input to the other dendrite results in a local depolarization of the membrane. The soma is located at the center of this voltage divider and its membrane potential is accordingly increased through the excitatory input.
The difference in the somatic membrane potential between the activation of excitatory and inhibitory synapses located on the same or on two different dendrites may decide whether a spike is triggered or not. In cerebellar granule cells this effect is not very prominent because these cells are small and electrotonically compact.