Access to all articles, new health classes, discounts in our store, and more!
The Foundation Principles of Dental Cataphoresis
Read before the Second District Dental Society, January 1898. Published in Items of Interest.
* * *
The detailed, progressive, modifications of application of cataphoresis to the dental organs are determined by great underlying principles, which principles are determined by conditions. It is these conditions, many of which are widely variable, and their relation to the process which we shall consider in this paper.
The process consists essentially, and exclusively in the following discussion, in the medication of a tooth by means of an electric current, where an interposing medicament is used under the electrode, which is in contact with the tooth.
The perfection of the application requires the placing in the tissue to be anesthetized, of a sufficient quantity of the medicament for that purpose. The successful placing of that quantity depends upon the current flowing (amperes), and the conditions of the tissue receiving it. The quantity of current flowing is determined by the pain limit (taking it for granted that we have sufficient voltage for any case). Now on what does this pain limit depend, and to what extent do its limits vary?
Constant and Pulsating Currents
Before attempting to answer this question it is imperative that we distinguish between the actual pain limit of a tooth for a constant current and the pain limit for a current coming in pulsations. The former implies that the controller is capable of furnishing a current of such perfectly gradual increase of potential, that there will be no pulsations, not even the sudden increase of the five-hundred thousandth part of an ampere, as will be shown later, as required for a perfect instrument, for any case.
The latter, the pulsating current, implies that the controller, while apparently furnishing a perfectly gradually increasing current, is actually furnishing one in a series of steps. Probably steps too small to be detected with ordinary commercial instruments, but very easily detected by the pain organs of the tooth. The practical application of this point to instruments will be made later, but at present we will refer to the method in which this pulsating current establishes a pain limit. All nerve tissues are stimulated to carry impulses of their normal functions, by a variation in the current passing through them. The acuteness of the nerve to receive these stimuli depends largely upon its normal function, which in this particular case, is pain, and is infinitely more acute than that of most other nerves. It is the variations which produce these stimulations, and all who have used cataphoresis on these organs, have observed very closely resembling phenomena in the make and break simulations, with those of motor nerves.
For a more thorough consideration of the anelectrotonic and catelectrotonic stimulations of the nerves, reference can be made to any good work on physiology, or to a previous article by the author.
It is true, as has been abundantly established, that every healthy tooth has a definite pain limit for a perfectly constant current. I have been able to establish this frequently, to within the one hundred-thousandth of an ampere, for a variety of total differences of potential, compensating with additional resistance.
To answer this question as to what determines this pain limit, as also other questions we must consider, it becomes necessary for us to make many inquiries which must be answered from clinical data. For example, what are the approximate differences in different teeth? And in the same tooth under different conditions?
The following data, compiled from one hundred and fifty successive cases, has been of the highest importance to me, both for the successful application to the individual cases, and for making general deductions. You will note by the different columns that the amperage and voltage and resistance at both start and finish are given.
The tooth number corresponds with Allport’s system of beginning 0 number from the superior, right, third, molar. Of course the age of the patient, as given, is only a guess, and the time, as shown by remarks, is very often extended to permit of completing another operation. The resistances have been worked out, but have not been corrected for the counter polarization current. Resistances of liquid conductors cannot be measured absolutely, directly, as can metals, by the method we use; but the results, for our purposes, are quite as accurate as we require. In the following, the anode was a small platinum wire, twisted with cotton; and the cathode, two pads on the temples, of large size.
Averages of Results
Average pain limit (Mill. amps.), at start of first 50 cases = 0.245
Average voltage at start of first 50 cases = 8.51
Average resistance at start of first 50 cases = 34,730 ohms.
Average pain limit (Mill. amps.), at finish of first 50 cases = 0.482
Average voltage at finish of first 50 cases = 12.25
Average resistance at finish of first 50 cases = 25,410 ohms.
Average pain limit(Mill: amps.), at start of second 50 cases = 0.155
Average voltage at start of second 50 cases = 5.2
Average resistance at start of second 50 cases = 33,540 ohms.
Average pain limit (Mill. amps.)t at finish of second 50 cases = 0.406
Average voltage at finish of second 50 cases = 18
Average resistance at finish of second 50 cases = 42,330 ohms.
Minimum pain limit at start 0.01 mill. amp. or 1/100000 amperes. In 17 per cent the pain limit at start was less than 0.1 mill. amp. or 1/10000 amperes. No commercial Mill. amp. meter on the market at present would give a clear reading of these 17 cases.
From the foregoing clinical data we are able to make very valuable deductions, with which we can, in connection with the laws of electro-physics and electro-chemistry, explain and determine most of the phenomena of dental cataphoresis.
Deductions from Records
Some of these are as follows:
- The relation of the results to the amperage is in direct proportion in most cases; but not where the result desired is to anesthetize a part of the tooth which is of relatively high resistance as compared with other parts of the path, as for example, the margins of a cavity, where the center of it is near the pulp, or where removing the pulp from a root, where the lateral resistance through the root walls is less than through the apex.
- The results are not directly related to the resistance alone for if the pain limit will permit, this is overcome by an increase of voltage. There are some conditions, however, where the pain limit will not permit, for example, case 74.
- The time is usually in inverse proportion to the amperage. The exceptions are the same as in the first.
- There is not a definite relation between the time and the resistance, though very often they are in direct proportion, the reason for which will be shown later.
- There is not necessarily a relation between the extent of surface dentine exposed, and the time, though there is a very definite relation between the results, and the relative resistance through different parts of that surface.
- There is a constant relation between time and results.
- The pain limit is very widely variable.
- The resistance of teeth is markedly in direct proportion to the age of patient.
- The pain limit is usually in indirect proportion to the age of patient.
From these observations it becomes clearly evident that the same relation of conditions does not exist when working in the roots as when working in the cavity, where the pulp is not exposed, for there seems to be an almost constant relation between the results and current in the latter, but not at all in the former. Now the amperage, or quantity of current, flowing, is the expression of the pain limit, hence the pain limit, or its source, does not bear the same relation to our work in preparing a cavity as it does in removing the pulp from roots.
These facts led me to investigate the relative resistance through the root walls of teeth, and through their apical foramena. The results were very startling to me; as no doubt they may be to some of you. Note the difference in the resistance of teeth in and out of the mouth, though all the latter had been soaking for weeks in water containing a few drops of camphophenique, simply to sterilize. (See Chart 2 and 3.)
Chart 2
Chart 3–Resistances Through Moist Teeth to Mercury Bath, Voltage 20. External Resistance in Circuit, 2,700 Ohms.
Fresh Teeth Readings Taken Immediately After Extraction
Direction of Current Flow
From these readings it is clearly evident that we have been mistaken in our assumption that the current was mostly all going through the tip of the root. On the contrary, it is an entire uncertainty which way the current is going, through the apical foramen or through the walls of a root. This at once explains why so often when we are trying to anesthetize the last remnant of pulp from a root it takes so much longer time than we should expect. Of course the ratio of the current flowing laterally through the walls is to that flowing through the apical foramen, as the resistance of the latter is to the former and the same relation exists between the different roots, if more than one, which accounts for the fact that often we can remove the pulp from one root long before we can from the other. In this case, if you will pardon a suggestion outside of the subject, before proceeding plug up the root from which you first remove the pulp tissue with an insulator. I have carefully prepared a table of resistance through the various sizes of apical foramena, taken from actual cases and have compared them with those observed in various sized openings in a tip of a glass tube drawn to as near as possible the shape of a pulp chamber in a single rooted tooth. You will observe that the resistances are in good relation though higher in the tooth than in the glass tube, probably because in the former there are shreds of tissues which partially close the foramen. In any case except a young patient it would seem that the resistance is just as likely as not to be greater through the foramen than through, the walls of the root. (See Chart 4.)
Chart 4–Resistance Through Apical Foramena of Increasing Size. Voltage 20. External Resistance in Series, 2,700 Ohms.
These diameters were determined by placing in the opening to be measured, as through the apical foramen, a very fine, gradually tapering, steel broach, specially prepared, and measuring its diameter at point of contact. I have measured the resistances of many cases in the mouth by taking readings before drying for root filling, and then again filling the end of the root, and have, by associating these readings with the previous records of pain limit, and results in removing pulp tissue, come very forcibly to the conclusion that almost invariably the pain limit is determined in the apical foramen. The exceptions are easily distinguished, and easily explained. If this be so, it will account largely for the actual results of experience.
Physical Effects of Electricity
Just here, let us consider some of the physical effects of an electric current. One of these is the production of heat. From the law of the conservation of energy, we know that energy cannot be created or lost; hence the energy lost, as electric energy, by an electric current, in passing through a conductor, is not lost, but must change to an equivalent of some other kind of energy. In a metallic conductor the loss of electrical energy is practically all changed to heat. In fact, in any system of a homogeneous conductor, the heat generated by the passage of a current can be absolutely calculated by knowing two things, the fall of potential and the amperage, or the resistance and the amperage. In brief, it is expressed as follows: “The heat developed in a homogeneous portion of any circuit, is equal to the square of the current in the circuit multiplied by the resistance of that portion.” This is known as Joule’s law. It holds good for any homogeneous circuit, or for all parts that are homogeneous.
There are modifications of conditions which may enter to make the circuit non-homogeneous, as for example, the difference of potential between a metal and a liquid, or two liquids, or the chemical changes taking place. If a gas is evolved, of course heat is absorbed. The increase, in the system, of chemical energy which would demonstrate itself as a counter, or polarization, current of the electrolysis, is also to be subtracted to make an absolute calculation. For our present purpose these may be neglected as they will practically be proportional in the different parts.
Let us suppose a practical case. A single rooted tooth, for simplicity say a central incisor, with large meslo-proximal cavity, extending halfway to the pulp.
Heat Generated by Current
Suppose the milliampere meter reads 0.4 and voltage is 25. Then the resistance of the circuit is 62,500 ohms; neglecting the polarization current.
Let us suppose the resistance through the dentine from the cavity to the pulp is 10,000 ohms, and from the pulp to the tissue, around the tooth, 45,000 ohms, and from this point to the negative electrode 7,500 ohms. Suppose, for simplicity, that the resistance from the pulp through the root walls is equal to that through the apical foramen. Then the path of our current will be, provided our cavity is perfectly insulated, as follows: All of it through the cavity and dentine to the pulp, and thence one-half through the root walls and one-half through the apical foramen, and thence to the negative electrode. As the current leaves the pulp, it has two paths, whose combined resistance is 45,000 ohms. Since the combined resistance of any shunt is equal to the product of the individual resistances of the paths divided by their sum, then the resistance of each of these two paths must be 90,000 ohms. Now, applying Joule’s law to the various parts of this circuit, we have, the heat generated in the dentine between the cavity and pulp, represented as below; using the centi-gram-second system of units, which we shall use exclusively. This will require us to express our previous equation: Amperes2 X Ohms X .236 = Calories. (a2 X O X 0.236 = C.)
A calorie is the amount of heat required to raise one gramme of distilled water one degree centigrade.
Hence 0.00042 X 10,000 X 0.236 = calories of heat developed in 1 second in the dentine = 0.0003776. But one calorie is the amount of heat necessary to raise one cubic centimeter of distilled water, one degree centigrade, for 1 gramme = 1 cubic centimeter of distilled water at its maximum density (4° C.); therefore to express the actual rise of temperature in this part of the circuit, per second, we must determine the volume of matter heated, and express it in cubic centimeters, for the rise of temperature is in inverse ratio to the volume. We must also know the specific heat of the substance, for if the matter in question has a greater or less specific heat than water, it would experience a relatively less or greater change of temperature, from the same heat unit. As a matter of fact, the specific heat of blood is slightly less than that of water; 1 calorie would raise that amount of blood more than 1 degree C. Since the tissues we must consider are so variable and complicated, and since the error from this source will be comparatively small, we shall not complicate the consideration with this correction.
I have cut out a section of dentine corresponding as nearly as possible to that portion through which the current was passing in the case we are supposing, and found its volume to be 0.001727 C. Cm. This was determined by displacement in a small capillary tube. Applying this to our calculated heat developed, we get 0.0003776 X 580 = Rise of temperature in the dentine in 1 sec. in degrees centigrade = 0.219, and expressed in Fahrenheit, 0.394°.
If this elevation of temperature were quite evenly distributed through the dentine lying in the path of the current, it should not produce discomfort. As a matter of fact, however, it will not be evenly distributed for two reasons. The resistance through the different parts of the dentine will vary largely; and again the current is conveyed through the dentine by the contents of the dentinal tubes whose total cross sectional area, and also volume, is very much less than that of the lime salts. If these tubuli were all the same size and length, the heat would be relatively evenly distributed throughout the entire volume of dentine in the path, but the actual heat produced in any one of them would be much more than that we have calculated. If the volume of the conducting matter in the tubuli is relatively very much less than that of the dentine surrounding them, then the rise of temperature in them will be inversely greater, and in the ratio of their volumes.
The current is practically all conducted by the animal matter which constitutes 28 parts of normal dentine by weight. If the ratio of the specific volume of these two substances were the same as the ratio of their specific weights, we could substitute; but they are not. The specific weight of dentine, with animal matter extracted, is more than 20 per cent greater than that of animal matter. This will make the specific volume of the animal matter about 33 per cent in ordinary dentine. Now, if all the tubuli are helping alike to carry the current, that is, have the same size and length, then the rise of temperature in each one will be three times greater than we have calculated, or 0.657° C., or 1.182° F. This should not produce pain.
Let us proceed in the same way and determine the heat developed in the other parts of this circuit. In the body beyond the tooth the resistance is 7,500 ohms, and the amperage 0.0004. Then the total heat developed in this part of the circuit is 7,500 X 0.00042 X 0.236 = Calories = 0.00028. This quantity of heat is developed in very many times the unit of volume, 1 C. C. M., hence the rise of temperature will be relatively that much less.
As a matter of fact, by far the larger part of this resistance through the patient, is found in the external layers of the skin, which fact, associated with Joule’s law, explains why we get a tickling sensation on the point of contact of a constant current, and not a tickling throughout the circuit. This has nothing to do with the sensation felt from a pulsation of current as a make or break. If most of the total current flowing is passing through the skin, through one or more minute areas, as through a hair follicle, or from a small point of any kind, we should get a sensation with a very low amperage. Hence use just as large an indifferent electrode as possible, both to reduce the total resistance of the circuit, and to diminish the possibility of sensation at that point.
Let us now determine the heat generated by the passage of the current through the root walls. Through this path we have 0.0002 amperes of current flowing, and the resistance is 90,000 ohms. The total heat generated is 0.00022 X 90,000 X 0.236 Calories = 0.0008496.
If the volume in which this is developed is more or less than 1 C. Cm., the rise of temperature will be less or more than this number of degrees centigrade. The total volume of substance in the root walls is probably occasionally as great as one-half a C. Cm., though generally less. In a central of average size it is probably about one-fourth. It would be practically impossible to determine the relative volume of the conducting matter, and the non-conducting matter of the substance of the root walls, without an analysis, but we know that since the surface is so great, the concentration of heat will not be great enough in the individual tubuli to cause much rise of temperature, provided the tubuli are comparatively uniform in size and length, or in other words, of uniform conductivity.
Let us now determine the heat developed in the apical foramen in this case. It is 0.00022 X 90,000 X 0.236 Calories = 0.0008496. If this were in a substance whose volume was 1 C. Cm., and whose specific heat was the same as that of water, the elevation of temperature in one second would be the above number of degrees C. But the volume is very much less.
We will assume without considerable error that the specific heat of the contents of the apical foramen is the same as that of water. The next thing for us to determine is the volume of the conducting matter in the apical foramen, through which the resistance is 90,000 ohms, and express it in terms of the unit 1 C. Cm. of water. This is one of the most difficult considerations we have, but I think it can be done very approximately. First we must determine how far up the pulp tissue we must consider. By measuring the resistance through the apical foramen of a root, and then gradually cutting it back from the tip, making readings frequently, it is easy to determine the relative resistance of the different areas. This can also be done by enlarging the same foramen and noting the resistance of certain measured sizes of openings. In this way I have determined that in all cases where the pulp chamber suddenly contracts at the apex, as most canals do, the resistance is almost all in the last one-eighth or often one-twentieth of an inch. For this reason, in these considerations I have neglected. the resistance through pulp tissue, since relatively it is very small as compared with the other parts of the teeth. In the determination we are to make of this root, I have taken the tissue for about 3 millimeters. It is practically an impossibility to take the tissue from the root of one of these cases, and measure it; it must be done by other means. In order to use the same units which we have been using, the substance used instead of pulp tissue must have as nearly as possible the same specific weight as that tissue, and must be something we can handle. Since green hard wood and blood and water have so nearly the same specific weight, which means the same specific volume, we can substitute this substance for the pulp tissue, and still retain the same units, besides having something we can shape and handle.
From the table of observed resistances, I would say that to have 90,000 ohms resistance, the apical foramen would be about four-thousandths of an inch in diameter.
According to these requirements I have prepared from green applewood, as nearly as possible, facsimiles of the shape and volume of the tissue in various sized apical foramena. These being of the same specific weight as water, could by their weight express the volume of the tissue in question in C. Cm. For the absolute weight of these while green, I am entirely indebted to Dr. Miller, Professor of Physics of Case School of Applied Science. He was able to weigh them to within one-ten-thousandth part of a gram. These show that the weight of the tissue in question for the particular case which we are now considering, as nearly as I could prepare the specimen, was 0.21 milligrams, or since its specific volume is the same as that of water, approximately, its volume is 0.00021 C. Cm, Therefore the rise of temperature in this part of the path is 0.0008496 x 100000/21 = 4.04 degrees Centigrade, or 7.27° F. Of course the surrounding tissues would absorb heat more or less rapidly, but it is to be remembered that this quantity of heat is being liberated every second. It seems very convincing to me that it is at this point that the pain limit is determined in the case which we are considering, as indeed in most cases.
Relation of Heat to Pain Limit
Now let us imagine some modifications of this case. Suppose the resistance through the dentine is 1,000 ohms instead of 10,000. What will be the changes of phenomena? The resistance of the circuit will be 53,000 ohms. Very clearly the pain limit will not change, so the milliampere meter will read the same. Really the only difference it will make will be that it will require less voltage, which will be 21.3 instead of 25.
Suppose the resistance through the dentine be 100,000 ohms. This will mean that for the same pain limit the voltage would be 61. In this case the heat generated in the dentine would be 100,000 X 0.00042 X 0.236 calories, which, using the same conditions of cavity which we had before, would make a rise of temperature in the conducting medium of the dentine of 9.2° C., or 16.7° F. This would probably be almost the same concentration of heat which we had in the apex, and if the conducting tissue of the dentine were more sensitive than that at the apex, we would probably have the pain limit determined at this point. Now, suppose it is, and suppose you were able to increase the amperage to only 0.0003, what will be the effect of cutting out part of this dentine?
Of course it will lower the resistance of the circuit, but besides, if the pain limit is determined at this point, we will find by a new application, that the pain limit has raised. It is in this way that we are able frequently to determine just where the pain limit is being determined, as in case No. 5.
Suppose now the resistance through the walls of the root of this tooth were 200,000 ohms; then the combined resistance of this path and shunt would be (200,000 X 90,000) ÷ (200,000 + 90,000) = 62,060 ohms, and the resistance of the circuit would be 79.560. The pain limit would clearly be found at the same place, though to produce the same concentration of heat at that point, the total amperage would not be so great. The pain limit of that apex is 0.0002 amperes, and the current flowing through these two paths is in inverse proportion to their resistance, hence the current flowing through the walls will be 0.00009 amperes, and the total .00029. This will require a potential of 23 volts. Here we have lowered the voltage by increasing the resistance; an apparent absurdity, nevertheless it is true.
Again, let us suppose the same case, but with the resistance through the root walls only 10,000 ohms. In this case the resistance of this part of the path, the two way part, will be: 90,000 X 10,000 ÷ (90,000 + 10,000) = 9,000, and the total resistance of the circuit is 26,500.
The pain limit of the apex is constant at 0.0002 amperes, and therefore the current flowing through the walls is to 0.0002 as 90,000 is to 10,000, or is .0018. Then the total current flowing is 0.0018 + 0.0002 = 0.002 amperes, or 2 milliamperes, with a voltage of 53. This would undoubtedly produce pain in the dentine, and the pain limit would in this case be determined in the dentine. On cutting out a part of the dentine, and taking a new reading of the pain limit, we would find it proportionately changed. This condition would be hard to identify unless you undertook to remove the pulp from the root, when you would be very much chagrined and surprised at the incredible length of time required as compared with the amperage. I have measured cases in the mouth that had given just such trouble in removing the pulp from the apical end of the root, and found the resistance through the wet walls, after filling the apex, but slightly greater than the total resistance before drying the tip for filling. If time would permit, these same relations should be applied to two and three roots of teeth, and they would explain quite perfectly the clinical data.
While we have these relations fresh in our minds, let us review the observations made from the clinical data. (See page xxx.)
The last two observations are undoubtedly due to the diminished size of the apical foramen, and the increased proportion of organic matter in the tooth substance with age. This matter of the relation of the resistance in a circuit to the relation of two paths in some part of the same circuit, should be clearly understood by the operator before he can give his patient his best services. I would advise every student of cataphoresis to make a study of it, for it is a factor to be considered in almost every cataphoric operation made on the teeth. It can be found in any good work on electricity. A quite thorough discussion of it can be found in the report of the Ohio State Meeting of December, 1896, in the February number of the Ohio Journal, or in the February and April numbers of Cosmos, by the author. No such condition as obtains in the teeth is found in the medication of other tissues of the body by the same means. And for two reasons: A difference in the nature of the tissue, and a great difference in the nature of the circuit.
Let us now consider the forces at work in the process. Except at infinite dilution of the medicines the electric current will not entirely disturb the internal forces within and between the various mediums, consequently we must consider these as well as the new ones arising from the presence of the current. First, what are the physical conditions that exist under the circumstances which we are considering?
Physical Conditions in Cataphoresis
Beginning with the anode we have a conductor of the first class (a metal) in contact with a conductor of the second class (an electrolyte). This electrolyte is a solution of a compound substance which is in contact with another solution which has the same solvent the medicament is in, an aqueous solution, though different substances in solution. This second solution is also an electrolyte and is the contents of the dentinal tubes. The first electrolyte is also in contact with an insoluble porous partition, if you choose to call it such, the matrix of the dentine, which is composed chiefly of insoluble inorganic salts. This porous partition, as also the second solution, is in contact with other solutions of the tissues surrounding the tooth. Besides these we have an organic cell membrane within the interstices of the porous partition.
The forces at work between these various substances, without the presence of an electric current, are those existing between liquids containing different substances in solution, in different concentrations, with or without the same solvent, and those forces arising from potential differences existing between a metal and a liquid and between two liquids.
Taking these up separately we have first the potential difference ;existing between the metal and the first electrolyte, due to the solution pressure of the ions of that metal and the counter osmotic pressure of the ions of the compounds of that metal, if they exist, in the solution. These factors depend entirely upon the metal forming the anode and the solution. With gold or platinum and the cocaine solution this force would be infinitely slight and would not produce any considerable potential difference.
Osmosis
Between the electrolytes, viz., the cocaine solution in the cavity and the contents of the tubes we would have the forces existing between all solutions. Of these Osmosis is the chief, and the only one which we need to consider. It is that force exerted by any substance held in solution in its efforts to fill all possible space. Osmosis does not require to take place through a diaphragm or wall of some kind, it takes place in any solution of uneven concentration, and is that force which makes the concentration uniform throughout. If a partition is in the way it will try to go through it, but if that partition is impermeable to that substance, though not to the solvent, it will then pull the solvent through to it. This force is enormous. In fact it is identical with the force that would be exerted by that same substance, in the same space, in the gaseous condition, if the solvent were removed. Time forbids any suggestion as to its relations to the other forces. In the solutions which we are considering we have certainly different concentrations, and if there is no semipermeable membrane these substances held in solution will, by their efforts to equalize the concentration, diffuse each into the other solution. If there exists a membrane impermeable to them, but not to the solvent, they will try to draw the solvent of the other solution to them. As a matter of fact the cell tissue of these dentinal tubes have in their limiting membranes a membrane semipermeable to many solutions. This would not prevent the cocaine from entering, but would probably prevent some of the substances held in solution forming the contents of the cells, though not all. If all, then the cell would expand to take in water.
Between the cocaine solution and the solid substance of the dentine there would probably be a very slight potential difference, not a thousandth part of a volt, however, arising from the solution pressure of the ions of the latter in the former, forming, as between the metal and the first electrolyte, an electrical double layer. This force would be very slight.
Influence of Electric Current
Let us now consider the forces existing under the same conditions when an electric current is passing through them.
Since an electric current cannot pass through any conductor of the second class except by means of the movement of ponderable matter, we must consider this force.
In every solution the molecules of the dissolved substance are to a greater or less extent dissociated. These dissociation products contain electric changes, either positive or negative, but always the same quantity of each in the solution. During the passage of an electric current these ions are attracted toward their opposite sign, and, at the electrodes, give up their electric charges and combine with it if possible, if not, are liberated to react in the solution or are given off as gas. Exactly the same quantity of ions must be liberated at the two electrodes at the same time, otherwise there would result an accumulation of positive or negative electricity in the solution, which is an impossibility, the detailed reason for which time will not permit.
In all parts of the solution there will be a migration of ions toward their respective attraction, but the velocity of this migration will depend upon this ion itself, and the concentration of the solution, with increased concentration a decrease of velocity, though not of conductivity. If the concentration of the ion gets low around the electrode new ions are formed from the molecules in the solution. At infinite dilution the dissociation is complete. This varies for different substances, but for cocaine hydrochlorate in water is far greater than any solution we would use. Of course the difference of concentration of the particular ion will produce an osmotic pressure of this particular ion. Owing to the different migration velocities of ions, the amount going each way would not be equivalent at a particular point in cross section unless they had the same velocities, for example, K and NH4; K and Cl. or K and L. have almost identical velocities. These velocities are quite easily determined. Please note this, as I did not make it clear in a recent paper.
In brief, “The quantity of an electrolyte decomposed is directly in proportion to the quantity of electricity which passes through it; or, the rate at which a body is electrolyzed is proportional to the current strength.”
If the same current pass through different electrolytes the quantity of each ion evolved is proportional to its chemical equivalent. “The chemical equivalent is the weight of the radical of the ion in terms of the atom of hydrogen, divided by its valency.” Which is equivalent to saying that, “The number of electro-chemical equivalents evolved in a given time by the passage of any current through any electrolyte is equal to the number of units of electricity which pass through the electrolyte in the given time.”
From this we can determine the exact quantity of cocaine carried into the tooth by electrolysis. The formula for cocaine hydrochlorate is C19H27NO4HCl. The best authorities I have been able to get on this subject say that the Cl. forms the negative ion going to the positive pole, and the balance of the molecule forms the positive ion going to the negative pole. If there is no other substance in solution to help carry the current these must do it. We know the migration velocity of Cl; it is, at infinite dilution, 0.00069 cm. per sec. under a potential gradient of volt per cm. So far as I know the exact migration velocity of the other ion of cocaine hydrochlorate has not been determined until done by Prof. Morley for this paper. It can be approximately guessed from its size and constitution, though not accurately.
He finds it to be about one-tenth that of Cl or Na.
We can easily determine the quantity of the alkaloid that has actually started toward the negative pole, though we cannot absolutely determine just how far any portion of it has advanced without knowing its migration velocity. In order to decompose an exact equivalent of any substance it is necessary to send 96,540 coulombs of electricity through the circuit. This is known as the electro-chemical unit of electricity. To find the electro-chemical equivalent of hydrochlorate of cocaine we divide its molecular weight by its valency, giving us 369 grams decomposed by 96,540 coulombs. Suppose the current to be running for 30 minutes at 0.5 M.A. Then 369/96540 X 1800 X 5/10000 X 1000 = milligrams of cocaine, hydrochlorate decomposed, equals 3.43. Of this 3.11 milligrams has started toward the negative pole. This is a sufficient quantity to anaesthetize a considerable tissue, and especially in this nascent condition.
What are the other forces existing in this system during the passage of the current? The osmosis of the undissociated molecules has practically not been disturbed. The differences of potential between the.electrode and the electrolyte has been changed or increased, as also between the electrolytes, and between the first electrolyte and the matrix of the dentine. This is probably the point of greatest interest of this paper. This we spoke of a few minutes ago as the electrical double sheet. It is produced by ions going off from a substance, the dentine in this case, into the solution by their own solution pressure. The substance they leave becomes negatively charged toward the substance they go to. Equilibrium is only established when the solution pressure of the ions is equaled by the electrostatic force thus set up. This is the electrical double sheet. Suppose a partition of clay, or better, unglazed earthen, with a solution on each side and an electrical current, is passed, what takes place? In most cases a movement toward the negative pole, though not always. Remember the solution is positive towards the substance from whence came these ions, and since the increase of positive charge to the liquid, the theory is that the substance of the porous partition, on account of the unbalanced electric charges, attracts the nearest film of the substance, and in this way drags it through the interstices in the form of a simple current. The measure of the result is determined by the quantity of current and the nature of the solution and partition. This is true electrical endosmose.
Question: To what extent does it occur in the process of cataphoresis as applied to the dental organs? We should say in passing that it is this electrical double sheet and its effect on the surface tension that produces the phenomena which we observe when we place a globule of mercury between the electrodes in a sulphuric acid solution. The extent of this electrical double sheet is determined largely by the specific resistance of the solution, and in fact is in direct proportion to it. The nature and especially the minute structure of the partition have a great deal to do with it.
Experimental Tests for Osmosis and Electrolysis
An experimental test is the simplest way to make the determination required for the answering of the question just asked. If we select a substance of about the same resistance as the cocaine solutions used, and of very delicate test, we should with great thoroughness be able to come to some conclusions. For this purpose I have made a great many quantitative tests using as early as possible the same conditions as exist in the actual operation. To give an infinitely greater surface of dentine for the porous partition, I placed the solution within the pulp chamber and root canals after hermetically sealing the apical foramen. The teeth themselves were placed through cards of gutta percha, and the cavity perfectly separated from any possible connection with the outside solution, which was distilled water. The first solution used was sodium iodide and tests made frequently by the flame test for the sodium which appeared at the cathode in about ten minutes. Various concentrations and lengths of time were given and the solutions very carefully tested for iodine, and even after two hours none could be found. But the question arose, did any of the sodium go through, or did it come out of the tooth? To obviate this question a substance was selected that did not exist in the tooth, namely, lithium, and which has a very delicate test. Lithium iodide was used in many cases, in every one of which the lithium was more or less pronounced in accordance with the time. In 30 minutes it was very marked, and in 2 hours profuse. In no case could a trace of iodine be found. I had Prof. Morley, ex-president of the American Association for the Advancement of Science, repeat the tests, and he said he knew there was not the one ten-thousandth part of a gram of iodine came through, for he could not find a trace. He made a quantitative test. He detected the lithium by means of the spectroscope, and was unqualified in his assertion that the lithium got there by electrolysis. In fact, it arrived there at the time calculated from its migration velocity by electrolysis.
The question now arises, why should we not be assisted by this force of electric endosmose? For several reasons. The dentine contains tubes to be sure, but they are not open so a current can flow through them. If the solution passed through them it would have to penetrate the limiting membranes of the cell, which is a slow process. It might be suggested that it could go between the cells and tube walls, but the total cross sectional area of the intercellular spaces exposed in a cavity would be extremely small. Another great factor is the specific resistance of the solution which does not favor it.
As a matter of fact the phenomena of electrical endosmose are very often chiefly the result of the forces of osmosis acting naturally upon the products of electrolysis, or of cyclical chemical processes in connection with electrolysis, as for example, the particles of carbon or many other substances in a solution. The carbon particles are insoluble, of course, but they are conductors of the first class, and when the current is passing it goes through them because they have less resistance than the solution. But where a current is passing from the surface of a conductor of the first class to a conductor of the second class, there must be either of two things, a liberation of the ion as gas, or it must unite with the electrode, or in a compound reaction with the substances of the solution. In this way the carbon particles enter into a compound molecule which later is broken up by dissociation, the carbon becoming a part of a positive ion, and is hurried along toward the negative pole. On its way it meets a positive ion for which it has a greater affinity than the electric charge carrying it, and it again forms a new compound, which if insoluble is left suspended in the solution. In this ionic form it could penetrate cell tissue or anything else that contained an electrolyte and be deposited.
Gentlemen, I regret the length of this paper, for I had hoped to have time to make some practical conclusions. This is really just the preface to the subject. In behalf of the needs and absolute requirements for the most successful application of this process, I appeal to the manufacturers for better apparatus. There is not delicacy or accuracy enough in our milliampere meters. We must have them reading to 1 milliampere in hundredths. Mine reads to hundredths of millionths of amperes; hundredths of thousandths of amperes will do for practical work. The controllers are yet far from what the sensitiveness of some teeth, to pulsations of current, demand.