Invalidity of Using In Vitro Results to Substantiate In Vivo Overdosage Claims

Bryan J. Stephens, PhD

It is important to understand the order of magnitudes involved when it comes to applications in radiation. Far too often do people present generalizations without at least a relative scale. Even when printing graphs of data, people neglect the axis-labels, whether it be through a lack of units or the superposition of two plots that have different units. As such, these graphs lead to inaccurate conclusions about the point attempting to be made.

A prime example of such hand-waving arguments is the ubiquitous citation of the Arndt-Schulz law, which refers to “U” shaped dose response curves for external agents: below a threshold there is no effect, a small amount of something has small effect, a moderate amount has a large effect, and a large amount has either no effect or an adverse effect. This “law” was originally formulated in the world of pharmacology, has come in and out of favor several times, and now serves as one of the foundations of homeopathy. There is no doubt that there are issues relevant to laser therapy in which this idea applies; the creation of reactive oxygen species (ROS) or free-radicals is an obvious example. Radiation oncology takes special advantage of free-radicals as they are potent DNA breakers; in fact, the hydroxyl radical that comes as a by-product of ionized water accounts for about 2/3 of all radiation induced, mammalian DNA damage (1). In lower levels, however, ROS’s serve as cell-signal carriers as well as to induce an endogenous response that leads to an increased long-term defense capacity against exogenous radicals and other foreign toxins.

But, it is crucial to remember that this is not a “law” at all, nor is it based on fundamental principles or cellular processes, and so to claim that more than X amount of radiation is inhibitory because the Arndt-Schultz law says so, is completely unfounded.

Virtually all of the empirical investigations that attempt to narrow the optimal treatment parameters have been performed in vitro. These studies have the advantages that the majority of the parameters can be easily measured and well controlled, and many of the results of these experiments have indeed shown an optimal dose region for biostimulation above which inhibition takes place. There are, however, inherent limitations in extrapolating these results to conclusions on the effects in bulk tissue, as well as some fundamental shortcomings in the breadth of their investigations.

The first is simply the range of doses used and the a priori assumption that there is only one peak in the biostimulatory spectrum. Tiina Karu, among others, has shown this to be an invalid assumption, and that for a given cell line, there may be several peaks of similar biostimulatory effect separated by several orders of magnitude of doses (2). So the “U” shaped dose response curve cited by a particular study may illustrate only one of the several potential peaks in a curve, whose full range has not been measured.

The second major shortcoming of extrapolating in vitro results to in vivo conclusions is the idea that the reciprocity rule (i.e. the idea that the biological effect of treatment is directly proportional to the dose irrespective of the administration technique or treatment time), is simply not valid, in general. There have been several studies, even on the same cell line with the same laser that show that in different dose regions of the same response curve, the reciprocity rule is obeyed and broken (3). This speaks again to the idea that studies who claim this rule is strictly obeyed probably have not investigated the full dose domain.

When studies do attempt to explore the higher dose range, a third limitation presents itself; one of thermal accumulation. Whatever energy of radiation is absorbed in the monolayer of cells and the serum environment is converted to heat, and in a Petri dish thermal diffusivity is extremely low. Dose is defined as energy density and so the higher the dose, the more energy is absorbed, and thus the higher thermal accumulation. To get a real idea of what contribution this has to the cellular environment, lets do a very first-order thermodynamic calculation to see if higher doses even have a chance at biostimulation before creating thermal damage.

Imagine we are testing the viability of 100 J/cm² of 980 nm radiation on a monolayer of cells in a Petri dish (or more realistically, a multi-well plate) of 1.5 cm diameter. Standard radiobiology protocols suggest irradiation in nutrient-rich growth medium to simulate in vivo pH and temperature. An appropriate amount of serum for such a plate would be something on the order of 3.5 mL, which in this dish would rise to a 0.5 cm height above the cell layer. The absorption coefficient of water at this wavelength is 0.43 cm^-1(4), which means the percent of radiation absorbed in the first 0.5 cm is 19% (1-e^{-0.43 • 0.5}). The area of the plate is 7.1 cm² and our target dose is 100 J/cm² so we must expose the cells to a total energy of 710 Joules. (Note: Most studies do not account for the attenuation of the the serum, and so expose the dish to this amount of energy. This is a critical miscalculation, since this 19% beam loss is not at all insignificant. There is, however, a good deal of forward scatter of the beam that slightly compensates for the absorption loss, but this is a necessary calculation that is absent from virtually all published in vitro studies. For the sake of simplifying this example and maintaining a parallel comparison, we too will ignore this correction here.) So neglecting any absorption in proteins or chromophores in the solution or the cells, the culture will have absorbed 135 Joules of energy. Assuming the specific heat of water and serum are substantially equivalent (c__H2O=4.186 J/g C°) this would correspond to a temperature increase of 9.1° C (Q=mcΔT, where m is the mass of the water (density of water is 1 g/cm³ times 3.5 mL is 3.5 g), and Q is the heat energy absorbed in Joules).

Cell cultures are incubated at 37° C, again to mimic the body’s ambient, and so this would raise the cell culture to above 46° C. It is well known that bulk tissue can undergo irreversible tissue damage when raised above 40° C, never-mind in a monolayer of cells with only two degrees of freedom to dissipate heat. In fact, this thermal accumulation is often taken advantage of, and clinical hyperthermia is a increasingly popular technique in oncology. In hindsight then, to raise the cell culture to this threshold temperature, keeping all other parameters constant, only 44 Joules need be absorbed in that first half centimeter of serum, which means that we would expose only 230 Joules of energy to the dish, yielding a dose to the cells of 33 J/cm². With this first-order, high school physics calculation, we can see how testing any more than about 30 J/cm² of 980 nm beam of radiation on cell cultures will never yield positive results.

Remember this effect is simply an artifact of in vitro experimentation, where there is (intentionally) a lack of thermal diffusivity to maintain cell viability. The body, on the other hand, is very well suited to deal with both internal and external heat or cooling sources. After all, we live in environment that ranges from much cooler to marginally warmer than our internal temperature; we also have the ability to drink hot coffee or hold an ice cube in our mouths without experiencing hyper- or hypothermia. To properly simulate this effect in vitro some micro-fluidics designed to measure real-time temperature and simultaneously carry away heat would have to be employed.

In any case it is clear that while in vitro experimentation is highly necessary to isolate individual chromophore absorption characteristics and cellular mechanisms of action, the Petri dish environment is quite different from our bodies. This idea resonates throughout the entire biological community: the reaction of a macroscopic matrix of cells that form tissue is NOT the sum of the reactions of each of the individual cells. One of the great mysteries of biology involves the complexity of cell-cell signaling and the ubiquity of bystander effects. A prime example of this intrinsic communication is in radiation oncology where researchers have used X-ray needles (microscopically narrow beams of x-rays) to irradiate individual cells growing in a monolayer. Amazingly, cells far away from the irradiated region somehow received information from the irradiated cells and underwent apoptosis (programmed cell death) in a way that is characteristic of cells that absorbed the ionizing radiation (even though they didn’t). Accordingly, we have to narrow the scope of individual cell and single cell monolayer studies to the search for absorption sites and the cellular functions affected by these sites, and stay away from making broader tissue-scale generalizations.

1) Hall, E., Giaccia, A. J., 2006. Radiobiology for the Radiologist, 6th Edition. Lippincott Williams and Wilkins.

2) Karu, T.I., Pyatibrat, L.V., and Ryabykh, T.P. 1997. Nonmonotonic Behavior of the Dose Dependence of the Radiation Effect on Cells In Vitro Exposed to Pulsed Laser Radiation at 820 nm. Lasers Surg. Med. 21:485-492.

3)Karu, T., Tiphlova, O., Esealiev, R., and Letokhov, V. 1994. Two Different Mechanisms of Low-Intensity Laser Photobiological Effects on Escherichia coli. J. Photochem. Photobiol. B: Biol. 24, 155-161.

4)Hale, G.M. and Querry, M.R. 1973. Optical Constants of Water in the 200 nm to 200 µm Wavelength Region. Appl. Opt. 12:555-563.