# A New Calculation Model for Laser Therapy

How to obtain more accurate dosage emission, energy density and time of treatment values considering the laser beam volumetric energy distribution.

**Abstract**

**Background and purpose**. In laser acupuncture, a Low Level Laser Therapy (LLLT), low power lasers (mainly between 1 to 500 mW) are generally applied against skin to stimulate acupuncture points. To calculate the energy level given to a targeted point, a traditional calculation model for an irradiated surface is used. Because acupuncture points are not plane areas and most of them are below skin surface, the purpose of this article is to propose a more accurate calculation model to determine dosage emission, received energy density and treatment time for three-dimensional embedded targets.

**Methods**. In this paper, it will be demonstrated, by mathematical conceptualizations and visual representations, how and why the current calculation model is inaccurate for laser stimulation of targets under skin surface*. *Then, a new calculation model will be proposed to establish dosage emission (emitted energy), received energy density and treatment time according to residual energy (after energy losses) inside the beam generated volume comprising the targeted point. An application for this volumetric (new) calculation model will then be demonstrated using a clinical example and obtained values will be compared to those of the traditional model.

**Results**. According to the new calculation model, in some conditions, dosage emission reommendations per point are close to traditional recommendations (1 to 10 joules), and in other conditions, they are significantly increased, very close to some recent recommendations (ref. 1) based on clinical observations and research (over 100 Joules per point) without breaking the current Arndt-Shultz law therapeutic window applied to LLLT.

**Contributions.** Additionally, there will be a discussion on energy densities traditional recommendations for LLLT therapeutic window according to Arndt-Shultz’s law and on how the volumetric calculation model could be use to review them. To this extent, the volumetric calculation model could help set more accurate energy density recommendations and effective modulations (frequencies, type of emission, etc.) from research data and proposed protocols.

**Conclusion**. Overall, it will be demonstrated how the volumetric calculation model allows us to get outside of general, nonspecific and unreliable traditional recommendations. It leads us toward more accurate energy density recommendations and personalized dosage emission and treatment time values for a specific chosen laser.

**Key Indexing Terms **: laser therapy, traditional and volumetric calculation model, dosage, treatment time, beam volumetric energy distribution, residual energy, energy density.

**Issues with the traditional calculation model for embedded targets**

First off, the beam progression to get through matter and reach its target, is determine by the employed laser technical values (section: The fundamentals for an improved calculation model) and the treated region absorbance. This gives a singular aspect to the beam and its distributed energy is designated, in this paper, as the **Beam Volumetric Energy Distribution **(BVED). The BVED generates an irradiated **Volume** (V) in which laser energy is distributed. The value of distributed energy on its corresponding irradiated volume is equal to the **Volumetric Energy Density** (VED) received by every cubic unit composing the irradiated volume, including the targeted point (Figure 2). Therefore, because the traditional calculation model uses an irradiated surface **Area** (A) value instead** **of an irradiated volume (V) one, **it doesn’t aknowledge **the **Beam** **Volumetric** (true) **Energy Distribution** (Figure 1).

Thus, from a units point of view, the mishandling of **Surface Energy Density **(SED)used in the traditional calculation model, can easily be deducted as it should be a volumetric one. The latter takes into account the real three-dimensional aspect of an embedded target being irritated by a beam/light needle (Figure 2). Thereby, the traditional calculation model lets us establish stimulation dosage and time of treatment only from a **Surface Energy Density** **recommendation** while, ideally, **it should be from a volumetric one**. A method of conversion, when applicable, is proposed in Annexe -section “Conversion of Surface Energy Density (SED) into Volumetric Energy Density (VED) ”.

Also, parameters, such as **reflection, dissipation, refraction and absorption,** that could interfere with the energy distribution, as the beam travels to the point, are not included in the traditional calculation model. Thus, when the traditional calculation model perceives the target received energy as equivalent to total emitted energy, it is false because **Energy Losses** and the **Beam Volumetric Energy Distribution **to reach the target location, are **unconsidered** (Figure 1). Issues arising from this false assumption are further demonstrated in Table II of section *“ *Example with an acupuncture point stimulation and results*”* and explained in “Analysis and interpretation of results”, using tangible comparative examples.

# T**he three fundamentals for an improved calculation model**: the **Volumetric Energy Density** (VED), the **Volume** (V) and the **Residual Power** (P residual).

An improved calculation model would have to take into account the Beam Volumetric Energy Distribution (BVED) and its corresponding **Volume** (V) and **Volumetric Energy Density** (VED) for the whole irradiation light beam* *volume comprising the target. No matter its dimension or location within the known light beam volume, the target will receive a more genuine VED. To consider the effect of volume variation on time of treatment and dosage, the enhanced equation should take into account of some laser technical values as **beam divergence**, **aperture dimension**, and the chosen wavelength **penetration depth** (Figure 2).

Ideally, an even better model would also include most of the behavior of light — **reflection, refraction, energy dissipation**, etc. — while it dives into matter; here being biological tissues. This would allow to measure and consider the **Residual Power (P residual) **needed for the determination (Annexe II -Equation 2.2) of the (true) **Received Energy** by the irradiated volume and leading ultimately to** **the** Volumetric Energy Density** received by the embedded target.(Figure 2)

Aforementioned, the traditional calculation model is maladapted to a three-dimensional reality; which characterizes a laser beam and an a targeted point by nature. Currently, most of dosage recommendations (ref. 2) are based on old assumptions arising from the traditional calculation model misconceptions. Therefore, because these are general recommendations and non specific to the employed laser technical values, they are unreliable to address the real tree-dimensional aspects of embedded targets stimulations. A new calculation model comprising new fundamentals, as discussed above, should, at least, be used to review and corroborate validate the community current accepted laser treatment recommendations: working with **Volumetric Energy Densities** will allow users to **properly compare**, with a common and **reliable measurement unit**, stimulations between different employed lasers.

Furthermore, a new calculation model will also enable effective isolation, observation and comparison of other variables/modulations effects such as type of emission (continuous, pulse or superpulse) and frequencies regarding a specific energy density. Hopefully, it will lead to setup **new energy density recommendations** and **significant modulations** to effectively and truly simulate an acupuncture point as our mind conceives it (section: Determination of more accurate energy density recommendations and effective modulations).

# A Comprehensive Visual Summary

**Example with an acupuncture point stimulation and results**

*Please consult the full text and see sections on the corresponding terms for more details on them and Annexe I-III for their related equations. See *volumetric calculation model template* for easy calculations on the web site stephanbott.com

**Analysis and interpretation of results**

Using the volumetric calculation model to obtain an initial energy density recommendation of 1J/*cm² *at acupuncture point *Spleen 9*, the dosage and irradiation time values are both **6,45 times greater** than those coming from the traditional calculation model. These differences are, obviously, consequent on the inclusion of the beam volumetric energy distribution self-generated volume and the residual power value in the volumetric calculation model.

According to** Arndt-Schulz’s law**, while low doses stimulate, moderate doses inhibit and high doses kill. Following this same law, in Low Level Laser Therapy (LLLT), one standard therapeutic window of recommended Surface Energy Densities (SED) sets is **limits between 1 J/cm² and 10 J/cm²**

**to observe cellular bio-stimulation**(ref. 3). Therefore, according to this therapeutic window, it is possible to emit 10

*Joules*on a surface and still observe a bio-activation (section: Determination of more accurate energy density recommendations and effective modulations). Overpassed this energy density, bio-inhibition (physiological processes declination) is predicted.

Traditionally,emitted dosage recommendations values seems to match those for LLLT recommended SED presented above. For example, recommendations to stimulate an ear located acupuncture point are between 0,5 to 1 *Joules*. Whereas, larger regions, like *Spleen 9*, have average recommendations generally varying between 3 *J/pt *and* 10 J/pt*, depending on the author’s clinical recommendations (ref. 4). An acupuncture point dimension is approximated, by most practitioners, to 1 *cm²*. This is why, some authors give dosage recommendations, without distinction, in dose per point and/or energy per *cm² *; thus matching emitted dosage recommendations to recommended energy densities.

Matching recommended surface energy density values to those of emitted dosage, when treating a flat surface of 1*cm²*, makes some sense when a same seize aperture is directly applied against it and it is stimulated with a short range laser (Figure 1). Though, when treating a embedded three-dimensional acupuncture point, considering the beam volume energy distribution and energy losses, this shortcut cannot be taken without the risk of creating inaccuracies and major uncertainties (section: Issues with the traditional calculation model for embedded targets).

For example, targeting *Spleen 9* point with the **maximum** Arndt-Shulz’s law therapeutic window limit value of 10 *J/cm² *(SED) will generate a maximum dosage emission of **10 Joules**, as conceived by the traditional calculation model and traditional recommendations. Using the same laser, when converting this surface energy density (SED) value into a volumetric one (VED), with the volumetric calculation model, a dosage emission of

**204**is obtained. This dosage value is

*Joules***20 times greater**than the one expected with the traditional calculation model to attain the same energy density recommendation of 10

*J*/

*cm².*Thus, theoretically, according to the volumetric model, a

*Spleen 9*bio-stimulation will be observed even with a 204

*J*dosage for the laser in use.

To sum up, according to the volumetric calculation model and the laser used in the example, a dosage emission between 6,45 *J* and 204 *J***,** corresponds to initial recommended Energy Density variation from 1 *J*/*cm² *to 10 *J*/*cm²*, satisfying the used Arndt-Schulz’s law LLLT therapeutic window limits.

# Determination of more accurate energy density recommendations and effective modulations

The volumetric calculation model was tested with energy densities from a given **Arndt-Schulz’s law LLLT therapeutic window**. It seems that this particular therapeutic window was first elaborated from the studies of skin diseases treated by laser irradiation (ref. 5) . Thus, its given values are the closest to reliable surface energy density (SED) values as conceived by the standard equation since they are actually **from surface treatment studies**; they can be converted in Volumetric Energy Density (VED) to be used in the cubic equation. This is why this particular therapeutic window (between 1 *J*/*cm² and 10* *J*/*cm²*) was chosen, among others for LLLT, to test the cubic equation as presented in this document.

The most recent SED recommendations address a variety of specific conditions or treated regions, but they mainly concern acupuncture point at deeper level into the body. Thus, as mentioned in the previous section *,* “**energy per point**” or “**per cm²** ” are more likely, in this situation, to be

**equivalent to an initial emitted energy**before it enters and distributes itself in a considerable irradiated volume

**than to a true energy density.**Therefore, assuming that laser emitted energy (ex: dose per point, per

*cm²*), in those studies, truly equals a received energy density recommendation is false because energy losses and the beam volumetric energy distribution are not considered. This is why, we cannot take their “delivered doses” or “energy densities” and convert them into volumetric energy densities:

**they are unreliable surface energy density values**.

This issue brings out our first question: If energy losses and the Beam Volumetric Energy Distribution would had been aknowledged in these studies, what would have been their resultant (true) therapeutic window limits ?

Here is another reflexion that we might have : if there a specific therapeutic window when considering the three — dimensional apsects of a laser acupuncture stimulation, is that window the same for every type of emission and frequency in use ? In other words : is the total energy given to the cell the only condition to a succesfull biostimulation or is the way that the cell is receiving the energy (type of emission, frequency, etc.) also affecting the cell stimulation and changes the therapeutic window ? Some laser manufacturers like *BioFlex, RJ* and *Weber lasers*, among others, suggest variations of protocols, within the settings of their lasers, that are considering some of those possible modulations. But so far, no new therapeutic windows for Volumetric Energy Densities are suggested by those builders to support their findings and to compare efficiently research data among themselves.

To answer these questions, one solution would be to take any the given protocols or data along with their employed laser basic parameters (aperture dimension, penetration depth, beam divergence and laser power) and put them in the volumetric calculation model (Annex II -Equation 2.5 or with the previous link to template) and see what energy densities would come out of it. By doing that, **it would be possible to obtain and compare accurate different energy density values** for these protocols and maybe find that there is truly **specific therapeutic windows for different kind of treated conditions.** Also, it will allow **to efficiently isolate and observe the effects of variables/modulations such as types of emission and frequencies **for an identical initial energy density recommendation**. **This is how the low level laser therapy community could extracts informations from empirical data with the theoretical volumetric calculation model and create new improved recommendations in terms of energy density and other modulations needed to stimulate efficiently a targeted point for a specific health condition.

**Conclusion**

Nowadays, the use of lasers is exponentially spreading to almost every field of science and healthcare services. Following this ongoing expansion and progress, it is imperative to, at some point in time, revisit and/or upgrade its fundamentals. In low level laser therapy (LLLT), the traditional calculation model guiding us to irradiation settings for an embedded target should thus be reviewed for more accuracy, efficiency and safety.

Herein, we demonstrated the volumetric calculation model leads to more precise dosage emission, time of treatment and energy density values. To be applied and thus establish more refined and personalized recommendations for a targeted point stimulation, this calculation model requires the laser in use basic parameters: beam divergence, laser power, aperture dimension, wavelength penetration depth.

It is important to remind here, that, because of dosage emission and time of treatment variations are correlated to the specificity of the the laser in used laser basic parameters, universal dosage recommendations (emitted energy) charts applicable to all lasers are unreliable. **The volumetric calculation model has to be taken as a new way to get outside of inappropriate, general and nonspecific emitted dosage recommendations and thus, leading to more accurate and personalized dosage emission values for the laser in use and the desired stimulation** (recommended energy density). Thus, in some conditions, dosage emission recommendations per point are close to traditional recommendations (1 to 10 joules), and in other conditions, they (emitted energy) are significantly increased, over 100 Joules per point without breaking the current Arndt-Shultz law applied to laser therapy.

In conclusion, we now have a new calculation model to help us understand, interpret and compare properly results obtained by research and clinical observations. This volumetric calculaton model will allow efficient information extraction from published clinical and research data and thus promote a more profound understanding of LLLT treatments.

Hopefully, **this work will help the LLLT community improve the therapeutic window of recommended energy densities and effective modulations to attain optimal treatment results** for all sorts of health conditions.

**References**

1. **WEBER, M**., *Medical Low-Level-Lasertherapy- Foundations and clinical application*, First Edition, 2014, 423 pages, (p.262)

2. **WEBER, M., Kreisel,V**., *Laser Acupuncture* *successful treatment concepts*, Fuchtenbusch Verlag, 2012, 311 pages, (p.22)

3. **TUNER, J., HODE, L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.514)

4. **WEBER, M., Kreisel,V**., *Laser Acupuncture* *successful treatment concepts*, Fuchtenbusch Verlag, 2012, 311 pages. (p.63–68). **RJ-laser co**, *Therapy Refenrence Book, A practicale Guideline*, RJ-laser, 2012, 168 pages, (p.18–20)

5. **TUNER, J., HODE,** **L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.514).

# Annex I

# Annex II

# Annex III

# Annex IV

# Annex V

**Annexes references**

1. **TUNER, J., HODE, L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.537)

2. **TUNER, J., HODE, L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.121)

3. **TUNER, J., HODE, L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.510).

4. **TUNER, J., HODE, L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.119).

5. **TUNER, J., HODE, L**., *The New Laser Therapy Hanbook*, Prima Books, 2010, 847 pages, (p.118). **WEBER, M**., *Medical Low-Level-Lasertherapy- Foundations and clinical application*, First Edition, 2014, 423 pages., (p.256)22