Post History

There is no question Tunica albuginea being the one and foremost load-bearing structure both during the erection and under tension applied by PE maneuvers. There have been debates all over the boards concerning loading in a relation to the tensile strength characteristics of the tunica.

What we did know for a very long time is that the ultimate tensile strength had to be significantly high.
Literature supporting the idea as well, anecdotal findings from the hangers using extreme weights telling the same story.
Where on the stress-strain curve of the connective tissue we operate has been misunderstood by the PE community. Many of the known theories and practices aiming for the plastic region which unfortunately has shown to be false thinking.

There has been very rarely scientific research made for studying the TA, and the one often used as a reference (1990) has flaws in the testing protocols.
The elastic modulus suggested does not convince as it seems to be in conflict with the suggested ultimate tensile strength. It has been doubted in the literature a few times already.
A recent study published in 2019 sheds a light on the subject in a better way than any of the former studies.

And this time as it has been produced under the leadership of the engineering group, not by the medical scientists the testing procedures have taken into consideration the genuine characteristics of the material at hand.
It not only verifies the load strain relation at the magnitude we are operating but shares valuable info within.
Almost all the research for the tendons and ligaments has been conducted with stress levels at magnitude or two excessive, with strain rates high enough to tear the glans out of their place.

This time the approach is different as the stress level is well in our application range.
The study reveals few things which do confirm the findings we have made in our own experiments.
It does reveal the tunica albuginea E- modulus for the elastic region for being 32.9 MPa.

Another great piece of information is the confirmation for the stress level at the start of the elastic region to be 0,17 MPa. I will later show you what this means for load adjustment.
It also reveals the tunica albuginea stress relaxation properties, showing the tissue having 20% of relaxation in a relatively short time after the static load has been applied and the tissue fixed at static position.
We have already found the level of loading as we have been plotting the load-strain curves on our own.
The study does not only confirm the stress-strain curve being correct, but it also signifies the loads’ found by the simplified trial being straight on the spot.

Strain3.PNG
Focus on the threshold points, the absolute strain measured differently to the study.

TURNING THE RESEARCH INTO APPLICATION

The study reveals the stress levels at important thresholds, both the start and the exit of the heel region aka starting point of the elastic region. This is the area we are operating as we only slightly reach into the elastic region. Also known as a proportional region.

The study does not reveal the tensile strength of the TA, but rightfully so we don´t need such a piece of information either.
The research shows us the threshold tissue stress levels which are pointed out in megapascals (MPa), which can be transformed equaling N/mm^2.
The elastic region starting at 0.17 MPa (N/mm^2. )

For getting the force readings we would need to find out the cross-sectional area of the load-bearing element. This element being tunica albuginea.
I went to lengths for finding out how to estimate the tunica cross-sectional area as correctly as possible.

Then I got into the idea of modeling the penis cross-sectional area for the purpose.

Based on a theory of the penis circumference and the TA having a correlating relationship, I went looking for the cross-sectional pictures of the penis.
There were tens of histological, pathological examination cuts, histological slice pics available.
Pictures of the septum not apparent were only included as it best presents the weakest portion of the shaft when stretched longitudinally. The septum having significant openings at the distal end of the penis, this should be the place for the circumference measurements as well.

Importing these pictures into a CAD application I was able to draw the boundaries to be used for 3D- modeling of the cross-section of the penis. Having the models made in 3 - 5:1 scale should minimize the systemic error as some of the boundaries between TA and Buck´s fascia were hard to separate.
With these now available 3D models, it was easy to inspect the accurate cross-sectional areas and the circumference dimensions. 25 models were produced but only 22 were included in the further analysis with excel.
The data shows to be quite uniform and as theorized there can be seen a relatively cohesive correlation with small enough standard error.

The relation between the cross-sectional area of the shaft and the cross-sectional area of the TA is presented as a coefficient a.
The relation between outer circumference and the tunica outer boundary is presented as a coefficient c.
The relation between outer circumference and the TA cross-sectional area is presented as a coefficient d.
The relation of TA circumference and the TA cross-sectional area is presented as a coefficient e.

The most correlating relation was found with the coefficient c.
The circumferences correlating stunningly with an average factor of 1.3±0.02.
Having such uniform data and minuscule standard error it would be an easy case if there were accurate enough data available on tunica thickness.

There is only a handful of research prevailing the data, only one of them showing a decent amount of data points.
Combining all the available info showing average thickness of 2.4,2.4, 2.4, 1.4, and 1.5 mm,
we end up having an average of 2.05±0.9 mm TA thickness for calculations.

The second-best coefficient being coefficient a, with an average factor of 5.83±0.21.
Using these two as an example I went to calculate the cross-sectional area of my TA.
The results were amazingly cohesive with the load-strain curve plotted in action.
The threshold points were spot on as I have found the intersection of the heel to the elastic region being at 3.2-3.5 kg of load, the calculation with the 0.17 MPa resulted in 3.4 ±0.7 kg.

As an informative cross-checking value further solved calculation resulted in 2.13 mm TA thickness for the cross-sectional area based on the coefficient a, divided with the TA circumference based on coefficient c.
This again makes the numbers more trusted as the cross-checking resulting such realistic numbers.
Using the research-based TA thickness with a coefficient c rooted TA circumference it yields out 0.17 MPa stress equal of 3.3 ±1.5 kg.
The load is spot on, but the inaccurate data of tunica thickness produces a significantly bigger absolute error.

With the E modulus of 32.9 MPa, we will end up in a situation where we will need to increase the stress from the 0.17 MPa to 0.5 MPa for having 1 % additional strain at the elastic region.
This equals for flaccid 120mm circumference-based TA cross-sectional area resulting in load increment from 3.4kg to 9.9 kg. Such a significant increase in loading means that as the TA is not purely elastic the visco-elastic properties adding the time aspect into the play.

I have not yet trialed, but I would estimate a minimum of an additional 30 to 60 minutes stretching needed the additional 1% to occur. For getting through the toe and heel regions we need 30 minutes of 1- 3.4 kg incremental loading before the elastic region stretch to even start.
It does not sound tempting as the same amount of strain can be achieved with deep heat application by no more than 3.5 kg load in 20 minutes.

The research prompted the further developed load calculator to be used as a tool for determining the threshold loads.
The newest research supports the use of loads at the verge of the elastic region as there is evidence enough the tissue does not need to be affected with either the stress or strain capable of causing microdamage.
The slow strain rate, low load applications will produce permanent gains with a low as possible structural damage.

There is no plastic zone, no plastic region available for us. Neither it is not even needed.

All ballistic, fast strain rate applications are just plain lunacy, fighting against everything known from tissue elongation.

Research, Data analysis, and a load calculator are included in the attachments.

There is no question Tunica albuginea being the one and foremost load-bearing structure both during the erection and under tension applied by PE maneuvers. There have been debates all over the boards concerning loading in a relation to the tensile strength characteristics of the tunica.

What we did know for a very long time is that the ultimate tensile strength had to be significantly high.
Literature supporting the idea as well, anecdotal findings from the hangers using extreme weights telling the same story.
Where on the stress-strain curve of the connective tissue we operate has been misunderstood by the PE community. Many of the known theories and practices aiming for the plastic region which unfortunately has shown to be false thinking.

There has been very rarely scientific research made for studying the TA, and the one often used as a reference (1990) has flaws in the testing protocols.
The elastic modulus suggested does not convince as it seems to be in conflict with the suggested ultimate tensile strength. It has been doubted in the literature a few times already.
A recent study published in 2019 sheds a light on the subject in a better way than any of the former studies.

And this time as it has been produced under the leadership of the engineering group, not by the medical scientists the testing procedures have taken into consideration the genuine characteristics of the material at hand.
It not only verifies the load strain relation at the magnitude we are operating but shares valuable info within.
Almost all the research for the tendons and ligaments has been conducted with stress levels at magnitude or two excessive, with strain rates high enough to tear the glans out of their place.

This time the approach is different as the stress level is well in our application range.
The study reveals few things which do confirm the findings we have made in our own experiments.
It does reveal the tunica albuginea E- modulus for the elastic region for being 32.9 MPa.

Another great piece of information is the confirmation for the stress level at the start of the elastic region to be 0,17 MPa. I will later show you what this means for load adjustment.
It also reveals the tunica albuginea stress relaxation properties, showing the tissue having 20% of relaxation in a relatively short time after the static load has been applied and the tissue fixed at static position.
We have already found the level of loading as we have been plotting the load-strain curves on our own.
The study does not only confirm the stress-strain curve being correct, but it also signifies the loads’ found by the simplified trial being straight on the spot.

Strain3.PNG
Focus on the threshold points, the absolute strain measured differently to the study.

TURNING THE RESEARCH INTO APPLICATION

The study reveals the stress levels at important thresholds, both the start and the exit of the heel region aka starting point of the elastic region. This is the area we are operating as we only slightly reach into the elastic region. Also known as a proportional region.

The study does not reveal the tensile strength of the TA, but rightfully so we don´t need such a piece of information either.
The research shows us the threshold tissue stress levels which are pointed out in megapascals (MPa), which can be transformed equaling N/mm^2.
The elastic region starting at 0.17 MPa (N/mm^2. )

For getting the force readings we would need to find out the cross-sectional area of the load-bearing element. This element being tunica albuginea.
I went to lengths for finding out how to estimate the tunica cross-sectional area as correctly as possible.

Then I got into the idea of modeling the penis cross-sectional area for the purpose.

Based on a theory of the penis circumference and the TA having a correlating relationship, I went looking for the cross-sectional pictures of the penis.
There were tens of histological, pathological examination cuts, histological slice pics available.
Pictures of the septum not apparent were only included as it best presents the weakest portion of the shaft when stretched longitudinally. The septum having significant openings at the distal end of the penis, this should be the place for the circumference measurements as well.

Importing these pictures into a CAD application I was able to draw the boundaries to be used for 3D- modeling of the cross-section of the penis. Having the models made in 3 - 5:1 scale should minimize the systemic error as some of the boundaries between TA and Buck´s fascia were hard to separate.
With these now available 3D models, it was easy to inspect the accurate cross-sectional areas and the circumference dimensions. 25 models were produced but only 22 were included in the further analysis with excel.
The data shows to be quite uniform and as theorized there can be seen a relatively cohesive correlation with small enough standard error.

The relation between the cross-sectional area of the shaft and the cross-sectional area of the TA is presented as a coefficient a.
The relation between outer circumference and the tunica outer boundary is presented as a coefficient c.
The relation between outer circumference and the TA cross-sectional area is presented as a coefficient d.
The relation of TA circumference and the TA cross-sectional area is presented as a coefficient e.

The most correlating relation was found with the coefficient c.
The circumferences correlating stunningly with an average factor of 1.3±0.02.
Having such uniform data and minuscule standard error it would be an easy case if there were accurate enough data available on tunica thickness.

There is only a handful of research prevailing the data, only one of them showing a decent amount of data points.
Combining all the available info showing average thickness of 2.4,2.4, 2.4, 1.4, and 1.5 mm,
we end up having an average of 2.05±0.9 mm TA thickness for calculations.

The second-best coefficient being coefficient a, with an average factor of 5.83±0.21.
Using these two as an example I went to calculate the cross-sectional area of my TA.
The results were amazingly cohesive with the load-strain curve plotted in action.
The threshold points were spot on as I have found the intersection of the heel to the elastic region being at 3.2-3.5 kg of load, the calculation with the 0.17 MPa resulted in 3.4 ±0.7 kg.

As an informative cross-checking value further solved calculation resulted in 2.13 mm TA thickness for the cross-sectional area based on the coefficient a, divided with the TA circumference based on coefficient c.
This again makes the numbers more trusted as the cross-checking resulting such realistic numbers.
Using the research-based TA thickness with a coefficient c rooted TA circumference it yields out 0.17 MPa stress equal of 3.3 ±1.5 kg.
The load is spot on, but the inaccurate data of tunica thickness produces a significantly bigger absolute error.

With the E modulus of 32.9 MPa, we will end up in a situation where we will need to increase the stress from the 0.17 MPa to 0.5 MPa for having 1 % additional strain at the elastic region.
This equals for flaccid 120mm circumference-based TA cross-sectional area resulting in load increment from 3.4kg to 9.9 kg. Such a significant increase in loading means that as the TA is not purely elastic the visco-elastic properties adding the time aspect into the play.

I have not yet trialed, but I would estimate a minimum of an additional 30 to 60 minutes stretching needed the additional 1% to occur. For getting through the toe and heel regions we need 30 minutes of 1- 3.4 kg incremental loading before the elastic region stretch to even start.
It does not sound tempting as the same amount of strain can be achieved with deep heat application by no more than 3.5 kg load in 20 minutes.

The research prompted the further developed load calculator to be used as a tool for determining the threshold loads.
The newest research supports the use of loads at the verge of the elastic region as there is evidence enough the tissue needs to be affected with neither the stress nor strain capable of causing microdamage.
The slow strain rate, low load applications will produce permanent gains with a low as possible structural damage.

There is no plastic zone, no plastic region available for us. Neither it is not even needed.

All ballistic, fast strain rate applications are just plain lunacy, fighting against everything known from tissue elongation.

Research, Data analysis, and a load calculator are included in the attachments.