here we illustrate the design process using our rowstim(iii ) system with 4 channels of electrical stimulation ( quads + hamstrings ) as described in .
the rowing machine used was based on the fixed stretcher concept 2 model ( d ) ergometer.the fes rowing subject rg and co - author was 57yrs , 75 kg male , 1.72 m height with a t4 ais ( a ) injury sustained 11 years previously .
the data was acquired in 2012 and rg started fes rowing in 2003 and has maintained 2 - 3 30 min sessions per week since then . following an initial 10 minute warm - up the subject was asked to row as hard as he could for approximately 20 strokes .
the normal foot stretchers were replaced by cantilevers attached to two floor mounted or6 - 7 force plates as shown in fig 1(a ) .
kinematic and force data was acquired using a vicon12 mx camera system running nexus software .
the next step was to develop a beam model scaled to the tibial dimensions of rg .
stress distribution was calculated across the tibial bone model , assuming the tibia was fixed at the knee joint and forces were applied at the distal end of the tibia ( i.e. a cantilever ) .
capozza et al ( 2008 ) . calculated , the periosteal perimeter , cortical thickness and second moment of inertia ( in the longitudinal , lateral - medial and anterior - posterior axis ) from 18 pqct scans of the entire tibia at intervals equivalent to 5% of the bone s length .
this data was combined with lateral , compressive and bending forces obtained from fes rowing , to calculate the stress along the tibial bone .
the perimeter of each pqct slice was used to calculate the external radius . using the values for cortical thickness
the area of each section was obtained by assuming a hollow cylinder . to calculate the total stress we used standard moment and stress equations , i.e. 

 where rout is the outer radius , ilm and ipa are the second moment of inertia in the lateral - medial and posterior - anterior axes respectively and
we then applied the frost threshold stress mesm , i.e. bone s genetically determined modeling threshold strain range , in and above which modeling usually turns on to strengthen a bone . where mesm , 10001500 microstrain ; ~20 mpa , or ~2 kg / mm .
the fringing occurring at the edge of the threshold is an artefact due to the graphical colour interpolation and has no physical significance .
the biomechanical calculation of joint contact forces , as shown in figure 1(b ) , exceed the 1.5 times body weight threshold proposed in dudley - javoroski s , shields rk ( 2008 ) .
however , these plots not indicate how the loading is distributed throughout the bones such that regions of osteogenesis can be predicted .
figure 2 is a typical single frame taken from a movie at the point of peak force and viewed from one perspective .
matlab software was written to enable 3d rotation to facilitate visual analysis . in this example
, it is revealed that in no regions are unsafe levels of stress applied and that the frost mesm threshold is exceeded in an extensive region of the tibia where one might expect osteogenesis
. it also reveals regions that are under stressed such as the distal region and the posterior plateau .
nb : here the cross sectional tibial measurements were obtained from healthy subjects . to the author s knowledge
it is therefore possible that some of these measurements such as the thickness of the cortical bone and moment of inertia , would change in sci subjects  this is an area where further radiographic studies are required to determine a model sci tibia .
the analysis was based simple beam theory using a point load applied to the distal tibia constrained as a cantilever so deflections , forces and boundary conditions are approximations .
the actual stress patterns illustrated can only be regarded as approximations but should be indicative of gross distributions and trends . however , at this stage the analysis presented here serves mainly to illustrate the proposed design technique .
for example , in addition to the quadriceps , during the drive phase , it was expected that stimulating the ankle plantar flexors , in phase with the quadriceps during drive would extend distally the region that is above the mesm threshold 20mpa . however , in practice , figure 4 illustrates that this was not the case , with our beam model in which the ankle joint was simplified , however , the above threshold region around the condyle was extended , indicating that stresses in the distal tibia are similar the 4-ch fes case and a little more widely distributed in the proximal region .
for example , electrically stimulating the hip extensors or changing the rowing style ( e.g. the coordination between handle force and seat position during the drive phase ) or the type of rowing ergometer used , e.g. floating versus fixed stretcher types . at each step in the design process
the above stress analysis is performed and compared with alternatives to check progress towards a solution .
thus relatively few subjects would be involved in finding a solution that provides the best distribution of stress .
this would support the follow on clinical trials , involving larger groups of subjects , to validate the predictions .
the personalized beam model may be extended to other bones that are compromised by osteoporosis .
the beam model is computationally very efficient providing results in the order seconds on a windows i7 pc .
the present beam model may underestimate the ankle region , due to the tibia , ankle joint and foot being represented by a single cantilever - this we plan to improve .
the stress distribution modelling may be further extended , with greatly increased computation time , by using a finite - element model derived from high resolution pqct scans .
the stress distribution model may be improved by adjusting thresholds that better predict actual clinical scan data and further extended by including a porosity stage that may provide a deeper understanding of the basic mechano - transduction , poroelastic fluid low and cellular signaling .
the proposed technique may also be extended using simulated force data derived from biomechanical models of the therapeutic activity  in this case it may even be possible to design and evaluate a candidate fes bone therapy in - silico prior to clinical trials .
this is illustrated in figure 5 where the bi - lateral force actions of the gluteus maximus muscles were biomechanically simulated and added to the quadriceps actions during the drive phase .
these modest changes due to additional extensors . to demonstrate a more dramatic change in distribution
we simulates a floating stretcher type rower by putting the acceleration of the center of mass of the upper body to zero ( figure 6 ) .
in conclusion , the approach appears to offer a quantitative design tool and method to assess potential bone therapy benefits for fes assisted exercise activity .
 fes assisted activities such as standing , walking , cycling and rowing induce forces within the leg bones and have been proposed to reduce osteoporosis in spinal cord injury ( sci ) . 
 however , details of the applied mechanical stimulus for osteogenesis is often not reported . 
 typically , comparisons of bone density results are made after costly and time consuming clinical trials . 
 these studies have produced inconsistent results and are subject to sample size variations . 
 here we propose a design process that may be used to predict the clinical outcome based on biomechanical simulation and mechano - biology . 
 this method may allow candidate therapies to be optimized and quantitatively compared . to illustrate the approach we have used data obtained from a rower with complete paraplegia using the rowstim ( iii ) system . 
Material and Methods
Results and Discussion