as used herein and in the claims , “ comprising ” means including the following elements but not excluding others . as used herein and in the claims , “ couple ” or “ connect ” refers to electrical coupling or connection either directly or indirectly via one or more electrical means unless otherwise stated . referring to fig1 , a simplified arterial network model of a human being according to one embodiment of the present invention is shown . the pulse waveform generated by the heart ( not shown ), also known as aortic pulse , first propagates along the aortic arch 20 . when it reached the bifurcation between aortic arch 20 and brachial artery 22 , part of the aortic pulse will propagate to the radial artery 24 via the brachial artery 22 and eventually measured by a sensor ( not shown ) placed near the radial artery 24 . on the other hand , the rest of the aortic pulse continues to propagate down to the thoracic aorta 26 and upper abdominal aorta 28 until it reaches the first reflection site 32 , which is the bifurcation between upper abdominal aorta 28 and renal arteries 30 . at the first reflection site 32 , part of the aortic pulse will be reflected back and reaches the radial artery 24 via upper abdominal aorta 28 , thoracic aorta 26 and brachial artery 22 ; whereas the remaining aortic pulse will continue to propagate down to the lower abdominal aorta 34 until it reaches the second reflection site 38 which is the bifurcation between lower abdominal aorta 34 and iliac arteries 36 . at the second reflection site 38 , part of the aortic pulse will be reflected back to the radial artery 24 via lower abdominal aorta 34 , upper abdominal aorta 28 , thoracic aorta 26 and brachial artery 22 ; whereas the remaining aortic pulse will continue to propagate down to the lower limbs of the human being . it should be noted that the pulse waveform measured by the sensor near the radial artery 24 , also known as radial pulse , includes three components : ( 1 ) originated from the heart and propagate directly to the radial artery 24 ; ( 2 ) reflected from the first reflection site 32 ; and ( 3 ) reflected from the second reflection site 38 . fig2 shows a typical radial pulse measured at the wrist of a human subject . mathematically , the aforesaid simplified arterial network model , which governs the relationship between the aortic pulse and the radial pulse , can be expressed by the equation ( 1 ). y ( t )= x ( t ) h ( t )= x ( t ) h 1 ( t )+ x ( t ) h 2 ( t )+ x ( t ) h 3 ( t ) ( 1 ) where y ( t ) is the radial pulse measured by the sensor , x ( t ) is the aortic pulse and h ( t ) is the impulse response of the arterial network . the impulse response h ( t ) further includes : ( 1 ) h 1 ( t ) which is the impulse response of the path from the aortic arch 20 directly to the radial artery 24 via the brachial artery 22 ; ( 2 ) h 2 ( t ) which is the impulse response of the path from aortic arch 20 to the first reflection site 32 and back to the radial artery 24 and ( 3 ) h 3 ( t ) which is the impulse response of the path from aortic arch 20 to the second reflection site 38 and back to the radial artery 24 . the method , according to one embodiment of the present invention , first constructs an approximated aortic pulse x ( t ) in the form of a gaussian function based on the inflexion point of the first rising phase of the radial pulse y ( t ). the inflexion point is characterized by its value b and the slope s . these two parameters are calculated by setting the second derivative of the radial pulse y ″( t ) to zero and substituting the corresponding result back to the radial pulse y ( t ) and the first derivative of the radial pulse y ′( t ) respectively . the general form of a gaussian function is expressed in the equation ( 2 ). the first derivative and the second derivative of the gaussian function are shown in equation ( 3 ) and equation ( 4 ) respectively . where a is the amplitude and b related to the width of the gaussian function in order to locate the inflexion point of a gaussian function , the second derivative of the gaussian function as shown in equation ( 4 ) is set to zero which yield the solution of t =− b or t = b . as such , the value and the slope at the inflexion point of the gaussian function , which are the same as that of the radial pulse , are determined by equation ( 5 ) and equation ( 6 ) respectively . based on the intermediate results of equation ( 5 ) and equation ( 6 ), the parameters a and b can be determined . by substituting the parameters a and b as shown in equation ( 5 ) and equation ( 6 ) back into equation ( 2 ), the approximated aortic pulse can be expressed as equation ( 7 ). the approximated aortic pulse x ( t ) obtained using equation ( 7 ) based on the radial pulse y ( t ) as shown in fig2 is shown in fig3 . where b is the value of the inflexion point of the first rising phase of the radial pulse y ( t ) and s is the slope of the same inflexion point . after obtaining the approximated aortic pulse x ( t ), the impulse response of the arterial network can be deconvoluted from the arterial network model as shown in equation ( 1 ). in matrix form , the arterial network model as shown in equation ( 1 ) can be rewritten as equation ( 8 ). however , it is impossible to find h directly as x is not invertible . according to one embodiment of the present invention , least square method as shown in equation ( 9 ) is used to obtain the impulse response h . the reconstructed impulse response obtained thereof based on the radial pulse as shown in fig2 and the approximated aortic pulse as shown in fig3 is shown in fig4 . where x t is the transpose of x and λ is a small number & gt ; 0 , for instance 0 . 1 . after obtaining the reconstructed impulse response h of the arterial network , segmentation is employed to identify the three segments : ( 1 ) originated from the heart ; ( 2 ) reflected from the first reflection site 32 ; and ( 3 ) reflected from the second reflection site 38 of the impulse response h . in one embodiment of the present invention , the segmentation is conducted based on the anatomy of a human being . the travelling time of a pulse from the heart to the thoracic aorta 26 , the upper abdominal aorta 28 , the lower abdominal aorta 34 and iliac arteries 36 are approximately 36 ms , 14 ms , 27 ms and 34 ms respectively . therefore the time delay between the peak of the first component of the radial pulse and the peak of the second component of the radial pulse is 100 ms ( i . e . the back and forth travelling time of the thoracic aorta 26 plus the back and forth travelling time of the upper abdominal aorta 28 is 2 ×( 36 ms 14 ms )= 100 ms ); whereas the time delay between the peak of the first component of the radial pulse and the peak of the third component of the radial pulse is 222 ms ( i . e . the back and forth travelling time of the thoracic aorta 26 plus the back and forth travelling time of the upper abdominal aorta 28 plus the back and forth travelling time of lower abdominal aorta 34 plus the back and forth travelling time of iliac arteries 36 is 2 ×( 36 ms 14 ms + 27 ms + 34 ms )= 222 ms ). based on the aforesaid time delays , the reconstructed impulse response h can be segmented in time domain into three segments , i . e . h 1 ( t ), h 2 ( t ) and h 3 ( t ). the end point of each segment is defined as the local minimum point of the impulse response h with a predefined time interval . the time interval is based on the aforesaid time delays plus certain tolerance . in this embodiment , the end points of the first segment h 1 ( t ) and the second segment h 2 ( t ) are defined as the local minimum point of the impulse response h within 50 - 150 ms and 170 - 270 ms respectively . the corresponding segmentation result of the impulse response as indicated in fig4 is shown in fig5 , which shows the first segment 40 ( from the start to 50 ms ), the second segment 42 ( from 50 ms to 210 ms ) and the third segment 44 ( beyond 210 ms ). it should be noticed that , the impulse response h 1 ( t ) is assumed to die down beyond the first segment 40 ( i . e . h 1 ( t )= 0 for t & gt ; 100 ms ); the impulse response h 2 ( t ) is zero in the first segment 40 and third segment 44 ( i . e . h 2 ( t )= 0 for 100 ms ≦ t & lt ; 444 ms ) and the impulse response h 3 ( t ) is zero in the first segment 40 and second segment 42 ( i . e . h 3 ( t )= 0 for t ≦ 444 ms ). with the first segment 40 , the second segment 42 and the third segment 44 of the impulse response , the radial pulse can then be decomposed into three components based on equation ( 1 ), wherein the first component , the second component and the third component are x ( t ) h 1 ( t ), x ( t ) h 2 ( t ) and x ( t ) h 3 ( t ) respectively . the corresponding decomposed components of the radial pulse as indicated in fig2 is shown in fig6 , which shows the first component 46 , second component 48 and third component 50 . the peak of the first component 46 , second component 48 and third component 50 are known as early systolic peak , late systolic peak and diastolic peak respectively . the arterial stiffness index is calculated as the ratio of the late systolic peak to the early systolic peak , i . e . the ratio of the peak of the second component 48 and that of the first component 46 . the arterial stiffness index is positively correlated with various diseases , for instance coronary artery diseases , myocardial infarction , heart failure , hypertension , stroke , diabetes mellitus , end - stage renal disease , hypercholesterolemia and inflammation . referring now to fig7 , an arterial stiffness index measuring device 52 according to one embodiment of the present invention is shown . the arterial stiffness index measuring device 52 is of a c - shape . at the bottom side of the cavity surrounded by the c - shape structure is an arm holder 54 . the arm holder 54 has a convex upper surface configured to accept a human arm during operation . on the other hand , an inflatable cuff 56 is disposed at the upper side of the same cavity . as shown in fig8 , there is a pressure sensor 58 disposed at the lower surface , which is the surface that would be in contact with the wrist 60 of the human subject during operation , of the cuff 56 thereby allowing the pressure sensor 58 to capture the radial pulse of human subject and transfer the same to the microprocessor 62 . the cuff 56 is also in connection with a pump 64 , which is controlled by the microprocessor 62 . the microprocessor 62 is further coupled to a non - transitory computer - readable storage medium 66 . the storage medium 66 is encoded with computer - readable instructions for causing the microprocessor 62 to execute the steps of the method of determining the stiffness index of an arterial network as stated above . during operation of the arterial stiffness index measuring device 52 , a person first puts his arm , with his palm facing upward , into the cavity of the arterial stiffness index measuring device 52 and rests on the arm holder 54 . the microprocessor 62 will then activate the pump 64 to inflate the cuff 56 . the pressure sensor 58 disposed with the cuff 56 is pushed against the radial artery of the person . the inflation process stops when a predefined pressure is achieved with the cuff 56 . subsequently , the pressure sensor 58 starts recording the radial pulse waveform and transfers the same to the microprocessor 62 . the storage medium 66 is encoded with computer - readable instructions for causing microprocessor 62 to calculate the arterial stiffness index based on the method as stated above . the exemplary embodiments of the present invention are thus fully described . although the description referred to particular embodiments and realizations , it will be clear to one skilled in the art that the present invention may be practiced with variation of these specific details . hence this invention should not be construed as limited to the embodiments set forth herein . for instance , although wrist is chosen as the measurement of the pulse waveform , it should be obvious to one skilled in the art to notice that other measurement sites , for instance neck and thigh , could also be adopted in order to measure the corresponding pulse waveform . it should also be notice that , depending on the measurement sites , different arterial model will be adopted accordingly . regarding the approximation of the aortic pulse , it is approximated to be a gaussian function in the above - mentioned embodiments . nonetheless , other bell shape functions , for instance log - normal and rayleigh , could also be used to approximate the aortic pulse . furthermore , the value and slope of the inflexion point of the first rising phase of the radial pulse are used as the basis in the approximation step . it should be clear to one skilled in the art that other methods can also be used . moreover , other features of the first rising phase of the pulse waveform can be used in the approximation step , for instance the slope and values of any two arbitrary points within the first rising phase of the pulse waveform . propagation time delays between components of the radial pulse are used in the segmentation of impulse response . however , the segmentation can be done by associating the impulse response segments with particular analytical functions and segmenting the impulse response accordingly . other methodologies , for instance curve fitting and principal component analysis , could also be adopted . the travelling time of a pulse from the heart to the thoracic aorta 26 , the upper abdominal aorta 28 , the lower abdominal aorta 34 and iliac arteries 36 used can be within 10 % of the above mentioned travelling time .
a method of determining stiffness index of an arterial network is disclosed . the method comprises the steps of : obtaining a pulse waveform related to the arterial network ; estimating a source pulse based on at least one predetermined feature of the pulse waveform ; determining a plurality of characteristics of the pulse waveform based on a relationship between the pulse waveform and the source pulse ; and calculating the stiffness index of the arterial network based on the plurality of characteristics of the pulse waveform . an arterial stiffness index measuring device employing the above methodology is also disclosed therein .