Urodynamic Model of the Lower Urinary Tract

Transcription

1 Urodynamc Model of the Lower Urnary Tract A. Sorano Payá, J. M. García Chamzo, F. Ibarra Pcó, F. Macá Pérez Depto. Tecnología Informátca y Computacón, Unversdad de Alcante, Apdo. 99, E-38 Alcante, Span Abstract. In ths artcle we present a model of the lower urnary tract wth the am of a better understandng of how t functons. Based on urodynamc measurements (ntravescal pressure, detrusor pressure, abdomnal pressure and electromyography of the external sphncter) we have de veloped a model based on artfcal neuronal networks, n partcular we have used an Ortogonal Assocatve Memory. Wth ths model we can study the behavor of the lower urnary tract. The answers obtaned from the model durng the smulaton, as well as the urodynamc curves used, ft those of a human beng. The objectve s that the results of ths study permt an mprovement of dagnostc technques and processng, as well as the development of possble prosthess. 1. Introducton The Lower Urnary Tract (LUT) s a system made up of the urnary bladder, the external sphncter and the urethra [1-2]. The bladder s a chamber of non-strated muscle, known as detrusor muscle, made up of two parts: the body and the vescal neck, the latter made up of a muscle known as the nternal sphncter. The urethra, whch crosses the urogental daphragm, contans a layer of strated muscle known as the external sphncter. Ths muscle s under voluntary control and s the man cause of contnence and mcturton. The LUT s one of the few parts of the human body whch s nfluenced by both the voluntary and nvoluntary nervous system. Ths s one of the characterstcs whch makes t so complex. It s manly controlled by the upper centers of mcturton stuated above the protuberance, and whch act as on-off swtches, ndcatng whether the system s n the fllng phase (storage) or n the emptyng phase [3-4]. The act of mcturton s the emsson of urne stored n the bladder to the exteror through the urethra. Ths result s the vescal receptors' answer to tenson above a threshold whch oscllates between 5 and 15 cm of H 2 O and depends on a spnobulbospnal reflex whch passes through the protuberance [3-4]. The man varable whch ntervenes n the LUT s the nervous sgnal whch passes through the pelvc nerves, pudendal nerves and hypogastrc nerves, amongst others. However, n order to gan a better understandng of the workngs of the system t s also necessary to measure other varables. Fgure 1 shows the dynamcs of the system's curves durng the fllng and emptyng phases, and where we can see the exstence of non-lnearty and the two phases of the system. The exstence of coordnaton between the ntravescal pressure and the nervous sgnal whch acts on the external sphncter permts voluntary control of the act of mcturton. As the ntravescal pressure ncreases, ntally due to the nput of urne, the nervous sgnal from the external sphncter ncreases wth the am of mantanng the urne n the bladder. When the mcturton process begns, a clear coordnaton between the external sphncter and the detrusor

2 s observed, n the way that the nervous sgnal from the external sphncter practcally reduces to zero, whlst the nervous sgnal from the detrusor ncreases consderably, beng ths fact that whch provokes the expulson of urne from the bladder to the urethra, and from there to the exteror. Input Flow entrada Q I Intravescal Pressure P Abdomnal Pressure P a Detrusor Pressure P d Output Flow Qs Internal Sphncter Electromyography esfínter nterno External Sphncter Electromyography EMGe EMG ee Detrusor Electromyography EMGd Tme Fgure 1. System varables. The LUT s a non-lnear multvarable dynamc system varant n tme and subjected to nternal alteratons (convulsons, dsfunctons, nfectons, etc.) and external alteratons (coughng, sneezng, exercse, lstenng to runnng water, fear, cold, etc.). Moreover, untl now ts control has not been able to be descrbed by means of control theores based on a strong mathematcal foundaton, manly due to: The data obtaned from the process s ncomplete, or mprecse. Most of the nformaton about the process s avalable n qualtatve form. There s not a complete mathematcal model of the process whch we wsh to control. Despte the fact that ths system has been studed for a long tme, researchers do not agree on the way t works. Dfferent models [5-1] have been proposed based on mechancal propertes, or on neural propertes, but wthout contemplatng all of the system's aspects and, n many cases, adjustng the parameters manually. Due to the system's characterstcs we are gong to propose a model whch uses urodynamc measurements, snce they are the most well-known at the moment, treatng the system as a black box [11] n the sense that when faced wth nput data t gves an answer. The model wll be based on neural networks, snce they are a tool whch adapts well to ths type of system [12-14] n havng a hgh tolerance to faults, low senstvty to nose and ease wth modelng non-lnear functons. In partcular, the neural network whch we are gong to use n our model s an Ortogonal Assocatve Memory (OAM) [15].

3 2. Urodynamc model The pressure exerted by the external sphncter s that whch allows urne to pass to the exteror, or not. Ths pressure bascally depends on the detrusor pressure, the abdomnal pressure and the desre to mcturate, the latter manly provoked by the ntravescal pressure (detrusor pressure added to abdomnal pressure). If we dentfy whch s the non-lnear temporal functon that controls the external sphncter pressure, startng from the detrusor pressure and the abdomnal pressure, we wll have obtaned a model of the dynamc behavor of the LUT. In order to esteem ths functon we are gong to use a neuron network OAM whch wll have the detrusor pressure and the abdomnal pressure as nput and the external sphncter pressure as output. Moreover, n order to better esteem the temporal functon, we are gong to feed the system back wth certan outputs from the system employed as nputs. Therefore, we are gong to assume that the LUT s lke a black box whch receves nputs and generates outputs, and that the content of ts nteror s an unknown non-lnear system, but adapts to an expresson whch posesses the followng form, pe te ( τ 1 te td ta ) = f ( pe( τ ), pd( τ ), pa( τ )) (1) where: pe(t) s the external sphncter pressure (output), pd(t) s the detrusor pressure (nput), pa(t) s the abdomnal pressure (nput), f(...) s the unknown non-lnear functon to be esteemed by the OAM, te τ group of values of the external sphncter pressure of sze te td τ group of values of the detrusor pressure of sze td ta τ group of values of the abdomnal pressure of sze ta The model whch esteems the non-lnear temporal functon whch allows us to obtan the external sphncter pressure from the detrusor pressure, the abdomnal pressure and the external sphncter pressure wll have the structure shown n fgure 2. pd(t) pa(t) z z -td+1 z z -ta+1 Neural Network z pe(t ) z -te+1 pe(t) z -te z -2te+1 OAM Fgure 2. Structure of the network. The OAM s based on the use of ortogonal matrxes and on the establshment of ntermedate assocatons between the nput and output patterns of the system [15]. The man

4 advantages of the OAM are ts large storage capacty and ts hgh tolerance to nose. The tranng phase of the OAM conssts of obtanng two synaptc weghted matrxes T T W = f A) f ( Q ) and V = f Q) f ( B ) (2), (3) 1 ( 2 2 ( 1 where the matrx A are the nput patterns, the matrx B are the output patterns, the ntermedate matrx Q s an ortogonal matrx of the Householder matrx type [16], the functon f 1 (...) s a classc bpolar flter and the functon f 2 (...) s another bpolar flter dependent on the ortogonal matrx used. The recognton of an unknown pattern a s drectly obtaned through the equaton T b = f f ( f ( a ) W) ) (4) 1( 2 1 V As can be observed n the prevous defnton, t s not necessary to terate as n other models, makng the tranng and recognton phases rapd. Moreover, n usng ortogonal matrxes, both overlappng and the possble nose whch mght be present n the nput and output patterns are consderably reduced. 3. Smulaton In order to obtan the model, we have frst developed a pressure curve generator of patents. Below, we have used the aforementoned curves to tran the OAM. Fnally, to valdate the model, we have made the OAM nfer output curves from artfcally generated nput curves. The curve generator s a smulator of acceptable artfcal curves of detrusor pressure, abdomnal pressure and external sphncter pressure (t depends on the nervous sgnal whch acts on the external sphncter), meanng that ther values are wthn the possble levels of a human beng [1]. The values of the external sphncter pressure curve are normalzed n the range [,1], whlst the values of the detrusor pressure and the abdomnal pressure are expressed wth ther real values. In ths way, the generator supples deal curves n whch there s no knd of alteraton, as well as curves wth alteratons correspondng to alteratons produced by coughng, convulsons, etc. In fgure 3 we see some examples wth deal curves and curves wth alteratons. We obtan the tranng patterns of the OAM from the urodynamc curves. Each curve, made up of a maxmum number of ponts (MaxP), s dvded nto c k groups of sze τ. The pars of patterns (a,b ) whch the network has to learn are constructed from the groups of curves n the followng way: t t a [ pd c ) pa( c ) pe( c )] and [ pe c )] = ( k k k 1 b = (5) and (6) Startng from a group of q tranng pars (a,b ) wth =1,...,q belongng to the vectoral spaces R n and R m respectvely, we construct the nput matrx A and the output matrx B, where the patterns of dmenson n correspond to the columns of the matrx A, whlst the patterns of dmenson m correspond to the columns of the matrx B. ( k

5 4 Pressure (cm of H 2 O) 6 pe pa p pd Tme (hours) Fgure 3. The frst graph represents the pressure curves n a patent wthout any alteratons. The second graph represents the pressure curves of a patent wth alteratons produced by coughng, convulsons, etc. (Pe: external sphncter pressure; Pa: abdomnal pressure; P: ntravescal pressure; Pd: detrusor pressure). Once we have the nput and output matrxes, we construct the model by means of the tranng of the network of matrxes. We have carred out varous experments n order to analyze the model. The results of the experments are shown below by means of graphs. They show the external sphncter pressure obtaned by the functon generator (pe?) and the external sphncter pressure recognzed by the network (rpe?). (A) Recognton of patents' curves wthout alteratons. As we can see n fgure 4, the model correctly nfers the external sphncter pressure n the curves used n tranng (pe1-rpe1), whlst curves not used n the tranng (pe2-rpe2) are also nferred well. Pressure (normalzed [,1]) pe1 rpe1 pe2 rpe2 Pressure (normalzed [,1]) pep1 rpep1 pep2 rpep2 Fgure 4. Patents wthout alteratons. Tme (hours) Fgure 5. Patents wth alteratons. (B) Recognton of patents' curves wth alteratons. In fgure 5 we can see that the patterns used (pep1-rpep1) n tranng, as n the frst experment, are correctly nferred by the model. The recognton of patents' curves wth alteratons (pep2-rpep2) not used n tranng mantans the correct dynamcs, but produces ncontnence when dsrupton s generated.

6 4. Conclusons We have developed a model whch permts the study of the urodynamc behavor of the LUT and a better understandng of the way t works. By means of the functon generator developed we have obtaned dfferent artfcal urodynamc curves. The use of smulated curves to construct the model has allowed us to generate a large casustry n order to tran the network and, n ths way, generate a more refned model. Nevertheless, n order to mprove the model, the tranng of the network wll be carred out usng real ndvdual's curves, wth,or wthout pathology. In ths way, ths model could be used as a base for developng artfcal mplants whch control certan dsfunctons due to neurogenc causes, such as ncontnence and retenton. In ths sense, we are dong research on a new model whch we hope wll dentfy alteratons n such a way that ncontnence s not produced. References [1] J. Salnas and J. Romero, Urodnámca clínca, Merck Sharp & Dohme, [2] P.C. Walsh, Campbell, urología, Edtoral Médca Panamercana, [3] N. Yoshmura et al., Neural control of the lower urnary tract, Internatonal Journal of Urology, 4 (1997) [4] M.V. Knder et al., Neuronal crcutry of the lower urnary tract; central and perpheral neuronal control of the mcturton cycle, Anat Embryol, 192 (1995) [5] J. Frohlch et al., Computer model of the bladder, Zentralbl Neurochr, 38 (1977) [6] R.A. Hosen and D.J. Grffths, Computer smulaton of the neural control of bladder and urethra, Neurourol- Urodyn, 9 (199) [7] U. Hübener and R. van Mastrgt, Computer smulaton of mcturton, Urodnamca, 4 (1994) 81-9 [8] H.F. Tannr and W.D. Tmmons, A Qualtatve Model of the Bladder Control System, BME COMMUNICATIONS, 1 (1994) [9] E.H. Bastaanssen et al., A myocybernetc model of the lower urnary tract. J-Theor-Bol, 178 (1996), [1] F. Van Dun et al., A computer model of the neural control of the lower urnary tract, Neurourol-Urodyn, 17 (1998) [11] Lennart Ljung, System Identfcaton. Theory for the user, Prentce -Hall, [12] K.S. Narendra and K. Parthasarathy, Identfcaton and control of dynamcal systems usng neural networks, IEEE Trans. Neural Networks, 1 (199) [13] K.S. Narendra, Neural networks for control: theory and practce, Proceedngs of the IEEE, 1 (1996) [14] S. Lu and T. Basar, Robust nonlnear system dentfcaton usng neural-network models, IEEE Trans. Neural Networks, 3 (1998) [15] F. Ibarra, Análss de Texturas Medante Coefcente Morfológco. Modelado Conexonsta Aplcado, Unversty of Alcante, [16] A. Householder, Theory of matrx n Numercal Analyss, Blasdell Edtor, 1964.