Mechanical fatigue performance of PCL-chondroprogenitor constructs after cell culture under bioreactor mechanical stimulus

In tissue engineering of cartilage, polymeric scaffolds are implanted in the damaged tissue and subjected to repeated compression loading cycles. The possibility of failure due to mechanical fatigue has not been properly addressed in these scaffolds. Nevertheless, the macroporous scaffold is susceptible to failure after repeated loading-unloading cycles. This is related to inherent discontinuities in the material due to the micropore structure of the macro-pore walls that act as stress concentration points. In this work, chondrogenic precursor cells have been seeded in Poly-ε-caprolactone (PCL) scaffolds with fibrin and some were submitted to free swelling culture and others to cyclic loading in a bioreactor. After cell culture, all the samples were analyzed for fatigue behavior under repeated loading-unloading cycles. Moreover, some components of the extracellular matrix (ECM) were identified. No differences were observed between samples undergoing free swelling or bioreactor loading conditions, neither respect to matrix components nor to mechanical performance to fatigue. The ECM did not achieve the desired preponderance of collagen type II over collagen type I which is considered the main characteristic of hyaline cartilage ECM. However, prediction in PCL with ECM constructs was possible up to 600 cycles, an enhanced performance when compared to previous works. PCL after cell culture presents an improved fatigue resistance, despite the fact that the measured elastic modulus at the first cycle was similar to PCL with poly(vinyl alcohol) samples. This finding suggests that fatigue analysis in tissue engineering constructs can provide additional information missed with traditional mechanical measurements.

Relatório de atividade profissional

Relatório de atividade profissional de mestrado em Ciências - Formação Contínua de Professores (área de especialização em Biologia e Geologia)

Autonomic Modulation of the Heart in Systemic Arterial Hypertension

OBJECTIVE: To analyze the heart rate variability in patients with mild to moderate systemic arterial hypertension. METHODS: Thirty-two healthy (group I) and 70 systemic arterial hypertensive (group II) individuals, divided according to age (40 to 59 and 60 to 80 years old, respectively) and with a similar distribution by sex were studied. Thirty-one had left ventricular hypertrophy (LVH), 22 were overweight, and 16 had Type II diabetes mellitus. Smoking, alcohol ingestion, and sedentary habits were the same between groups. Variability in heart rate was analyzed in the time domain, using standard deviations of normal RR intervals (SDNN) and the differences between maximal brady- and tachycardia (D-BTmax) during sustained inspiration. Analysis of the frequency band of the power spectrum between 0.05 and 0.40 Hz at rest and during controlled respiration was chosen for analysis of the frequency domain. RESULTS: In both time and frequency domains, variables were lower in group II than in group I. Within groups, statistically significant variables were only found for individuals in the 40 to 59 year old group. The presence of LVH, overweight, or diabetes mellitus did not influence the variability in heart rate to a significant extent. CONCLUSION: Variability in heart rate was a valuable instrument for analyzing autonomic modulation of the heart in arterial hypertension. The autonomic system undergoes significant losses in cardio-modulatory capacity, more evident in subjects between 40 and 59 years old. In those over 60 years old, reduced variability in heart rate imposed by aging was not significantly influenced by the presence of systemic arterial hypertension.

Modulación de la activación de células dendríticas por antígenos de Fasciola hepatica y ligandos para receptores Toll: Potencial terapéutico en respuestas anti-inflamatorias. Fasciola hepatica antigens and TLR ligands modulate dendritic cells activation: therapeutic potential in anti-inflammatory responses.

Antecedentes: En nuestro laboratorio hemos demostrado que antígenos (Ags) de Fasciola hepatica inducen en células dendríticas murinas (CD), diferentes propiedades tolerogénicas como la incapacidad por si mismos de inducir la maduración de las células, la resistencia a la maduración por ligandos de TLR, el incremento en la producción de IDO y también la capacidad de esta estas células de dirigir la respuesta inmune hacia un perfil Th2 y T reg. Por otra parte ha sido bien documentado que CD con características tolerogénicas, ya sea inmaduras o semimaduras, son útiles para reducir respuestas inflamatorias excesivas tales como las que ocurren en enfermedades autoinmunes. Además hemos demostrado que CD tratadas con Ags del parásito en conjunto con un ligando Toll (CpG-ODN) producen altos niveles de citoquinas anti-inflamatorias (IL-10 y TGF-) bajos de citoquinas proinflamatorias (TNF, IL-6, IL-12). Hipótesis: El fenotipo semimaduro alcanzado en las CDpodría ser utilizado para reducir la inflamación en un modelo de enfermedad autoinmune en donde existe una exacerbada respuesta Th1 y Th17, ya que la producción elevada de IL-10 y TGF- podría inhibir o controlar estas respuestas de manera directa o a través de la inducción de células T regulatorias. Objetivos: En este proyecto nosotros proponemos la inmunización de animales susceptibles (ratones DBA1/j), al desarrollo de artritis inducida por colágeno (AIC) con CD tratadas con Ags de F. hepatica en conjunto con CpG-ODN para reducir los síntomas clínicos de la enfermedad. Materiales a utilizar: En nuestro laboratorio hemos desarrollado un modelo de artritis inducida por colágeno (AIC) mediante dos inmunizaciones de ratones DBA1/j con colágeno tipo II bovino y adyuvante de Freund. El modelo permitió establecer un índice clínico mediante la hinchazón en las patas de los animales. Doce días posteriores a la primera inmunización los animales serán inyectados con CD tratadas con: 1. PBS, 2.Extracto total de F.hepatica (TE) + CII, 3. CpG + CII, 4. TE+CpG+CII Se realizará la observación macroscópica diaria, a partir de los 7 días de la 2a inmunización Luego del sacrificio las articulaciones de las patas se prepararán para realizar un análisis histológico. Se detectará en suero los niveles de anticuerpos IgG1 (perfil Th2) y de IgG2a (perfil Th1) mediante la técnica de ELISA. Se detectará también el perfil de citoquinas en los nódulos drenantes por la técnica de ELISA y adicionalmente la poblaciónes celulares de células T regulatorias (Treg) CD4+CD25+Foxp3 o células Tr1. Resultados esperados: Pensamos que el tratamiento de los animales que desarrollan AIC con CD semimaduras (por el tratamiento con TE y CpG), serán capaces de migrar a los órganos linfaticos y secretar TGF-be(inductora de células T reg), IL-10 (inductoras de células Tr1), IDO inhibitoria de la respuesta de Li T y promotor de células T reg, también podría generarse una respuesta Th2 (por la presencia de antígenos del parásito), y estas respuestas aisladas o en forma sinérgica podrían inhibir las respuestas de tipo Th17 y Th1 asociadas a la patología en esta enfermedad. Importancia del proyecto: En el desarrollo de la artritis existe un aumento de la inmunidad mediada por células, asi como de la respuesta inmune humoral hacia componentes de la matriz del cartílago. El tratamiento convencional de la artritis recae en general en el uso de inmunosupresores no-específicos, los cuales poseen una variedad de efectos adversos y la inhibición de la respuesta inflamatoria no es específica. En este proyecto proponemos el uso de CD tratadas con antígenos del helminto F. hepatica y CpG ligando Tol que capacita a estas células para generar una respuesta adaptativa de tipo regulatoria, útil en la inhibición de las respuestas inflamatorias como la que ocurre durante la progresión de artritis reumatoidea en un modelo experimental en ratones. We have shown that F. hepatica Ags-treated dendritic cells (DC) together with a TLRl ligand (CpG-ODN) produce high levels of anti-inflammatory cytokines (IL-10 and TGF-Beta) and low of proinflammatory cytokines (TNF, IL-6, IL -12). Hypothesis: The semimature phenotype achieved by DC, could be used to reduce inflammation in a model of autoimmune disease. The high production of IL-10 and TGF-Beta by these cells could directly or through the induction of T reg cells inhibit the inflammatory response. Objective: In this project we propose the immunization of DBA1 / j mice, susceptible to the development of collagen-induced arthritis (CIA) with F. hepatica-treated DC in conjunction with CpG-ODN to reduce clinical signs of disease. Materials: In our laboratory, we developed the CIA model by two immunizations of DBA1 / j mice with bovine type II collagen and Freund's adjuvant. The model allowed to stablish a clinical index by swelling in the legs of animals. Twelve days after the first immunization the animals are injected with DC treated with: 1. PBS 2. F.hepatica Extract (TE) + CII, 3. CpG + CII, 4. TE + CpG + CII Macroscopic observation will take place daily from 7 days of the 2nd immunization. After sacrifice the joints of the legs will be prepared for histological analysis. Serum levels of IgG1 antibodies (Th2 profile) and IgG2a (Th1 profile) will be detected by ELISA. It will also detected the cytokine profile in draining lymph nodes by ELISA and additionally the cell populations of regulatory T cells (Treg) CD4 + CD25 + Foxp3 or Tr1 cells. Expected results: We believe that the treatment of animals that had developed CIA with DC will be able to migrate to lymphatic organs and secrete TGF-B (T reg cell-inducing), IL-10 (inducing Tr1 cells), IDO (inhibitory of T cells and inducing of T reg cells) could alone or in synergy inhibit Th17-type responses and Th1 associated with the pathology in this disease.

Association of Peripheral Arterial and Cardiovascular Diseases in Familial Hypercholesterolemia

Background: Familial hypercholesterolemia (FH) is an autosomal dominant genetic disease characterized by an elevation in the serum levels of total cholesterol and of low-density lipoproteins (LDL- c). Known to be closely related to the atherosclerotic process, FH can determine the development of early obstructive lesions in different arterial beds. In this context, FH has also been proposed to be a risk factor for peripheral arterial disease (PAD). Objective: This observational cross-sectional study assessed the association of PAD with other manifestations of cardiovascular disease (CVD), such as coronary artery and cerebrovascular disease, in patients with heterozygous FH. Methods: The diagnosis of PAD was established by ankle-brachial index (ABI) values ≤ 0.90. This study assessed 202 patients (35% of men) with heterozygous FH (90.6% with LDL receptor mutations), mean age of 51 ± 14 years and total cholesterol levels of 342 ± 86 mg /dL. Results: The prevalences of PAD and previous CVD were 17% and 28.2 %, respectively. On multivariate analysis, an independent association between CVD and the diagnosis of PAD was observed (OR = 2.50; 95% CI: 1.004 - 6.230; p = 0.049). Conclusion: Systematic screening for PAD by use of ABI is feasible to assess patients with FH, and it might indicate an increased risk for CVD. However, further studies are required to determine the role of ABI as a tool to assess the cardiovascular risk of those patients.

Debranching Solutions in Endografting for Complex Thoracic Aortic Dissections

Background: Conventional surgical repair of thoracic aortic dissections is a challenge due to mortality and morbidity risks. Objectives: We analyzed our experience in hybrid aortic arch repair for complex dissections of the aortic arch. Methods: Between 2009 and 2013, 18 patients (the mean age of 67 ± 8 years-old) underwent hybrid aortic arch repair. The procedural strategy was determined on the individual patient. Results: Thirteen patients had type I repair using trifurcation and another patient with bifurcation graft. Two patients had type II repair with replacement of the ascending aorta. Two patients received extra-anatomic bypass grafting to left carotid artery allowing covering of zone 1. Stent graft deployment rate was 100%. No patients experienced stroke. One patient with total debranching of the aortic arch following an acute dissection of the proximal arch expired 3 months after TEVAR due to heart failure. There were no early to midterm endoleaks. The median follow-up was 20 ± 8 months with patency rate of 100%. Conclusion: Various debranching solutions for different complex scenarios of the aortic arch serve as less invasive procedures than conventional open surgery enabling safe and effective treatment of this highly selected subgroup of patients with complex aortic pathologies.

Chronic murine myocarditis due to Trypanosoma cruzi: an ultrastructural study and immunochemical characterization of cardiac interstitial matrix

In an attempt to define the mouse-model for chronic Chagas' disease, a serological, histopathological and ultrastructural study as well as immunotyping of myocardium collagenic matrix were performed on Swiss mice, chronically infected with Trypanosoma cruzi strains: 21 SF and mambaí (Type II); PMN and Bolivia (Type III), spontaneously surviving after 154 to 468 days of infection. Haemagglutination and indirect immunofluorescence tests showed high titres of specific antibodies. The ultrastructural study disclosed the cellular constitution of the inflammatory infiltrate showing the predominance of monocytes, macrophages with intense phagocytic activity, fibroblasts, myofibroblasts and abundant collagen matrix suggesting the association of the inflammatory process with fibrogenesis in chronic chagasic cardiomyopathy. Artertolar and blood capillary alterations together with dissociation of cardiac cells from the capillary wall by edema and inflammation were related to ultrastructural lesions of myocardial cells. Rupture of parasitized cardiac myocells contribute to intensify the inflammatory process in focal areas. Collagen immunotyping showed the predominance of Types III and IV collagen. Collagen degradation and phagocytosis were present suggesting a reversibility of the fibrous process. The mouse model seems to be valuable in the study of the pathogenetic mechanisms in Chagas cardiomyopathy, providing that T. cruzi strains of low virulence and high pathogenecity are used.

Safe dissection of the distally based anterolateral thigh flap.

Background The distally based anterolateral thigh (ALT) flap is an interesting reconstructive solution for complex soft tissue defects of the knee. In spite of a low donor site morbidity and wide covering surface as well as arch of rotation, it has never gained popularity among reconstructive surgeons. Venous congestion and difficult flap dissection in the presence of a variable anatomy of the vascular pedicle are the possible reasons.Methods An anatomical study of 15 cadaver legs was performed to further clarify the blood supply of the distally based ALT. Our early experience with the use of preoperative angiography and a safe flap design modification that avoids distal intramuscular skeletonization of the vascular pedicle and includes a subcutaneous strip ranging from the distal end of the flap to the pivot point is presented.Results The distally based ALT presents a constant and reliable retrograde vascular contribution from the superior genicular artery. Preoperative angiography reliably identified and avoided critical Shieh Type II pedicled flaps. The preservation of a subcutaneous strip ranging from the distal flap end to the upper knee was associated with the absence of venous congestion in a short case series.Conclusions Preoperative angiography and a flap design modification are proposed to allow the safe transfer of the distally based ALT to reconstruct soft tissue defects of the knee.

Structure-function relationships for the interleukin 2 receptor system

Receptors for interleukin 2 (IL-2) esit in at least three forms which differ in their subunit compositio, their affinity for ligand and their ability to mediate a cellular reponse. Type I receptors occur following cellular acitivation and consist of the 55,000 m. w. glycoprotein Tac. These receptors bind IL-2 with a low affinity, do not internalize ligand and have not been definitively associated with any response. Type II receptors, on the other hand, conssit of one or more glycoproteins of 70,000 m. w. which have been termed "beta ([beta]) chains." They bind IL-2 with an intermediate affinity and rapidly internalize the ligand. [Beta] proteins mediate many cellular IL-2-dependent reponses, including the short-term activation of natural killer cells and the induction of Tac protein expression. Type III receptors consist of a ternary complex of the Tac protein, the [beta] chain(s) and IL-2. They are characterized by a paricularly high affinity for ligand association. Type III receptors also internalize ligand and mediate IL-2-dependent responses at low factor concentrations. The identification of two independent IL-2-binding molecules, Tac and [beta], thus provides the elusive molecular explanation for the differences in IL-2 receptor affinity and suggests the potential for selective therapeutic manipulation of IL-2 reponses.

Influence of Trypanosoma cruzi strain on the pathogenesis of chronic myocardiopathy in mice

The murine model of chronic Chaga's myocardiopathy was developed in 201 inbred and outbred mice. The experimental groups consisted of 1st: 73 inbred AKR and A/J mice inoculated with one of the following. Trypanosoma cruzi strains: Peruvian (Type I), 12 SF (Type II) or Colombian (Type III); 2nd: 128 outbred Swiss mice, chronically infected either with Type II or Type III strains isolated from human patients from different geographical areas. All T. cruzi strains were previoulsly characterized by their morphobiological behaviour in mice and by isoenzymatic patterns. For the 1st group the inoculum was 5 x 10**4 for the Peruvian strain and 1 x 10**5 for the 12 SF and Colombian strains. In the 2nd group-Swiss mice the inoculum size varied from 2 x 10**4 to 2 x 10**5. The inbred animals were killed at a 3 time-point scale (90, 180 and 240 days) post-infection. The Swiss mice were killed from 180 to 660 days after infection. The evaluation of parasitemia and serology (xeodiagnosis and indirect immunofluorescent test) was performed. The incidence of macroscopic alterations of the heart and cardiac index were evaluated. Histopathological lesions of the myocardium were graded. The influence of T. cruzi strain on the intensity of cardiac lesions was evaluated by the Chi-square test; the incidence of inflammatory lesions and its relationship to the parasite strain was evaluated by the Fisher test. The influence of the duration of infection was evaluated by using the Gamma Coefficient of Kruskal and Goodman and its measure of significance. Slight to severe microscopic alterations occurred in 85% of the chronically infected nice. There were a clear predominance on the incidence and intensity of inflammatory and fibrotic alterations for the mice infected with Type III strains. Statistical analysis has shown significant differences among the infected groups, in the inflammatory and fibrotic lesions. Macroscopic alterations (right cavities dilatation and apex aneurism of left ventricle), differed in incidence according to mice strains; in Swiss and AKR mice, significant differences were seen in mice infected with different T. cruzi strains, but the A/J mice failed to show significant differences correlated with different parasite strains. The duration of infection, from 90 to 240 days, could not be correlated with the degree of lesions in the several groups.

Beyond Intermediates: The Role of Consumption and Commuting in the Construction of Local Input-Output Tables

It is a well-established fact in the literature on simulating Input-Output tables that mechanical methods for estimating intermediate trade lead to biased results where cross-hauling is underestimated and Type-I multipliers are overstated. Repeated findings to this effect have led to a primary emphasis on advocating the accurate estimation of intermediate trade flows. This paper reviews previous research and argues for a qualification of the consensus view: When simulating IO tables, construction approaches need to consider spill-over effects driven by wage and consumption flows. In particular, for the case of metropolitan economies, wage and consumption flows are important if accurate Type-II multipliers are to be obtained. This is demonstrated by constructing an interregional Input-Output table, which captures interdependencies between a city and its commuter belt, nested within the wider regional economy. In addition to identifying interdependencies caused by interregional intermediate purchases, data on subregional household incomes and commuter flows are used to identify interdependencies from wage payments and household consumption. The construction of the table is varied around a range of assumptions on intermediate trade and household consumption to capture the sensitivity of multipliers.

Okun’s law – A meta analysis

This paper seeks to identify whether there is a representative empirical Okun’s Law coefficient (OLC) and to measure its size. We carry out a meta regression analysis on a sample of 269 estimates of the OLC to uncover reasons for differences in empirical results and to estimate the ‘true’ OLC. On statistical (and other) grounds, we find it appropriate to investigate two separate subsamples, using respectively (some measure of) unemployment or output as dependent variable. Our results can be summarized as follows. First, there is evidence of type II publication bias in both sub-samples, but a type I bias is present only among the papers using some measure of unemployment as the dependent variable. Second, after correction for publication bias, authentic and statistically significant OLC effects are present in both sub-samples. Third, bias-corrected estimated true OLCs are significantly lower (in absolute value) with models using some measure of unemployment as the dependent variable. Using a bivariate MRA approach, the estimated true effects are -0.25 for the unemployment sub-sample and -0.61 for the output-sub sample; with a multivariate MRA methodology, the estimated true effects are -0.40 and -1.02 for the unemployment and the output-sub samples respectively.

Legal Uncertainty, Competition Law Enforcement Procedures and Optimal Penalties

In this paper we make three contributions to the literature on optimal Competition Law enforcement procedures. The first (which is of general interest beyond competition policy) is to clarify the concept of “legal uncertainty”, relating it to ideas in the literature on Law and Economics, but formalising the concept through various information structures which specify the probability that each firm attaches – at the time it takes an action – to the possibility of its being deemed anti-competitive were it to be investigated by a Competition Authority. We show that the existence of Type I and Type II decision errors by competition authorities is neither necessary nor sufficient for the existence of legal uncertainty, and that information structures with legal uncertainty can generate higher welfare than information structures with legal certainty – a result echoing a similar finding obtained in a completely different context and under different assumptions in earlier Law and Economics literature (Kaplow and Shavell, 1992). Our second contribution is to revisit and significantly generalise the analysis in our previous paper, Katsoulacos and Ulph (2009), involving a welfare comparison of Per Se and Effects- Based legal standards. In that analysis we considered just a single information structure under an Effects-Based standard and also penalties were exogenously fixed. Here we allow for (a) different information structures under an Effects-Based standard and (b) endogenous penalties. We obtain two main results: (i) considering all information structures a Per Se standard is never better than an Effects-Based standard; (ii) optimal penalties may be higher when there is legal uncertainty than when there is no legal uncertainty.

Optimal Universal and Categorical Benefits with Classification Errors and Imperfect Enforcement

We determine he optimal combination of a universal benefit, B, and categorical benefit, C, for an economy in which individuals differ in both their ability to work - modelled as an exogenous zero quantity constraint on labour supply - and, conditional on being able to work, their productivity at work. C is targeted at those unable to work, and is conditioned in two dimensions: ex-ante an individual must be unable to work and be awarded the benefit, whilst ex-post a recipient must not subsequently work. However, the ex-ante conditionality may be imperfectly enforced due to Type I (false rejection) and Type II (false award) classification errors, whilst, in addition, the ex-post conditionality may be imperfectly enforced. If there are no classification errors - and thus no enforcement issues - it is always optimal to set C>0, whilst B=0 only if the benefit budget is sufficiently small. However, when classification errors occur, B=0 only if there are no Type I errors and the benefit budget is sufficiently small, while the conditions under which C>0 depend on the enforcement of the ex-post conditionality. We consider two discrete alternatives. Under No Enforcement C>0 only if the test administering C has some discriminatory power. In addition, social welfare is decreasing in the propensity to make each type error. However, under Full Enforcement C>0 for all levels of discriminatory power. Furthermore, whilst social welfare is decreasing in the propensity to make Type I errors, there are certain conditions under which it is increasing in the propensity to make Type II errors. This implies that there may be conditions under which it would be welfare enhancing to lower the chosen eligibility threshold - support the suggestion by Goodin (1985) to "err on the side of kindness".

Reversibility of cardiac fibrosis in mice chronically infected with Trypanosoma cruzi, under specific chemotherapy

This investigation was performed to verify the effect of specific chemotherapy (Benznidazole or MK-346) on the inflammatory and fibrotic cardiac alterations in mice chronically infected with the strains 21 SF (Type II) and Colombian (Type III) of Trypanosoma cruzi. To obtain chronically infected mice, two groups of 100 Swiss mice each, were infected with either the 21 SF or the Colombian strain (2x 10 [raised to the power of] 4 and 5x 10 [raised to the power of] 4 blood forms respectively). The rate of morality in the acute phase was of 80% for both groups. Twenty surviving mice chronically infected with the 21 SF strain and 20 with the Colombian strain were then divided in treated and untreated groups. Excluding those that died during the course of treatment, 14 mice chronically infected with the 21 SF strain and 15 with the Colombian strain were evaluated in the present study. Chemotherapy was performed with Benznidazole (N-benzil-2-nitro-1-imidazolacetamide) in the dose of 100mg/k.b.w/day, for 60 days, or with the MK-436(3(1-methyl-5 nitroimidazol-2-yl) in two daily doses of 250 mg/k.b.w, for 20 days. Parasitological cure tests were performed (xenodiagnosis, haemoculture, subinovulation of the blood into newborn mice), and serological indirect immunofluorescence test. The treated and untreated mice as well as intact controls were killed at different periods after treatment and the heart were submitted to histopathological study with hematoxilineosin and picrosirius staining; ultrastructural study; collagen immunotyping, fibronectin and laminin identification by immunofluorescence tests. Results: the untreated controls either infected with 21 SF or Colombian strain, showed inflammatory and fibrotic alterations that were mild to moderate with the 21 SF strain and intense with the Colombian strain. Redpicrosirius staining showed bundles of collagen in the interstitial space and around cardiac fibers. Increased deposits of mitritial components and collagen fibers, macrophages and fibroblasts appeared at the ultra structural examination. Deposits of fibronectin, laminin, pro-III and IV collagens were seen, most intense in those infected with the Colombian strain. Treated nice, parasitologically cured, presented clear-cut regression of the inflammatory lesions and of the interstitial matrix thickening. Mice infected with the Colombian strain and treated with MK-436, was parasitologically cured in 5/6 cases and showed mild inflammatory infiltration and fibrosis. The mice treated with Benznidazole (Colombian strain) did not cure and showed moderate fibrosis and inflammation. Treatment of the nice infected with the 21 SF with Benznidazole determined parasitological cure of all animals, that showed mild inflammation and fibrosis of the myocardium. The cured mice of all groups and treated but uncured showed collagen degradation at electronmicroscopy and decrease of immunofluorescence pattern of the matrix.